spinning disc membrane electrolyzer : performance of cation- exchange ... · the membrane cell...

Spinning disc membrane electrolyzer : performance of cation-exchange membraneCitation for published version (APA):Moshtari Khah, S. (2016). Spinning disc membrane electrolyzer : performance of cation-exchange membrane.Eindhoven: Technische Universiteit Eindhoven.

Document status and date:Published: 13/10/2016

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:[email protected] details and we will investigate your claim.

Download date: 12. Jul. 2020

https://research.tue.nl/en/publications/spinning-disc-membrane-electrolyzer--performance-of-cationexchange-membrane(5a5f29a3-aa74-4f0e-98d0-7ccb2494d156).html

Spinning disc membrane electrolyzer: performance of cation-exchange membrane

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag

van de rector magnificus prof.dr.ir. F.P.T. Baaijens,

voor een commissie aangewezen door het College voor Promoties, in het openbaar te

verdedigen op donderdag 13 oktober 2016 om 16:00 uur

door

Shohreh Moshtarikhah

geboren te Teheran, Iran

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecommissie

is als volgt:

voorzitter: prof.dr.ir. R.A.J. Janssen

1e promotor: prof.dr.ir. J.T.F. Keurentjes

2e promotor: prof.dr.ir. J.C. Schouten

co-promotor: dr.ir. J. van der Schaaf

leden: prof.dr. E. Ahlberg (University of Gothenburg)

prof.dr.ir. J.R. van Ommen (TUD)

prof.dr.ir. D.C. Nijmeijer

dr. M.T. de Groot (Akzo Nobel)

Het onderzoek of ontwerp dat in dit proefschrift wordt beschreven is uitgevoerd in

overeenstemming met de TU/e Gedragscode Wetenschapsbeoefening.

کایت همچنان باقیست ... هب پایان آمد این دفتر ،ح

Spinning disc membrane electrolyzer: performance of cation-exchange membrane

S. Moshtarikhah

Eindhoven University of Technology, 2016

The work presented in this thesis was funded by the Action Plan Process Intensification of the

Dutch Ministry of Economic Affairs (project PI-00-04).

Printed by Gildeprint

Cover designed by Prisca Arosio

A cataloge record is available from the Eindhoven University of Technology Library

ISBN: 978-90-386-4137-9

Table of contents

Summary xi

1 Introduction .......................................................................................................................... 1

1.1 Process intensification ...................................................................................................... 1

1.2 Chlor-alkali process .......................................................................................................... 1

1.3 Cation-exchange membranes ............................................................................................ 2

1.4 Intensification of chlor-alkali process in spinning disc membrane electrolyzer .............. 6

1.5 The scope and structure of thesis ...................................................................................... 7

Bibliography ........................................................................................................................... 8

2 Cation-exchange membrane performance under high current density ........................ 11

Abstract ................................................................................................................................. 11

2.1 Introduction .................................................................................................................... 12

2.2 Theoretical background .................................................................................................. 14

2.3 Experimental ................................................................................................................... 15

2.3.1 Materials .................................................................................................................. 15

2.3.1 Experimental set-up ................................................................................................. 16

2.3.1 Experimental procedure for conductivity measurements......................................... 17

2.3.2 Experimental procedure for permselectivity measurements .................................... 18

2.4 Results ............................................................................................................................ 18

2.5 Discussion ....................................................................................................................... 24

2.6 Conclusion ...................................................................................................................... 27

Bibliography ......................................................................................................................... 28

Appendix .............................................................................................................................. 32

3 Nernst-Planck modeling of multicomponent ion transport in a Nafion membrane at

high current density 35

Abstract ................................................................................................................................. 35

3.1 Introduction .................................................................................................................... 42

3.2 Model approach .............................................................................................................. 44

3.3 Results and discussion .................................................................................................... 50

3.4 Conclusion ...................................................................................................................... 53

Bibliography ......................................................................................................................... 56

Appendix A. Non-linear potential gradient .......................................................................... 60

Appendix B. Transport equations ......................................................................................... 61

Appendix C: Donnan equilibrium at the interface ................................................................ 61

4 Multicomponent ion transport in a mono and bilayer cation-exchange membrane at

high current density 65

Abstract ................................................................................................................................. 65

4.1 Introduction .................................................................................................................... 66

4.2 Model approach and assumptions ................................................................................... 66


4.3.1 Concentration profiles inside the membrane ........................................................... 71

4.3.1 Membrane voltage drop and permselectivity ........................................................... 74

4.4 Discussion ....................................................................................................................... 75

4.5 Conclusion ...................................................................................................................... 76

Bibliography ......................................................................................................................... 78

Appendix .............................................................................................................................. 81

5 Maxwell-Stefan modeling of multicomponent ion transport inside a cation-exchange

membrane 83

Abstract ................................................................................................................................. 83

5.1 Introduction .................................................................................................................... 84

5.2 Model approach and assumptions ................................................................................... 85

5.2.1 Input parameters ....................................................................................................... 89

5.2.1 Maxwell-Stefan diffusion coefficients ..................................................................... 89


5.4 Conclusion ...................................................................................................................... 94

Bibliography ......................................................................................................................... 95

Appendix .............................................................................................................................. 98

6 Gas bubble removal from a gauze surface in a thin film spinning disc reactor ......... 101

Abstract ............................................................................................................................... 101

6.1 Introduction .................................................................................................................. 102

6.1.1 Hydrogen peroxide decomposition ........................................................................ 102

6.2 Experimental ................................................................................................................. 103

6.2.1 Material .................................................................................................................. 103

6.2.2 Palladium coated nickel gauze ............................................................................... 103

6.2.3 Experimental technique.......................................................................................... 104

6.3 Mathematical description ............................................................................................. 105

6.3.1 Overall reaction rate parameter and residence time ............................................... 105

6.3.2 Analysis of the liquid film on the rotating gauze ................................................... 106

6.4 Results .......................................................................................................................... 107

6.5 Discussion ..................................................................................................................... 111

6.6 Conclusion .................................................................................................................... 112

Bibliography ....................................................................................................................... 113

7 Intensification of the chlor-alkali process by using a spinning disc membrane

electrolyzer 117

Abstract ............................................................................................................................... 117

7.1 Introduction (1)

.............................................................................................................. 118

7.1.1 Spinning disc membrane electrochemical reactor (SDMER) ................................ 120

7.2 Experimental (1)

............................................................................................................. 122

7.2.1 Experimental setup ................................................................................................. 122

7.2.2 Analytical techniques ............................................................................................. 124

7.3 Results and discussion .................................................................................................. 125

7.3.1 Rotor-stator spinning disc membrane electrolyzer ................................................ 125

7.3.1 Thin-film spinning disc membrane electrolyzer (2)

................................................ 132

7.4 Conclusions .................................................................................................................. 134

Bibliography ....................................................................................................................... 134

8 Conclusions and outlook .................................................................................................. 137

8.1 Conclusion .................................................................................................................... 137

8.2 Outlook ......................................................................................................................... 139

8.2.1 Membrane performance ......................................................................................... 139

8.2.2 Concentration visualization of ions in cation-exchange membranes using NMR

technique ......................................................................................................................... 140

8.2.3 Combined reactor and membrane model for chlor-alkali process in the spinning

disc membrane electrolyzer ............................................................................................ 142

Bibliography ................................................................................................................... 146

xi

Summary

The availability of small high productivity equipment and more efficient production is

increasingly important in the chemical industry. This challenge to develop more compact,

more environmentally friendly and more efficient technology was coined process

intensification. The chlor-alkali process is one of the most energy intensive industries. In the

chlor-alkali process chlorine, sodium hydroxide, and hydrogen are produced from the

electrolysis of sodium chloride solution. Chlorine and sodium hydroxide are among the top

chemicals produced worldwide. The membrane cell technology is the benchmark of the chlor-

alkali industry because it has the lowest environmental impact and the highest energy

efficiency. Research and development in the past focused on reducing the cell voltage and

increasing the current efficiency to achieve a lower power consumption, however, there is still

a need of transporting a large amount of the produced chlorine in public; which brings risks of

environmental disasters and legislation is increasingly more stringent. Therefore, on-site

production of chlorine is of great interest. The produced chlorine is then immediately

consumed by the customer. The SPINCHAL project aimed to develop a small-scale, compact

and transportable ‘plug and produce’ production unit for the chlor-alkali process with a 10

kton per year production capacity. The electrolysis of the brine is the heart of the chlor-alkali

industry, and the cation-exchange membrane is the key component in the membrane cell

electrolyzer. In the past, the performance and efficiency of the membrane cell technology

have been improved by using more novel electrode materials, developing more robust

membranes, and the use of the zero-gap design of the electrolyzer. Currently, the chlor-alkali

plants operate at current densities up to 7 kA.m-2

, however, the aim of this project was to

increase the current density further and to evaluate the energy costs at the corresponding

higher production rates. In this thesis an intensified membrane cell electrolyzer is developed

with a focus on studying the performance of the cation-exchange membrane in the intensified

process.

In the first step, the performance of different types of mono- and bilayer cation-exchange

membranes was investigated experimentally in a sodium hydroxide system. The

conductivities and permselectivities were measured in different electrolyte concentration and

temperature as a function of current density up to 20 kA.m-2

. A non-ohmic increase of the

membrane voltage drop with increasing the current density was observed. In addition,

increasing the electrolyte concentration resulted in the decrease of the membrane conductivity,

loss of sodium selectivity and a decrease in water transport.

In the next step, we modeled the experiments by developing a Nernst-Planck model of the ion

transport inside the membrane at high current densities. The membrane voltage drop and

permselectivity were calculated based on the flux of species at the steady state in a single

layer Nafion, N-1110. The model output was compared with the experimental results. It was

shown that the increase in the membrane conductivity at high current density can be explained

with a swelling model which assumes the opening of the pore structure of the cation-exchange

membrane, thereby activating a higher number of pore channels for ion transport.

xii

The cation-exchange membranes used in the chlor-alkali process are bilayer membranes.

Therefore, the Nernst-Planck model was extended to a bilayer membrane and the

concentration profiles of ions and water in the membrane with increasing the current density

were calculated in a mono- and bilayer membrane in the chlor-alkali cell. The membrane

performance was compared in the mono- and bilayer membrane and it was proved that the

bilayer membranes are more efficient in comparison with the mono layer membranes. The

extra carboxylate layer added on the cathode side of the membrane is the reason of better

permselectivity and higher resistance of the membrane, especially at high current density. The

Maxwell-Stefan equation was investigated as another modeling approach for investigating the

ion transport inside the membrane. It was observed that having reliable data for binary

diffusion coefficients is the bottleneck of this model approach.

The intensification of the membrane cell electrolyzer has been achieved by designing a

spinning disc membrane electrolyzer based on the concept of the spinning disc reactor

technology and zero-gap membrane cell. In the spinning disc membrane electrolyzer high

shear forces induced with high velocity gradient or high-gravity results in fast mixing of the

fluids by laminar or turbulent mixing. The past studies have proved that the mass transfer

between the solid and liquid and between the liquid and gas improves the heat and mass

transfer by one to two orders of magnitude in the spinning disc reactor. The spinning disc

membrane electrolyzer is a rotating electrode-membrane-electrode sandwich. In the thin film

configuration, the electrolyte enters through the horizontal cavity forming a jet of liquid. Due

to rotation a thin film of liquid flowing radially outward is formed on the rotating electrodes.

The produced gas is collected on top of the liquid film. The collected mixture of gas and

liquid at the rim of the rotating electrodes exits the reactor via the concentric cavity of the

stator axis. Experimental results of the chlor-alkali electrolysis showed a promising high

performance and lower cell voltage compared to the conventional parallel plate cells. The cell

voltage and current efficiency in the spinning disc membrane electrolyzer were investigated

as a function of current density, rotation speed, temperature and concentration of anolyte and

catholyte electrolytes. The reduction of 0.9 V in the cell voltage with increasing the rotation

speed from 40 rad.s-1

to 60 rad.s-1

at 6 kA.m-2

was observed, and the effect of increase in

rotation speed was more pronounced especially at high current densities. The higher rotation

speed helps the better removal of the produced gas from the surface of the electrodes and

creates a clean surface for evolution of gas bubbles. Increasing the temperature from 40 ºC to

80 ºC resulted in a 1 V reduction in the cell voltage. The current efficiency of the membrane

increased up to 99 % with increasing the current density up to 20 kA.m-2

which was shown by

the theoretical Nernst-Planck model as well.

The more efficient gas bubble removal was proven in the thin-film spinning disc reactor by

performing decomposition of hydrogen peroxide as a reaction model for gas evolving

processes using a gauze as a rotating disc. The increase of the overall reaction rate parameter

with increasing the rotation speed in the mass transfer limited condition proved that gas

removal from the gauze surface becomes more efficient with increasing rotation speed.

xiii

These results show that a higher current density operation of the chlor-alkali process is

possible. It improves the permselectivity of the process. However, it increases the potential

drop which costs more energy. The increase in potential drop can be compensated by going to

higher temperature or by using thinner membranes.

Introduction

Process intensification 1.1

Process intensification has been defined in different ways throughout the history. It is an

increase in the reaction rate in the eyes of a chemical engineer and it is giving the same

process experience to all the molecules involved in the process in the eyes of a chemist [1].

Intensifying a process can be done in several ways, i.e. improving the energy efficiency,

reducing the capital costs and reducing the equipment size, which has been elaborated in the

literature [1–5]. In chemical engineering developing a cleaner, compact, more energy efficient

and environmentally friendly technology is termed process intensification [3].

Chlor-alkali process 1.2

The chlor-alkali industry is one of the most energy intensive industries and one of the largest

electrochemical operations in the world [6,7]. It is the producer of chlorine, sodium hydroxide

and hydrogen [7], which is done by the electrolysis of brine. Chlorine and sodium hydroxide

are used in the manufacture of many daily used products. Chlorine is used in the pulp and

paper industry, in water purification, in the production of organic and inorganic chemicals

such as polyvinyl chloride, ethylene chloride, titanium oxide, bromine, metals and in many

other applications. Sodium hydroxide is used in the pulp and paper industry, in the petroleum

and natural gas industry and in the soap and detergent industry. It is also used in production of

organic and inorganic materials. There are three technologies used in the chlor-alkali industry,

i.e the diaphragm process, the mercury process and the membrane process. The mercury

process does not require complex brine purification to produce high quality sodium

hydroxide. However, it has the highest energy consumption (~3.6 MWh/t Chlorine) among all

[8]. The benchmark of the chlor-alkali industry is the membrane technology which is known

as the most energy efficient process. This is because of its low energy consumption compared

to the diaphragm and mercury processes. Additionally, it has less environmental emissions

1

Introduction

2

compared to the other technologies because it uses a cation exchange membrane instead of

mercury or asbestos. The average electricity consumption per unit of product of all plants with

the membrane technology has been reported to be 2.75 MWh/t chlorine [7].

In the membrane cell technology a cation-exchange membrane separates the anode and

cathode compartments. A schematic of the cell is depicted in Figure 1.1. It shows that when

saturated brine is present in the anolyte compartment chlorine is produced at the anode. The

main functions of the cation-selective membrane used in the chlor-alkali process are

separation of hydrogen and chlorine, separation of caustic from chlorine and the acidic

sodium chloride solution, and selective transfer of sodium ions and water from the anolyte to

the catholyte compartment. In the cathode compartment ~30-32 wt% sodium hydroxide is the

input stream. The sodium ions that come through the membrane combine with the hydroxyl

ions which are the product of water decomposition to hydrogen and hydroxyl. In this way the

concentration of the sodium hydroxide increases to 32-35 wt%.

Figure 1.1. Schematic drawing of the chlor-alkali electrolyzer. It consists of anode and cathode

compartments. The two compartments are separated with a cation exchange membrane which allows

the selective transport of sodium ions. Chlorine is produced at the anode and hydrogen and sodium

hydroxide are produced at the cathode.

Over the past 20 years the efficiency and performance of the membrane cell technology has

been increased by improving the membrane, the electrodes and brine purification

technologies. Besides that, the zero-gap cell construction and providing a more uniform

concentration of the electrolytes close to the membrane-solution interface has reduced more

than 30 % of the ohmic loss [9].

Cation-exchange membranes 1.3

Perfluorinated cation exchange membranes are used in the chlor-alkali cells due to their high

thermal and chemical stability as well as their great ionic transport capability. There are three

membrane suppliers; Asahi Kasei, Dupont (now Chemours) and Asahi Glass. Nafion

Chapter 1

3

(Perfluorosulfonic membrane) is produced by Dupont. Flemion (Perfluorocarboxylic

membrane) is produced by Asahi Glass and Asahi Kasei is the producer of Aciplex (Bilayer

Perfluorosulfonic and carboxylic membrane). These membranes are named based on their

charged groups, i.e., sulfonic (–SO3-) or carboxylic (–COO

-) and they are cation selective due

to their negative charges [6]. Figure 1.2a-b shows the chemical formula of perfluorosulfonic

and carboxylic polymers respectively.

(a) (b)

Figure 1.2. Chemical formula of (a) perfluorosulfonic, and (b) perfluorocarboxylic polymers [6].

Various structure models have been discussed in the literature for perfluorinated membranes

including the Cluster-Network model, the Core-Shell and Lamellar Spacing model and the

Tortuous Pore Network model [6]. These models were proposed based on characterization of

the membranes with different techniques, i.e., X-ray spectroscopy, neutron scattering or

Small-angle X-ray scattering (SAXS). The Cluster-Network model is the most popular

depiction of the membrane structure. According to this model the polymer consists of two

phases: a crystalline phase (polytetrafluoroethylene) and an aqueous phase of ionic groups. As

can be seen in Figure 1.3 the phase of fixed ions, counter ions and water molecules consists of

spherical domains (4 nm diameter) connected with channels of 1 nm. The distance between

clusters is approximately 5 nm. The cluster diameter can vary by the water content of the

membrane. Dehydration of the polymer results in a decrease of the clusters’ diameter and an

increase in the number of clusters. Furthermore, a decrease in water content can impede the

effective passage of counter ions because several clusters will be connected with a sole

channel.

Figure 1.3. Cluster network model of Nafion perfluorosulfonic acid membrane [6].

Introduction

4

Yeager et al. [10] showed the structure of Nafion as illustrated in Figure 1.4 with the aid of

spectroscopic techniques. Three distinct regions are indicated. Region A contains the

fluorocarbon backbone matrix and region C contains the ionic clusters. Region B is the

interfacial region between A and C. It contains part of the counter ions and a small amount of

the sulfonate exchange sites which are not merged into the clusters.

Figure 1.4. Three phase structure of Nafion membrane [10].

The first generation of commercially developed perfluorinated membranes for the chlor-alkali

process were capable of producing 2-40 wt % sodium hydroxide with a current efficiency of

85 %. Nowadays, membranes for producing 32 wt% caustic at about 97 % efficiency are

available [6]. One of the developments that has led to an increased current efficiency is the

bilayer membrane. Bilayer cation-exchange membranes are developed by modifying the

catholyte side of the membrane or adding an extra layer of sulfonate with a different

equivalent weight or a carboxylate group polymer. This results in having perfluorinated

sulfonate/sulfonate or sulfonate/carboxylate polymers. Carboxylic and sulfonic types of

polymer have several advantages and disadvantages which are shown in Table 1.1. The lower

water content of carboxylic polymer is an advantage in preventing the back transport of

hydroxyl ions from the catholyte to the anolyte side.

Table 1.1. Properties of sulfonic and carboxylic polymers

Carboxylic base polymer Sulfonic base polymer

Higher current efficiency Lower current efficiency

Lower water uptake Higher water uptake

Higher electrical resistance Lower electrical resistance

The undesired side effects of back transport of hydroxide ions from the catholyte to the

anolyte are oxygen formation at the anode, formation of hypochlorous acid and chlorate due

to reaction of hydroxide with chloride ions and the loss of the desired caustic product. By

taking the advantageous of each polymer and combining them into a double layer membrane

the membrane characteristics can be improved. Although, the carboxylate layer increases the

Chapter 1

5

electrical resistance, a thin layer of carboxylic on the cathode side increases the current

efficiency. The optimal thickness of the carboxylic layer is 2-10 µm [11]. The bilayer

membrane is made either by laminating the ionomers or coextruding in the same die [6].

Figure 1.5 presents the chlor-alkali electrolyzer with a bilayer cation-exchange membrane

consisting of a sulfonate and a carboxylate layer.

Figure 1.5. Schematic drawing of the chlor-alkali electrolyzer on a microscopic level with anode and

cathode compartments separated by a bilayer cation-exchange membrane. The sulfonate layer is a

perfluorosulfonic polymer and the carboxylate layer is a perfluorocarboxylic polymer. The sodium

ions are transported from the anode to the cathode compartment. There is chloride transport and

hydroxide back transport which depends on the membrane efficiency.

The ion-exchange capacity of a membrane is a measure of number of fixed ionic groups per

unit volume or weight of membrane. It is defined as the millimoles of charge linked with

fixed ionic groups per gram of the polymer:

1

1

1 0 0 0( . )

( . )E W g e q

E C m g e q g

A typical ion exchange capacity for perfluorinated membranes is about 0.85 mmolg-1

and it

can be in the range of 0.5-1.2 mmolg-1

. Equivalent weight (EW) is used to describe the ion

exchange capacity defined as the weight of polymer in the H+ form that is neutralized by one

equivalent of alkali [6]. A high ion exchange capacity means a higher water content and as a

consequence a higher conductivity and permselectivity of the membrane.

Ion transport modeling

For prediction of ion and water transport through the membrane a mass transfer and

equilibrium model are required. An equilibrium model can describe the change of

concentration and potential between the porous membrane and the electrolyte solutions. When

the membrane is in contact with electrolyte solution an equilibrium state between the

Introduction

6

electrochemical potential of the ions inside and outside the membrane is stablished. The

electrochemical potential has two terms of chemical and electrical potential. The most popular

methods of describing the mass transfer inside the membranes are the Nernst-Planck and the

Maxwell-Stefan equations. The Nernst-Planck model which describes the transport due to

diffusion, electro-potential and convection. It neglects the interaction of ions with each other

by using the self-diffusivity of ions. Additionally, the water transport is not coupled with the

transport of charged ions. On the other hand, The Maxwell-Stefan model is a more

sophisticated model which takes into account the interaction of ions, and it includes the

prediction of the water transport in the transport equations. The main disadvantage of the

Maxwell-Stefan model is that it needs reliable data for diffusivities to have a correct

prediction of the effect of ions on each other.

Intensification of chlor-alkali process in spinning disc 1.4

membrane electrolyzer

Currently, the chlor-alkali industry operates up to 7 kA.m-2

[6]. Increasing the current density

results in higher production per square meter of membrane and lower investment per

produced ton, however, it increases the cell voltage and the power consumption. It is desirable

to operate the chlor-alkali process at high current density to reduce the electric power

consumption. It has been shown [9] that by increasing the electrolyte circulation in a small

laboratory cell to 30 times higher than in a large-scale electrolyzer, the current efficiency

remained almost unchanged with increasing the current density up to 10 kA.m-2

. Only a small

decrease occurred when increasing the current density up to 18 kA.m-2

. However, maintaining

a very high circulation in the large-scale electrolyzers is not possible. Additionally, increasing

the mass transfer efficiency at the membrane is necessary to have high current efficiency at

high current density [9].

A high mass transfer rate is why a new design of the membrane cell electrolyzer with the

spinning disc technology can be beneficial. In this way an extremely high mixing of the

electrolyte can be attained. Furthermore, a much higher current density can be applied without

increasing the size of the electrolyzer. The concept of the spinning disc reactors is based on

high-shear forces induced by a high velocity gradient or high-gravity [4]. Laminar or

turbulent mixing and surface renewal between aggregation phases is developed by the shear

forces. The two common types of the spinning disc reactors are the thin film and the rotor-

stator spinning disc reactors.

The concept of the thin film spinning disc reactor was patented by Ernst Buhtz [12]. This type

of reactor is mainly used for gas-liquid processes. The liquid enters either from the side or as

a jet flow from the top of the reactor. It forms a thin film over the disk. The mass transfer

from the gas phase to the liquid film, from the liquid film to the solid phase and the heat

Chapter 1

7

transfer rates have been reported to be high in the literature [13–17]. The hydrodynamics of

the thin film were studied by Woods [18]. He demonstrated experimentally that there are two

regions of inner zone without ripple and the wavy outer zone which break down into an

irregular flow. Additionally, Ozar et al. [19] showed the waves of the outer flow are because

of the hydraulic jump at the rim, and is formed because of extra pressure of surface tension

forces. The thickness of the liquid film decreases when increasing the rotation speed and

increasing the diameter of the disc. Furthermore, the increase of the viscosity and flow rate

increases the film thickness [20]. The application of this type of reactor has been studied by

several authors [21–24]. Two examples are polymerization and isomerization reactions.

The other type of reactor is the rotor-stator spinning disc reactor. In this design of the reactor

the rotating disc is used with a gap distance of 0.2-5 mm in the middle of a cylindrical

housing. The optimum gap distance for having a high mass transfer is up to 2 mm [4]. The

high velocity gradient between the rotor and the stator shears off the gas bubbles. The

centrifugal force pushes the gas bubble radially inwards. This results in a low gas hold-up of

the reactor. The gas hold-up increases with increasing the rotation speed and as a consequence

the size of the gas bubbles decreases. Besides that, increasing the rotation speed increases the

shear forces and as a result the mixing strength. This results in high gas-liquid and liquid-solid

mass transfer.

The scope and structure of thesis 1.5

This thesis is one of the four projects of SPINCHAL which aims to develop a compact and

transportable “plug and produce” production unit for the chlor-alkali process. Two of the

SPINCHAL projects were focused on the electrolysis as the heart of the chlor-alkali process;

one aims to study the electrodes and reactor modeling in the rotor-stator configuration of the

spinning disc membrane electrolyzer, and the other focuses on the membrane and the thin-

film configuration of the spinning disc membrane electrolyzer. The objective of this thesis is

the latter project which studies the role of the membrane in the development of an intensified

process as a replacement of the membrane cell electrolyzer. It describes a thin-film spinning

disc electrolyzer suitable for the chlor-alkali process with a focus on the performance and

efficiency of the cation-exchange membrane in the intensified process. Chapter 2 presents

experimental performance in terms of conductivity and permselectivity of several different

mono and bilayer cation-exchange membranes as a function of current density, various

sodium hydroxide concentrations and temperature in a sodium hydroxide electrolyte solution.

Chapter 3 describes a Nernst-Planck model of multicomponent ion transport in a monolayer

membrane, and validates the model with the experimental results presented in chapter 2. The

cation-exchange membrane used in the chlor-alkali process is a bilayer membrane. This is

why Chapter 4 presents a theoretical model for comparison of the ion transport in a mono

and bilayer membrane in the chlor-alkali membrane cell using the Nernst-Planck equation.

Introduction

8

Chapter 5 is about another ion transport model within the membrane, namely Maxwell-

Stefan. The challenges of this model is that it has a more complex modeling approach, and it

is important to have reliable diffusion coefficients for predicting the ion transport. Chapter 6

shows how a thin film spinning disc reactor makes the removal of gas formed on a gauze

surface more efficient with increasing rotation speed. This makes the thin film spinning disc

reactor favorable for gas evolving reactions. Chapter 7 is a joint chapter with Paola Granados

Mendoza and is a results of a joint work. It describes the spinning disc membrane electrolyzer

and presents the experimental results of the chlor-alkali process obtained in the intensified

spinning disc membrane electrolyzer. Additionally, it compares the cell voltage in the rotor-

stator and the thin film configuration of the spinning disc membrane electrolyzer. Finally,

Chapter 8 concludes all the results of the previous chapters and gives an outlook and

recommendation for the future work.

Bibliography

[1] D. Reay, C. Ramshaw, A. Harvey, Process intensification: engineering for efficiency,

sustainability and flexibility, Elsevier Ltd, Oxford., 2008.

[2] A. Stankiewicz, J.A. Moulijn, Re-Engineering the Chemical Processing Plant: Process

Intensification, CRC Press., 2003.

[3] A. Stankiewicz, J. Moulijn, Process intensification: transforming chemical engineering,

Chem. Eng. Prog. (2000) 22–34.

[4] J. van der Schaaf, J.C. Schouten, High-gravity and high-shear gas–liquid contactors for

the chemical process industry, Curr. Opin. Chem. Eng. 1 (2011) 84–88.

[5] K. Boodhoo, A. Harvey, Process Intensification Technologies for Green Chemistry:

Engineering solutions for sustainable chemical processing, John Wiley & Sons, Inc.,

2013.

[6] T.F. O’Brien, T.V. Bommaraju, F. Hine, Handbook of Chlor-Alkali Technology

Handbook of Chlor-Alkali Technology Volume I : Fundamentals, Springer, 2005.

[7] Questions and answers on the chlor alkali sector and the EU emission trading system

(ETS), 2010.

[8] I. Moussallem, J. Jörissen, U. Kunz, S. Pinnow, T. Turek, Chlor-alkali electrolysis with

oxygen depolarized cathodes: history, present status and future prospects, J. Appl.

Electrochem. 38 (2008) 1177–1194.

Chapter 1

9

[9] Y. Takahashi, H. Obanawa, Y. Noaki, New Electrolyser Design for High Current

Density, in: J. Moorhouse (Ed.), Mod. Chlor-Alkali Technol. Vol. 8, Blackwell Science

Ltd, London, 2001.

[10] H.L. Yeager, A. Steck, Cation and Water Diffusion in Nafion Ion Exchange

Membranes: Influence of Polymer Structure, J. Electrochem. Soc. 128 (1981) 1880–

1884.

[11] R.E. White, Electrochemical cell design, Plenum Press, New York, 1984.

[12] E. Buhtz, An Improved Method of and Apparatus For carrying out chemical reaction,

1927.

[13] H. Espig, H. Russell, Waves in a thin liquid layer on a rotating disk, J. Fluid Mech. 22

(1965) 671–677.

[14] R.J.J. Jachuck, C. Ramshaw, Process intensification: Heat transfer characteristics of

tailored rotating surfaces, Heat Recover. Syst. CHP. 14 (1994) 475–491.

[15] N. Brauner, D.M. Maron, characteristics of inclined thin films, waviness and the

associated mass transfer, Int. J. Heat Mass Transf. 25 (1982) 99–110.

[16] C. Ramshaw, The opportunities for exploiting centrifugal fields, Heat Recover. Syst.

CHP. 13 (1993) 493–513.

[17] G.M. Sisoev, O.K. Matar, C.J. Lawrence, Gas absorption into a wavy film flowing over

a spinning disc, Chem. Eng. Sci. 60 (2005) 2051–2060.

[18] W.P. Woods, The hydrodynamics of thin liquid films flowing over a rotating disc,

Newcastle, 1995.

[19] B. Ozar, B.M. Cetegen, A. Faghri, Experiments on the flow of a thin liquid film over a

horizontal stationary and rotating disk surface, Exp. Fluids. 34 (2003) 556–565.

[20] R.M. Wood, B.E. Watts, Flow, heat, and mass transfer characteristics of liquid films on

rotating disks., Trans. Inst. Chem. Eng. 51 (1973) 315–322.

[21] K.V.K. Boodhoo, R.J. Jachuck, Process intensification: spinning disk reactor for

styrene polymerisation, Appl. Therm. Eng. 20 (2000) 1127–1146.

[22] J.R. Boodhoo KVK, Process intensification: spinning disc reactor for condensation

polymerisation, Green Chem. (2000) 2–235.

Introduction

10

[23] K.V.K. Boodhoo, W.A.E. Dunk, M. Vicevic, R.J. Jachuck, V. Sage, D.J. Macquarrie,

et al., Classical cationic polymerization of styrene in a spinning disc reactor using

silica-supported BF3 catalyst, J. Appl. Polym. Sci. 101 (2006) 8–19.

[24] S.K. Vicevic M, Boodhoo KVK, Catalytic isomerisation of alphapinene oxide to

campholenic aldehyde using silica supported zinc triflate catalysts. II. Performance of

immobilised catalysts in a continuous spinning disc reactor, J. Chem. Eng. 133 (2007)

43–57.

Cation-exchange membrane

performance under high current

density

Abstract

An ion-exchange membrane is a key component in membrane electrolysis processes. The

membrane conductivity determines the potential drop over the membrane which generally is a

major contributor to the electrical power consumption of the process. Also, the current

efficiency of the process is often strongly influenced by the membrane permselectivity. In this

work, the conductivities and permselectivities of single and bilayer perfluorinated membranes

have been measured as a function of sodium hydroxide concentration (10-32 wt%),

temperature (40-80 ºC) and current density (0.86-20 kA.m-2). Most strikingly, the membrane

conductivity increases strongly with current density, which implies that membranes do not

show ohmic behaviour under the employed experimental conditions. It has also been found

that a current density increase leads to a lower sodium transport number and a higher water

transport number. In contrast, increasing the sodium hydroxide concentration leads to a lower

conductivity, a lower sodium transport number and a lower water transport number. These

results can be explained based on the water content and ion mobility in the membrane and

suggest that these parameters increase with increasing current density and decrease with

increasing sodium hydroxide concentration.

2

Cation-exchange membrane performance under high current density

12

Introduction

Electrochemical membrane cells are employed in a number of important commercial

processes including chlor-alkali electrolysis, water electrolysis, and fuel cells. The cells

consist of an anodic compartment and a cathodic compartment that are separated by an ion-

exchange membrane. The productivity of the cell is determined by the current density through

the cell and by the permselectivity of the ion-exchange membrane that separates the anode

and cathode compartments. In fact, by increasing the current density the production increases.

However, this also results in an increase in the cell potential, which in turn leads to increased

electricity consumption. Nevertheless, industrial electrolysers are preferably operated at high

current densities, since lower investment costs generally outweigh increased electricity

consumption.

In electrochemical membrane cells the membrane generally has the largest contribution to the

cell resistance. To suppress electricity consumption at high current densities, a membrane

with a low electrical resistance is of great interest. In addition, the membrane needs to have a

high permselectivity and a good thermal, chemical and mechanical stability. The electrical

conductivity of an ion-exchange membrane depends on several parameters, i.e. the

concentration of mobile ions in the membrane and the mobility of these ions. The ion mobility

is related to ion properties such as size and hydration level, but also to membrane properties

such as degree of cross-linking and water content [1]. These membrane properties are affected

by the concentration of the electrolyte adjacent to the membrane, which affects the amount of

electrolyte passing through the membrane and the swelling behaviour [2].

In the industrial chlor-alkali process [3] perfluorinated membranes are used which are

reinforced with a Teflon® mesh. A high current efficiency of the cation-exchange membrane

is achieved by using a sulfonic-carboxylic acid bilayer membrane. The reason for using a

bilayer membrane is that even though a single layer perfluorosulfonic acid membrane shows

good electrical conductivity, it does not have the desired high current efficiency due to back-

transport of hydroxide through the membrane. Applying a very thin layer of carboxylate

polymer on the catholyte side of the membrane prevents this back-transport and hence

improves the current efficiency of the process. Since the carboxylate layer is thin it does not

significantly affect the conductivity of the membrane.

Several authors have investigated how membrane properties depend on the process

parameters such as electrolyte concentration and temperature. Proton conductivity of Nafion

membranes has been investigated thoroughly for fuel cell applications [4–10]. The

conductivities of different types of Nafion membranes have been studied as a function of

electrolyte concentration up to 14 M and current density up to 3 kA.m-2 for chlor-alkali

industry. They showed a decrease in the membrane conductivity at higher external

Chapter 2

13

concentration of the electrolytes [11–15]. For example, Wodzki et al. [13] have shown that the

membrane volume fraction and cation mobility in the internal membrane phase decreases as

the external concentration of the solution increases. This causes decrease in the membrane

conductivity at higher external electrolyte concentration. Chandran et al. [15] have studied

conductivity and electrolyte uptake of Nafion 901 and concluded that at higher concentrations

than 9M the carboxylate layer of the membrane undergoes a structural change. They have also

found a maximum conductivity for Nafion 901 at 14 wt% sodium hydroxide solution. In

addition, some authors have studied the Arrhenius effect of temperature on membrane

conductivity as a function of concentration [12,15–17].

The permselectivity of membranes has also been investigated by a number of authors [18–20].

Gronowski et al. [18] have studied the permselectivity of several bilayer membranes in a

chlor-alkali electrolyser. They concluded that the membrane permselectivity has some

dependency on the anolyte concentration. However, it is a strong function of catholyte

concentration and good mixing at the catholyte side of the membrane. Lindheimer et al. [20]

have studied Nafion 125. They demonstrated that the selectivity of the swollen membrane is

less than the non-swollen membrane. They explained that this is because the ratio of counter-

ion mobility to co-ion mobility decreased from 4.1 in the non-swollen membrane to 2.1 in a

swollen membrane. The water transport number of cation-exchange membranes has been

measured previously and reported in the literature as well [18,21–24].

Interestingly, there has been little research into the effect of current density on membrane

properties. It seems to be generally assumed that membrane properties are independent of

current density, but the limited number of papers in which the effect of current density was

studied suggests otherwise. Taylor et al. [21] have measured the potential drop of a cation-

exchange membrane as a function of current density in high sodium hydroxide concentrations

and found non-ohmic behaviour. Also, Rondinini et al., Bergner et al. and Heitz et al. [25–27]

found a non-ohmic increase in the membrane potential drop with increase in current density

using sodium chloride as the anolyte and sodium hydroxide as the catholyte. Although

Chandran et al. [28] modelled the membrane voltage drop as a function of current density as a

straight line, their measurement points actually suggest a non-ohmic increase. Kressman et al.

[29] have investigated the dependency of sodium and chloride transport numbers on current

density for sodium chloride electrolyte and found that the transport number of sodium

increased from 0.5 to 0.87 with increasing current density in concentrated brine. Tombalakian

et al. [24] reported a decrease in water transport number from 3.3 to 2.2 with increasing

current density.

Most studies on conductivity and transport characteristics of cation-exchange membranes in

strong electrolytes have used current densities up to 3 kA.m-2 [10,11,18,19,21,30–32].

However, virtually no data exists on the performance of cation-exchange membranes at

current industrial operating conditions (e.g. 5-6 kA.m-2 for chlor-alkali) or even higher current


14

densities. Therefore, this chapter presents data for membrane conductivity and permselectivity

for both single and bilayer membranes at current densities up to 20 kA.m-2 at varying sodium

hydroxide concentrations and temperatures.

Theoretical background

The electrochemical membrane cell potential consists of a number of terms [Eq. (2.1)], i.e. the

thermodynamic potentials, the overpotentials at cathode and anode, the ohmic drop over the

solution, the electrical circuit potential and the membrane potential [33]. The thermodynamic

potential can be calculated from the free energy change of the overall reaction. In electrolytic

processes the overpotentials and ohmic drop terms represent energy inefficiencies.

C Ae e mC A CircuitCell SolE E E iR iR iR (2.1)

The electrical resistance of the membrane can be determined by measuring the potential drop

over the membrane. For this, Haber-Luggin capillaries can be used as presented in Figure 2.1.

The electrical resistance between Haber-Luggin capillary tips (Rm+s) consists of the solution

resistance Rs and the membrane resistance Rm. The membrane resistance Rm can be calculated

by carrying out experiments with and without a membrane:

m m s sR R R (2.2)

Figure 2.1. Schematic of electrical resistance terms between tips of Haber-Luggin capillaries. δm is the

membrane thickness and δl and δll are the solution distances from the capillary tips. RE is the reference

electrode.

The electrical resistance of the electrolyte solution Rs depends on the type of electrolyte, the

temperature and the concentration. Whereas at low concentrations the conductivity generally

increases linearly with concentration, this is no longer the case at high concentrations. For

example, the conductivity of sodium hydroxide exhibits a maximum at 15 wt% at 18 °C [3].

Chapter 2

15

Presumably, at concentrations higher than 15 wt% ion association occurs, which results in

formation of uncharged species not contributing to the electrical conductivity of the solution

[34]. At higher temperatures the maximum conductivity shifts to higher concentrations of

sodium hydroxide. By using Ohm’s law the membrane resistance Rm at constant temperature

and concentration can be determined from Eq. (2.2). The membrane conductivity κ can be

determined using the thickness L and the surface area A of the membrane:

.m

L

R A (2.3)

The permselectivity of the membrane is expressed by the ionic transport number t i, which is

defined as the amount of current carried by a certain ion. The permselectivity and the amount

of water transported through the membrane can be determined by measuring the concentration

change and total weight of the liquid in the anode and cathode compartments over time. The

ionic transport number and the water transport numbers are described by Eq. (2.4) and Eq.

(2.5) respectively:

ii

i

w Ft

Mw I t

(2.4)

waterwater

water

w Ft

Mw I t

(2.5)

The summation of the transport numbers of co-ions and counterions has to be unity. In case of

only sodium and hydroxide transport this means that a sodium transport number of 0.5

indicates that the membrane is not selective either to sodium or hydroxide ions. A sodium

transport number of 1 indicates 100 % selectivity to sodium over hydroxide ions.

Experimental

2.3.1 Materials

The following commercially available cation-exchange membranes have been investigated in

this work: Nafion N-324, Nafion NX-982, Nafion N-1110 (all Dupont Co.) and Flemion F-

988 (Fumatech Co.). The characteristics of these membranes are shown in Table 2.1. Sodium

hydroxide (≥98.5 % microprills; SIGMA-ALDRICH Co.) was used to prepare the electrolyte

solutions of 10 wt%, 15 wt%, 20 wt%, 25 wt% and 32 wt%. For titration of samples during

permselectivity experiments hydrochloric acid of 0.1 M, 0.5 M and 1 M (Merck Millipore

Co.) was used as a titrant. Phenol red was used as an indicator.


16

2.3.1 Experimental set-up

The electrical conductivity of the membranes was determined using a four-electrode direct

current technique in a temperature controlled H-Cell. The schematic of the experimental set-

up is shown in Figure 2.2. The H-Cell is a two compartment jacketed vessel connected to a

cooling unit (LAUDA Ecoline 003) to control the temperature during electrolysis. The

working electrodes are two nickel plates. To avoid concentration polarization at the surface of

the membrane, the electrolyte is circulated using a peristaltic pump (Watson Marlow 503U).

The solution temperature is monitored in the catholyte and anolyte compartments with VWR®

electronic stainless steel thermometers. Each compartment has a cooler on top using 15 °C tap

water in order to prevent water evaporation. Also, from the top of the cathode compartment

cooler, nitrogen is flushed to dilute the produced hydrogen and avoid formation of an

explosive mixture of hydrogen and air. The membrane is clamped between the half-cells

using rubber O-rings. The open surface area for the membrane is 3.14 cm2. The potential drop

over the membrane is measured using two Haber-Luggin capillaries with two Ag/AgCl

reference electrodes (QM710X; q-i-s Co.). The tips of the capillary tubes are at approximately

0.5 mm from either side of the membrane. Current is applied with a power supply (TDK-

Lambda; GEN 60-12.5) to the working electrodes. The potential drop between the Haber-

Luggin capillaries is measured using a 175 Autoranging multimeter (KEITHLEY Co.).

Table 2.1. Characteristics of investigated membranes [35].

Membrane

Type

Layers

N-1110 N-324 NX-982 F-988

Single layer Bilayer Bilayer Bilayer

Sulfonate Sulfonate Sulfonate Sulfonate Carboxylate Sulfonate Carboxylate

EWa

1100 1100 1500

not

specified

not

specified 950-1000 1050-1100

mmol Na+ or H+ /

g dry polymer a

0.90 0.90 0.67

not

specified

not

specified

1.05-1 0.95-0.90

Total dry

thickness (μm)b

254 150 not specified 270-280

Total wet

thickness (μm)c

270 340 240 310

Delivery form Dry wet wet wet

a EW: Equivalent Weight corresponding to the gram of polymer per mole of sulfonate or

caboxylate acid groups. b [35,36], Fumatech technical data sheet c measured with digital caliper (Mitutoyo Corp. accuracy: ±0.02 mm)

Chapter 2

17

Figure 2.2. Schematic drawing of a four-electrode jacketed H-Cell for determining the electrical

conductivity and permselectivity of cation-exchange membranes connected to a cooling unit with two

working electrodes in the vessels and two reference electrodes in the capillary tubes, coolers on top of

anode and cathode compartments, thermometers, double head peristatic pump and the membrane/O–

ring stack.

2.3.1 Experimental procedure for conductivity measurements

The delivered sheets of membranes were cut in circles of ~2.3 cm diameter. Prior to each

experiment the membrane was equilibrated in a sodium hydroxide solution with the same

concentration as the concentration used in the experiment. For every experiment the

membrane was then stacked using rubber O-rings on each side and clamped between the

compartments. Haber-Luggin capillaries and the electrolyte compartments were filled with

sodium hydroxide solution. The reference electrodes were placed in the Haber-Luggin

capillary tubes. Experiments were started after heating up the electrolyte vessels to the desired

temperature. The current density was increased stepwise from 0.86 kA.m-2 to 16 kA.m-2,

while measuring the potential drop between the reference electrodes. In most experiments a

stable potential was typically reached in less than one minute. However, at higher

concentrations of sodium hydroxide (32 wt%) it could take up to 5-10 minutes to reach a

stable potential. These measurements were also carried out without a membrane in order to

determine the solution resistance. From these measurements the distance between the

capillaries was calculated to be 0.13 ±0.01 cm. The reproducibility of the experiments was

checked by repeating 80 % of experiments.


18

2.3.2 Experimental procedure for permselectivity measurements

The membranes were pretreated and stacked with the same procedure as described in section

3.3. The anolyte and catholyte compartments were filled with an equal amount of a known

concentration (10 wt% - 15 wt% - 32 wt%) of sodium hydroxide after clamping the

membrane between the compartments. A constant current was applied to the electrodes for a

certain time. The length of every experiment was set based on an anticipated 2 wt% change in

the electrolyte solution concentration in order to avoid a concentration gradient effect in the

system and also to be able to accurately determine the concentration change with titration.

Samples were taken halfway through the experiment and at the end with a needle syringe

from each compartment. The titrations were done in triple under argon flow in order to

prevent the reaction of carbon dioxide in air with sodium hydroxide. The electrolytes were

drained and weighed at the end of each experiment. The amount of remaining solution in the

setup after draining (1-3 g) was taken into account.

Results 2.4

SEM images of the reinforced membranes N-324, NX-982 and F-982 are presented in Figure

2.3. The figure shows the sulfonate layer, the carboxylate layer and the reinforcements and

shows that there are some differences between the membranes. For example, the

reinforcements are placed differently: NX-982 has four Teflon strings whereas F-988 has only

two Teflon strings. N-324 is reinforced with a 10 x 10/cm leno weave of 400-denier brown

multifilament yarn [35]. Although not depicted in the figure, single layer N-1110 does not

have reinforcement. In general it can be said that the membranes are quite similar, with some

differences in layer thickness and reinforcement structure. Although a convex shape cannot be

seen for N-324 in this particular picture, this membrane also has this shape.

The conductivity of these membranes was determined as a function of concentration,

temperature and current density and is presented in the following figures. In this chapter only

a selection of the results will be presented, while a complete overview of the results is

available in the appendix.

The membrane potential drop as a function of current density for F-988 is shown in Figure

2.4a for different sodium hydroxide concentrations. It shows a non-linear increase of

membrane potential drop with increasing current densities, implying that the membrane

conductivity increases with increasing current density. This can be clearly seen in Figure 2.4b,

which depicts the membrane conductivity for the same experiments. It shows that increasing

the current density to 16 kA.m-2

can increase the membrane conductivity more than double

compared to low current densities. Except for the low current densities, the increase of

conductivity with current density follows a linear trend.

Chapter 2

19

Figure 2.3. SEM images of cross section cut of (a) N-324 with two sulfonate layers reinforced with a

leno weave of 400-denier brown multifilament yarn (b) NX-982 and (c) F-988 with sulfonate layer on

the anode side and a carboxylate layer on the cathode side.

(a) (b)

Figure 2.4. (a) Potential drop and (b) conductivity for F-988 as a function of current density at

anolyte/catholyte concentrations (in wt%) of 15/15, 32/32 and 15/32 at 80 °C.

(a) (b)

(a)

(c)

(b)


20

Figure 2.4 also shows that there is a strong influence of anolyte and catholyte concentration

on the membrane conductivity with a lower concentration resulting in higher conductivities.

The experiment with different concentrations in the anolyte (15 wt%) and the catholyte (32

wt%) bears most resemblance to the experiment with 15 wt% in both anolyte and catholyte.

So, the membrane potential drop seems to be more dependent on the anolyte concentration

than on the catholyte concentration. Figure 2.5 and Figure 2.6 present the conductivities of the

three bilayer and the single layer membranes in 15 and 32 wt% sodium hydroxide as a

function of current density. The graphs show that all membranes show a strong increase in

conductivity as a function of current density. Interestingly, at 15 wt% sodium hydroxide the

membrane conductivity seems to be constant at low current densities, whereas this does not

seem to be the case for 32 wt%. In the Appendix Figures A2.1 to A2.5 more data at different

temperatures and sodium hydroxide concentrations can be found. Some of these data also

show the “levelling off”-effect, but there does not seem to be a clear dependence on sodium

hydroxide concentration, membrane type or temperature. The conductivity of single layer N-

1110 drops below the other membranes at 32 wt% sodium hydroxide. N-324 has the lowest

conductivity among the studied membranes at all sodium hydroxide concentrations. NX-982

has a lower conductivity at 15 wt% sodium hydroxide compared to F-988. However, the

conductivity of NX-982 increases above F-988 at 32 wt%.

Figure 2.5. Conductivity of N-324, NX-982, F-988 and N-1110 as a function of current density in 15

wt% sodium hydroxide at 80 °C.

Chapter 2

21

Figure 2.6. Conductivity of N-324, NX-982, F-988 and N-1110 as a function of current density in 32

wt% sodium hydroxide at 80 °C.

Figure 2.7 shows the effect of concentration on the conductivity for the three bilayer

membranes at a current density of 6.6 kA.m-2 and a temperature of 80 °C. The data illustrate a

clear decrease in conductivity with sodium hydroxide concentration and also some differences

between the different membranes. Both N-324 and NX-982 show a maximum conductivity at

15 wt%, which is also typical for sodium hydroxide solutions. F-988 does not exhibit such a

maximum. Membrane conductivity data as a function of concentration at other temperatures

and current densities can be found in Appendix Figures A2.6 to A2.9 which show similar

trends as a function of concentration.

Figure 2.7. Conductivity of bilayer membranes N-324, NX-982 and F-988 as a function of sodium

hydroxide concentration at 6.6 kA.m-2 and 80 °C.


22

Figure 2.8. Conductivity of F-988 as a function of temperature for sodium hydroxide concentrations of

10, 15, 20, 25 and 32 wt% at 16 kA.m-2.

In Figure 2.8 the effect of temperature at different concentrations is shown for the F-988

membrane. It can be seen that conductivity generally increases with temperature, although the

increase is only relatively small in 32 wt% sodium hydroxide. By plotting the natural log of

the conductivity as a function of the inverse temperature it is possible to calculate the

activation energies (for graphs see Appendix). It should be remarked that these activation

energies are not very accurate, since they are only based on three data points. Nevertheless,

they do give an indication on how the activation energies depend on current density and

sodium hydroxide concentration. Figure 2.9 shows that for F-988 the activation energy has a

decreasing trend with both current density as well as sodium hydroxide concentration. These

trends can also be observed for the other membranes as shown in Appendix Figures A2.14 to

A2.16.

Figure 2.9. Activation energies of F-988 as a function of current density at sodium hydroxide

concentrations of 10, 15, 20, 25 and 32 wt%.

Chapter 2

23

Membrane permselectivity has been measured as a function of sodium hydroxide

concentration, membrane type, temperature and current density. The resulting sodium

transport numbers for single layer N-1110 and bilayer NX-982 are shown in Figure 2.10. The

figure clearly shows that sodium transport numbers are higher for the bilayer membrane than

for the single layer membrane, as expected. It can also be seen that an increase in

concentration and/or current density results in a lower sodium transport number. This implies

that the membrane permselectivity decreases with increasing current density and sodium

hydroxide concentration.

The water transport numbers are presented in Figure 2.11. The figure shows that increasing

the sodium hydroxide concentration results in a clear decrease of the water transport number.

It also shows that an increase in current density higher than 6 kA.m-2 leads to an increase in

the water transport number. There is no significant difference in water transport number

between the bilayer and single layer membranes.

After carrying out permselectivity experiments with F-988 at 32 wt% and 20 kA.m-2, it was

observed that the membrane had formed blisters as shown in Figure 2.12. From the SEM

image a clear delamination of the sulfonate layer and the carboxylate layer can be observed,

which is typical for blisters formed in chlor-alkali membranes [3]. It is interesting to note that

blister formation only occurred for F-988 and did not occur for NX-988 and N-324. It also did

not occur for lower sodium hydroxide concentrations. Permselectivity data for F-988 at 32

wt% are not shown here, since they are not considered reliable.

Figure 2.10. Sodium transport numbers for N-1110 as a function of concentration at 10 kA.m-2 and

also in 10 wt% sodium hydroxide for current densities of 2, 6, 10 and 20 kA.m-2, and for NX-982 as a

function of concentration at 20 kA.m-2 and also in 15 wt% sodium hydroxide at 6 kA.m-2.


24

Figure 2.11. Water transport numbers for N-1110 as a function of concentration at 10 kA.m-2 and also

in 10 wt% sodium hydroxide for current densities of 2, 6, 10 and 20 kA.m-2, and for NX-982 as a

function of concentration at 20 kA.m-2 and also in 15 wt% sodium hydroxide at 6 kA.m-2.

Figure 2.12. (a) SEM image of blistered F-988 after experiment in 32 wt% sodium hydroxide and at

20 kA.m-2 and 80 °C with the carboxylate detaching from the sulfonate layer (b) magnification of the

SEM image (a).

Discussion

Current density effect

Our results show a strong dependence of membrane properties such as conductivity, sodium

transport number and water transport number on current density. This implies that under the

conditions as presented in this paper the membrane no longer behaves as an ohmic resistor for

which the potential drop linearly increases with current density. This has quite some

implications for industrial electrolysis applications: the increasing membrane conductivity

with current density can make it possible to operate electrolysers at very high current densities

(a)

(b)

Chapter 2

25

without excessive energy costs. On the other hand, the decreasing sodium transport number

negatively affects the current efficiency of the processes.

Our observation that membrane properties change with current density is not completely new.

As mentioned in the introduction Taylor et al., Bergner et al., Rondinini et al. and Heitz et al.

[21,25–27] already found a non-ohmic increase of the membrane potential with an increase in

current density. Nevertheless, few other authors have made similar observations and we need

to consider why that is the case. One possible reason is that the current density effect only

becomes truly apparent above 3 kA.m-2 (as can be seen in Figure 2.5) and only very few

authors have ventured to these levels [25,28].

Key question is what causes this change in membrane properties. It is well known that the

membrane conductivity depends strongly on the water content of the membrane and therefore

the higher membrane conductivity suggests that the water content in the membrane increases

with current density. This higher water content is in line with the observed higher water

transport number (Figure 2.11). It is also in line with increasing hydroxide back-transport,

which leads to a decrease in the sodium transport number (Figure 2.10).

Currently, we can only speculate about the cause of the higher water content. It could be that

the increased potential drop over the membrane helps in opening up dead-end pores and

increases the number of active pores. It could also be that the high flow of sodium ions

through the membrane widens the pores by pushing away polymer side groups. Another

possibility is that heat dissipation caused by the sodium transport leads to local heating, which

in turn leads to a local increase in water content. To truly determine the reason for the higher

water content it will be required to carry out in situ characterization of the membrane while

operating at high current densities which is not straightforward.

Concentration effect

Our data show a strong decrease of membrane conductivity with increasing sodium hydroxide

concentration at concentrations higher than 15 wt%. This result is in line with the results of

others [11,12,15,21,28]. Scibona et al. [12] have discussed that membrane conductance

depends on the concentration and mobility of co-ions and counter-ions in the membrane. At

low concentration of external solution (< 0.4 wt%) only counter-ions contribute to the specific

conductance, since contribution of co-ions is negligible. Increase in external solution

concentration (0.4 wt% – 17 wt%) results in uptake of electrolyte (salt invasion) and as a

consequence both counter-ions and co-ions contribute to the membrane conductance.

Increasing the electrolyte concentration even further (> 17 wt%) results in ion pair formation

reducing the number of free ions and hence the membrane conductivity.

What is also likely to play an important role is that the increasing concentration increases the

osmotic pressure of the electrolyte. This osmotic pressure of the electrolyte draws the water


26

from the membrane and in this way reduces the water content. In turn this reduces the

conductivity. It is interesting to note that the experiment with different anolyte and catholyte

concentrations shows that especially the anolyte concentration has a strong influence on

conductivity (Figure 2.4). This is probably caused by the presence of the carboxylate layer on

the catholyte side of the membrane.

In line with our results several other studies have reported a decreasing trend in sodium

transport number and water transport number as a function of concentration [12,21,23,32].

The decreasing trend in sodium transport number is believed to be caused by salt invasion at

high concentrations [6]: the sodium hydroxide concentration in the membrane increases,

resulting in a higher hydroxide back-transport. The decreasing trend in water transport

number can be explained by the higher osmotic pressure, which reduces the water content in

the membrane.

Temperature effect

An increase in temperature results in a higher mobility of ions and a higher water content in

the membrane. This results in higher conductivity of the membranes. We also observed that

the activation energies decrease with increasing current density and sodium hydroxide

concentration. The effect of current density on the activation energy has not been reported in

the literature. Currently, we do not have an explanation for these decreasing activation

energies. Chandran et al. [15] have reported an increase in activation energy of Nafion 901 as

a function of concentration. Whereas there seems not to be a clear trend in the activation

energy values reported by Scibona et al. [12] for Nafion 125 and Yeo et al. [17] for Nafion

1200 EW as a function of concentration.

Membrane type

As shown in Table 2.1 and Figure 2.3 the membranes studied in this work have some

structural differences that cause differences in conductivity and permselectivity. N-324 has a

sulfonate layer on the anolyte side that has a higher equivalent weight compared to the anolyte

side sulfonate layer of F-988. Having a higher equivalent weight means a lower number of

fixed ionic groups and a lower water content. This could explain the lower conductivity of N-

324 compared to NX-982 and F-988.

Our results also show a higher permselectivity of the bilayer NX-982 compared to the single

layer N-1110. It can be explained based on the fact that the carboxylate layer on the cathode

side of the bilayer membrane prevents the back-transport of hydroxide ions and improves the

permselectivity [3].

The observed blister formation in F-988 is likely due to an imbalance in water transport

between the sulfonate and carboxylate layers leading to stresses on the boundary layer

resulting in delamination of the layers [3]. At low current densities such blister formation is

Chapter 2

27

unlikely to occur for these commercial membranes. However, at high current densities the

effect of the imbalance in water transport will be more pronounced, increasing the chances of

blister formation. Also, from our results it can be concluded that the F-988 membrane is more

prone to blister formation than the other bilayer membranes.

Conclusion

In this study the effect of current density, concentration and temperature on conductivities and

permselectivities of single and bilayer cation-exchange membranes was investigated in

sodium hydroxide solution. The main results of this work are: a non-ohmic change of the

membrane potential drop with increase in current density above 3 kA.m-2 and a loss of the

permselectivity at high current densities and concentrations. We have also concluded that

increases in current density and electrolyte concentration have opposite effects on the

conductivity and water transport properties of the studied membranes. High current density

enhances water transport and ion mobility and increases the conductivity. On the other hand, a

high sodium hydroxide concentration reduces the water transport and decreases the

conductivity. Also, the permselectivity of the membranes decreases at higher sodium

hydroxide concentrations, which is likely due to salt invasion at high concentrations.

For industrial electrolysis processes these results suggest that by going to higher current

densities higher production rates can be achieved without an excessive increase in energy

cost. However, the current efficiency of the process will decrease. This is why there is a

necessity for further improvement of the permselectivity of the bilayer membranes.

Nomenclature

Latin symbols

Am Membrane cross sectional area [m2]

EeA Equilibrium anode potential [V]

EeC Equilibrium cathode potential [V]

ECell Cell potential [V]

F Faraday constant [C.mol-1]

i Current density [A.m2]

I Current [A]

L Thickness [m]

Mw Molecular weight [g.mol-1]

RSol Solution resistance [Ω]

RCircuit Electrical circuit resistance [Ω]

Rm+s Membrane and solution resistance [Ω]

Rm Membrane resistance [Ω]

t Time [s]

ti Ionic transport number species i [-]


28

T Relative transport number [-]

w Weight [g]

wt% Weight percentage [g.g-1 solution]

Greek symbols

ηA Overpotential at anode [V]

ηC Overpotential at cathode [V]

Δ Difference [-]

κ Conductivity [ohm-1.m-1]

Bibliography

[1] H. Strathmann, Ion-exchange membrane separation processes, First ed., Elsevier,

Amsterdam, 2004.

[2] T. Sata, Ion Exchange Membranes; preparation, characterization, modification and

application, The royal society of chemistry, 2004.



[4] J. Hodakovska, J. Kleperis, L. Grinberga, G. Vaivars, Conductivity measurement of

different polymer membranes for fuel cells, Russ. J. Electrochem. 45 (2009) 657–661.

[5] C.H. Lee, H.B. Park, Y.M. Lee, R.D. Lee, Importance of Proton Conductivity

Measurement in Polymer Electrolyte Membrane for Fuel Cell Application, Am. Chem.

Soc. 44 (2005) 7617–7626.

[6] C.A. Ferreira, D.S. Azambuja, C. Alema, E. Armelin, Measuring the Proton

Conductivity of Ion-Exchange Membranes Using Electrochemical Impedance

Spectroscopy and Through-Plane Cell, Phys. Chem. 118 (2014) 1102–1112.

[7] G. Alberti, M. Casciola, L. Massinelli, B. Bauer, Polymeric proton conducting

membranes for medium temperature fuel cells (110 – 160 ◦C ), Membr. Sci. 185 (2001)

73–81.

[8] J. Sone, P. Ekdunge, D. Simonsson, Proton Conductivily of Nafion 117 as Measured

by a Four-Electode AC Impedance Method, Electrochem. Soc. 143 (1996) 1254–1259.

[9] S.J. Peighambardoust, S. Rowshanzamir, M. Amjadi, Review of the proton exchange

membranes for fuel cell applications, Int. J. Hydrogen Energy. 35 (2010) 9349–9384.

Chapter 2

29

[10] S. Slade, S.A. Campbell, T.R. Ralph, F.C. Walsh, Ionic Conductivity of an Extruded

Nafion 1100 EW Series of Membranes, J. Electrochem. Soc. 149 (2002) A1556.

[11] A. Lehmani, P. Turq, M. Perie, J. Perie, J. Simonin, Ion transport in Nation 117

membrane, Electroanal. Chem. 428 (1997) 81–89.

[12] G. Scibona, C. Fabiani, B. Scuppa, Eelectrochemical behaviour of Nafion type

membrane, J. Memb. Sci. 16 (1983) 37–50.

[13] R. Wodzki, A. Narbbska, W. Kwas, Percolation Conductivity in Nafion Membranes, J.

Appl. Polym. Sci. 30 (1985) 769–780.

[14] R.S. Yeo, J. Mcbreen, G. Kissel, F. Kulesa, S. Srinivasan, Perfluorosulphonic acid (

Nafion ) membrane as a separator for an advanced alkaline water electrolyser, J. Appl.

Electrochem. 10 (1980) 741–747.

[15] R.R. Chandran, R.S. Yeo, D.-T. Chin, Sorption and transport behavior of

perfluorinated ionomer membranes in concentrated NaOH solution, Electrochim. Acta.

30 (1985) 1585–1590.

[16] J.-W. Lee, C.-W. Yi, K. Kim, The Electrochemical Properties of the Porous Nafion

Membrane for Proton Exchange Membrane Fuel Cells (PEMFCs), Bull. Korean Chem.

Soc. 33 (2012) 1788–1790.

[17] R.S. Yeo, Intrinsic Conductivity of Perfluorosulfonic Acid Membranes and Its

Implication to the Solid Polymer Electrolyte (SPE) Technology, (n.d.).

[18] A.A. Gronowski, H.L. Yeager, Factors Which Affect the Permselectivity of Nafion®

Membranes in Chlor-Alkali Electrolysis, I., Electrochem. Soc. 138 (1991) 2690–2697.

[19] P. Meares, A.H.Sutton, Electrical Transport phenomena in a Cation-Exchange

membrane l. The determination of transport numbers and the ratios of tracer fluxes, J.

Colloid Interface Sci. 28 (1968) 118–133.

[20] A. Lindheimer, J. Molenat, C. Gavach, A study of the supers-perfluorosulfonic

memrranes of Nafion perfluorosulfonic membranes, Electroanal. Chem. Interfacial

Electrochem. 216 (1987) 71–88.

[21] E.J. Taylor, N.R.K. Vilambi, R. Waterhouse, A. Gelb, Transport and conductivity

properties of an advanced cation exchange membrane in concentrated sodium

hydroxide, J. Appl. Electrochem. 21 (1991) 402–408.


30

[22] N. Lakshminarayanaiah, Electroosmosis in Ion-Exchange Membranes, J. Electrochem.

Soc. 116 (1969) 338.

[23] H.I. Yeager, B.O. Dell, Z. Twardowski, Transport Properties of Nafion® Membranes

in Concentrated Solution Environments, J. Electrochem. Soc. 129 (1982) 85.

[24] A.S. Tombalakian, H.J. Barton, W.F. Graydon, Electroosmotic water transport across

ion-exchange membranes, Am. Chem. Soc. 66 (1961) 1006–1009.

[25] S. Rondinini, M. Ferrari, Resistivity behaviour of perfluorinated ionomer membranes

in the chlor-alkali electrolytic process, in: Electrochem. Soc., 1986.

[26] D. Bergner, M. Hartmann, H. Kirsch, Voltage-current curves: application to membrane

cells, in: N.M. Prout, J.S. Moorhouse (Eds.), Mod. Chlor-Alkali Technol. Vol. 4,

Elsevier aaplied science, 1990.

[27] E. Heitz, G. Kreysa, Principles of Electrochemical Engineering - Extended Version of a

DECHEMA Experimental Course, VCH, Weinheim, 1986.

[28] R.R. Chandran, D.T. Chin, Reactor analysis of a chlor-alkali membrane cell,

Elechtrochemical Acta. 31 (1985) 39–50.

[29] T.R.E. Kressman, F.L. Tye, The effect of current density on the transport of ions

through ion-selective membranes, Discuss. Faraday Soc. (1956) 185–192.

[30] Z. Twardowski, H.L. Yeager, B.O. Dell, A comparison of perfluorinated carboxylate

and sulfonate ion exchnage polymers: ll. Sorption and transport properties in

concentrated solution environments, Electrochem. Soc. 129 (1982) 328–332.

[31] T.A. Zawodzinski, C. Derouin, S. Radzinski, R.J. Sherman, V.T. Smith, T.E. Springer,

et al., Water Uptake by and Transport Through Nation® 117 Membranes, Electrochem.

Soc. 140 (1993) 1043–1047.

[32] H.L. Yeager, B. Kipling, Sodium Ion Diffusion in Nation® Ion Exchange Membranes,

J. Electrochem. Soc. 127 (1980) 2–6.

[33] D. Pletcher, F.C. Walsh, Industrial electrochemistry, Chapman and Hall, London,

1990.

[34] D.A. Lown, H.R. Thirsk, Proton Transfer Conductance in Aqueous Solution. Part 1.

Conductance of concentrated aqueous alkali metal hydroxide solutions at elevated

temperature and pressures., Trans. Faraday Soc. 67 (1971) 132–148.

Chapter 2

31

[35] W. Grot, Fluorinated Ionomers, William Andrew, Oxford, 2011.

[36] Q. Duan, H. Wang, J. Benziger, Transport of liquid water through Nafion membranes,

J. Memb. Sci. 392-393 (2012) 88–94.


32

Appendix

Current density effect:

(a) (b)

(c)

Figure. A2.1. Conductivity of N-324, NX-982 and F-988 versus current density in 10 wt% sodium

hydroxide at (a) 40 °C (b) 60 °C (c) 80 °C.

Chapter 2

33

(a) (b)

Figure. A2.2. Conductivity of N-324, NX-982, F-988 and N-1110 versus current density in 15 wt%

sodium hydroxide at (a) 40 °C (b) 60 °C.

(a) (b)

(c)

Figure. A2.3. Conductivity of N-324, NX-982 and F-988 versus current density in 20 wt% sodium



34

(a) (b)

(c)

Figure. A2.4. Conductivity of NX-982, F-988 and N-1110 versus current density in 25 wt% sodium


(a) (b)

Figure. A2.5. Conductivity of N-324, NX-982, F-988 and N-1110 versus current density in 32 wt%

sodium hydroxide at (a) 40 °C (b) 60 °C.

Chapter 2

35

Concentration effect:

Figure. A2.6. Conductivity of bi-layer membranes; N-324, NX-982 and F-988 at 2 kA.m-2 current

density as a function of sodium hydroxide concentration and temperature. Conductivity of Nafion 901

as a function of sodium hydroxide concentration and temperature.

Figure. A2.7. Conductivity of bi-layer membranes; N-324, NX-982 and F-988 at 6.6 kA.m-2 current



Figure. A2.8. Conductivity of bi-layer membranes; N-324, NX-982 and F-988 at 9.7 kA.m-2 current




36

Figure. A2.9. Conductivity of bi-layer membranes; N-324, NX-982 and F-988 at 16 kA.m-2 current



Temperature effect

(a) (b)

(c) (d)

Figure. A2.10. Arrhenius plot of N-324 conductivity for varying concentration at (a) 2 kA.m-2 (b) 6.6

kA.m-2 (c) 9.7 kA.m-2 (d) 16 kA.m-2.

Chapter 2

37

(a) (b)

(a) (b)

Figure. A2.11. Arrhenius plot of NX-982 conductivity for varying concentration at (a) 2 kA.m-2 (b) 6.6

kA.m-2 (c) 9.7 kA.m-2 (d) 16 kA.m-2.


38

(a) (b)

(c) (d)

Figure. A2.12. Arrhenius plot of F-988 conductivity for varying concentration at (a) 2 kA.m-2 (b) 6.6

kA.m-2 (c) 9.7 kA.m-2 (d) 16 kA.m-2.

Chapter 2

39

(a) (b)

(c) (d)

Figure. A2.13. Arrhenius plot of N-1110 conductivity for varying concentration at (a) 2 kA.m-2 (b) 6.6

kA.m-2 (c) 9.7 kA.m-2 (d) 16 kA.m-2.

Figure. A2.14. Change of the activation energy with increase in current density for N-324 at sodium

hydroxide concentrations of 10, 15, 20, 25 and 32 wt%.


40

Figure. A2.15. Change of the activation energy with increase in current density for NX-982 at sodium


Figure. A2.16. Change of the activation energy with increase in current density for N-1110 at sodium


Nernst-Planck modeling of

multicomponent ion transport in a

Nafion membrane at high current

density

Abstract

A mathematical model of multicomponent ion transport through a cation-exchange membrane

is developed based on the Nernst-Planck equation. A correlation for the non-linear potential

gradient is derived from current density relation with fluxes. The boundary conditions are

determined with the Donnan equilibrium at the membrane-solution interface, taking into

account the convective flow. Effective diffusivities are used in the model based on the

correlation of tortuosity and ionic diffusivities in free water. The model predicts the effect of

an increase in current density on the ion concentrations inside the membrane. The model is

validated with previously published experimental data. The effect of current density on the

observed increase in voltage drop and the decrease in perm-selectivity has been analyzed

using the available qualitative membrane swelling theories. The observed non-linear behavior

of the membrane voltage drop versus current density can be explained by an increase in

membrane pore diameter and an increase in the number of active pores. We show how the

membrane pore diameter increases and dead-end pores open up when the current density is

increased.

3

Nernst-Planck modeling of multicomponent ion transport in a Nafion membrane

42

Introduction

Ion-exchange membranes have several industrial applications, including fuel cells, the chlor-

alkali process, and water electrolysis. In order to explain the mass transfer in the membrane at

high current densities, a suitable mathematical model is required. There are different

approaches to describe the transport of ions inside the membrane. Rohman and Aziz have

reviewed mathematical models of ion transport in electrodialysis. They have proposed three

types of phenomenological equations in their irreversible thermodynamic approach: 1. the

Maxwell-Stefan (MS) equation which takes the interaction between each pair of components

into account; 2. the Kedem-Katchalsky (KK) equation that considers the membrane as a

geometric transition region between two homogenous compartments, and 3. the Nernst-

Planck (NP) equation which describes diffusion and electromigration in the ionic transport

without taking into account the interaction between ions. The latter is widely used because of

its simplicity [1]. Psaltis et al. have compared the Nernst-Planck and Maxwell-Stefan

approaches in transport predictions of ternary electrolytes. They have concluded that using

binary diffusivities (neglecting interaction between different solute species) and the full

Maxwell-Stefan model does not affect the final steady-state concentrations profiles in the

electrolyte solution of a multicomponent system. This shows that using the effective

diffusivities in the Nernst-Planck equation should give reasonable accuracy in the results [2].

Additionally, Graham et al. have shown that the Nernst-Planck equation is valid in modeling

diffusion of ions in ion-exchange resins of high concentrations (3-4 M) if taking into account

the effective diffusivities [3].

The morphological structure of an ion-exchange membrane is also important in modeling the

transport process in the pore volume of the membrane. This is because any change in the

morphology, i.e. the number and size of liquid pores, can alter the effective diffusivities inside

the pores and as a result the transport process. There have been several studies on the

morphological structure of ion-exchange membranes, particularly the Nafion membrane, i.e.

core shell model proposed by Fujimura et al. [4], a sandwich-like model proposed by Haubold

et al. [5], and a rod-like model proposed by Rubatat et al. [5]. The cluster-network model

presented by Mauritz et al. [6] is one of the earliest models widely used for understanding the

properties of Nafion membranes. This model is based on small angle X-ray scattering (SAXS)

measurements and estimates the cluster network of Nafion to consist clusters with a diameter

of ~4 nm with 1 nm channels connecting the pore clusters. Also, among the early models

Yeager et al. proposed a three phase model without any strict geometry of the clusters with an

interphase between the hydrophobic and hydrophilic regions [6]. Schmidt et al. simulated

parallel water-channel models for the structure of the Nafion membrane with water channel

diameters of 1.8 nm and 3.5 nm with an average of 2.4 nm at 20 vol% water [7]. Gebel et al.

have studied the structural evolution of perfluorosulfonated ionomer membranes from dry to a

highly swollen state with small angle X-ray scattering (SAXS) measurement [8]. They

characterized the structural evolution of Nafion 115 and 117 of 1100 EW. They concluded

Chapter 3

43

that as the membrane gets hydrated and swells, the cluster sizes increase. As a result of

opening up of the pores the pore clusters connect. At even higher hydration level the authors

observed that the swelling process for water content larger than 50 % causes an inversion of

the structure from a reverse micellar structure to a connected network of polymer rod-like

particles [8]. Based on their assumption for water swollen state the cluster radii is 2 nm and it

increases to 2.09, 2.18 and 2.35 nm for the case of N-methylformamide, ethanol and

formamide, respectively [8].

The transport of ions in the membrane with the Nernst-Planck approach have been studied by

other authors as well. Verbrugge et al. [9] have developed ion and solvent transport within a

sulfuric acid/perfluorosulfonic-acid membrane. Bouzek et al. [10,11] also modeled the ion

transport inside the membrane with and without considering the convection in the diffusion

layer. They predict the ion transport in the membrane up to 2.5 kA.m-2.

It is the purpose of this work to develop a Nernst-Planck model that can describe the transport

of ions in the membrane at high current densities. It is of great interest to understand the

membrane performance in terms of voltage drop and permselectivity at high current densities,

because the membrane has the biggest contribution to the cell voltage. Thus, it is vital to

include the membrane performance in the assessment of the electrochemical cell performance

and the process economics. In this study the transport of species inside the pore volume of the

membrane is described taking into account the effective diffusivities. Also, the morphological

structure of the membrane in this study is based on the model from Schmidt et al. and Gebel

because they give an indication of the size of channel diameters in dry and hydrated states.

One difference of the approach in this study and the work of Verbrugge et al. [9] is that they

use an empirical correlation for the partition coefficient at the solution-membrane interface.

Here a general Donnan equilibrium phenomena is used to describe the boundary condition. In

the work of Bouzek et al. [10,11] the model is already assumed to be at steady-state and

therefore requires accurate initial guesses to avoid convergence errors. In this study the model

is time dependent and not sensitive to initialization. Also, Bouzek et al. use self-diffusion

coefficients estimated by others whereas here the free solution diffusivities are used to

estimate diffusivities in the membrane. This is done by evaluating the channel size and

porosity of the membrane. Additionally, the focus of this work is on the membrane

performance at high current densities.

The Nernst-Planck model is validated with experiments which are elaborated in Chapter 2

[12]. The potential drop over the membrane and the membrane selectivity are determined

from the ionic fluxes in the membrane for current densities up to 20 kA.m-2 and in a 15 wt%

sodium hydroxide solution.


44

Model approach

The Nernst-Planck equation for modeling the transport of ions in an ion-exchange membrane

for an ideal solution can be written as Eq. (3.1) [13,14].

i i i i i i i

FJ D C z DC C v

RT (3.1)

It consists of three transport terms: diffusion, electro-potential and convection. The

convection term is affected by the osmotic pressure and electro-osmotic effects and it can be

defined as Eq. (3.2) with the Schlӧgl equation [9,15]. Electroneutrality is assumed everywhere

in the membrane and at the interface of the membrane and solution (Eq. (3.3)).

( )h m md z C F P (3.2)

0i i

i

C z (3.3)

Schlӧgl has defined the hydrodynamic permeability of the membrane based on Hagen-

Poiseuille presented in Eq. (3.4) [16].

2

32

p m

h

dd

(3.4)

The Schlӧgl equation seems to be able to describe the convective velocity as a constant value

in the membrane. Additionally, the mass continuity correlation (Eq. (3.6)) is required to

complete the system of transport equations. This means that the convective velocity needs to

be defined at every position in the membrane. This is because the density changes with the

variation of concentration inside the membrane. The convective velocity is calculated based

on Eq. (3.2) at the left side of the membrane with an initial guess of the membrane voltage

drop. Then using the sodium hydroxide density correlation (Eq. (3.5)) [17] the convective

velocity is determined at every position inside the membrane. The relation between the

current density and the flux of charged species is shown in Eqs (3.7). Eq. (3.8) is derived by

combining Eqs (3.1) and (3.7) as an expression for the potential gradient. The voltage drop

from Eq. (3.8) is then iterated using an initial guess until the solution is converged.

Eq. (3.9) describes the water flux. The concentration of water inside the membrane is

calculated based on the concentration of sodium and hydroxide ions at every posit ion using

the density correlation (Eq. (3.5)). It has been shown by several authors [12,18–21] that water

is not only transported in the hydrated shell of the positive ions, but also due to convection

and the electromotive force.

Chapter 3

45

3 4 2 3 5 210 1.006 0.0011 0.172 10 0.358 10 0.214 10NaOH NaOH c cW W T T (3.5)

( ) 0v (3.6)

1

n

i i

i

I F z J

(3.7)

1 1

2

1

n n

i i i i i

i i

n

i i i

i

Iz D C v z C

F

Fz D C

RT

(3.8)

1

n

i i water water

in water

v M N M N

(3.9)

In literature, the electrical conductivity of a membrane has been defined based on Ohm’s law;

dI

dx

and using the Nernst-Planck flux equation and also by neglecting the concentration

gradient and convection [13,14,17]. This is debatable to be valid since our experimental

results [12] show that the membrane conductivity depends not only on concentration and

temperature, but also on the current density. Additionally, we show here in Appendix A that

the potential gradient is not constant and its non-linear behavior is required to have equal

fluxes at the left and right sides of the membrane at the steady-state condition. Eqs (3.1) to

(3.8) make the system of transport equations inside the membrane complete without taking

into account the water dissociation effect. Water dissociation, proton and hydroxyl ion

production due to self-ionization of water is more important in anion-exchange membranes

than in cation-exchange membranes [22–32]. Tanaka has studied the mechanism of

concentration polarization and water dissociation in the boundary layer of ion-exchange

membranes. He has shown that the water dissociation in the strong acid cation exchange

membrane is more suppressed than in the strong base anion-exchange membrane because the

forward reaction rate constant in the cation-exchange membrane is lower. In fact, due to

stronger repulsive forces between the fixed ionic groups of the cation-exchange membrane

and the co-ions the water dissociation reaction is suppressed [32]. Also, this study is at a high

concentration of the electrolyte solution which is not known to cause water dissociation.

Boundary conditions [13,33,34]:

For the boundary condition, the flux of species at the steady state should be equal at the

membrane and solution interface which is shown in Eq. (3.10) for anode interface. This is


46

similar for the cathode interface. The mass transfer at the membrane surface is assumed very

high because of the very high mixing of the electrolyte at the membrane surface which is

elaborated in our earlier paper [12]. Thus, the boundary layer thickness is calculated from the

measured mass transfer in a rotor-stator spinning disc reactor which is proved to have a very

high mass transfer coefficient [35]. The concentration jump of ionic species at the solution

and the membrane interface for both anolyte and catholyte sides are depicted in Figure 3.1.

Am,int, ,int ,int Am,int Am,int

' '

1( ) ( D )

sA s A Ai ii i i i i i i i

diff

D dC F dC C vC z D C C

d RT dx x

(3.10)

Figure 3.1. Schematic drawing of the concentration of ionic species in the bulk solution, and at the

solution and at the membrane interface for both anolyte and catholyte sides.

The concentrations at the interface are defined based on the Donnan equilibrium phenomena

which is an electrochemical equilibrium between the membrane and solution phases (Eq.

(3.11)). At steady-state in equilibrium the electrochemical potential of all ions in the

membrane and the solution are equal [13] :

m m s s

i i i iz F z F (3.11)

The Donnan potential can be expressed with Eq. (3.12):

1[ ln ( )]

sm s s mi

i Donm

i i

aRT V P P

z F a (3.12)

Here the assumption of Higa et al. [34] that the surface of the membrane is always in the state

of Donnan equilibrium with the same partition coefficient for all of the ions is used. This way

the Donnan equilibrium gives a general correlation for all ions between the membrane and the

external solution. This is shown in Eq. (3.13) in which the osmotic pressure is neglected:

Chapter 3

47

i Don

i

Fzmzi RT

s

i

Ce K

C

(3.13)

We have used the electroneutrality condition in the solution to derive a correlation (Eq. (3.14)

) that relates the solution interface concentration and the membrane interface concentration

(See appendix C).

,0 ,0

, ,,int ,0 ,int ,0

, , , ,

,0 ,0

, ,

;

ions ions

ions ions

m m

i neg i posA m A m

i pos i p

N N

i i

Nos i neg i neg

m m

i pos i n

N

i i

eg

C C

C C C C

C C

(3.14)

It is also possible to define the membrane interface concentration based on the solution

interface concentration by using the electroneutrality condition in the membrane. However, it

might require solving a quartic, quantic, etc. equations depending on the valence and the

number of ions. This makes it more complicated to be solved.

Solver:

The pdepe solver of MATLAB is used. It iterates the system of equations over time and uses

one dimensional space to obtain the solution at the steady state. The complete set of

dimensionless equations is presented in detail in Appendix B. The grid points are set in a

logarithmic scale near the boundaries due to a larger gradient of concentration and linear in

the center part.

Model assumptions:

Constant pressure and temperature are assumed. The pressure contribution in the transport

equations and Donnan equilibrium approach is neglected especially because the same

concentration of sodium hydroxide as anolyte and catholyte is being used. Solutions are

assumed to be ideal. Properties of the Nafion single layer membrane, N-1110 [36], are used.

Constitutive equations:

The initial water concentration inside the membrane is calculated based on the water uptake

for perfluorinated membrane of 1100 EW as a function of sodium hydroxide concentration.

The water uptake is presented in weight percentage of dry polymer in Eq. (3.15) [17].

3 20.0052 (0.001 ) 0.165 (0.001 ) 2.708 (0.001 ) 36.68w NaOH NaOH NaOHW C C C (3.15)

In a polymeric matrix the path length of diffusion is not a straight line. Thus, diffusion

coefficients of ionic species in free water are used and converted into effective diffusivities.

This is shown in Eq. (3.16) where the diffusivities in the polymer matrix and in the free water

are related via tortuosity [37].


48

/sDij D ij (3.16)

The dependency of tortuosity to the polymer porosity has been shown in many models in the

literature [38–41]. Here the model predicted by Marshal which was used by Wesselingh is

used to define the tortuosity as presented in Eq. (3.17) [37].

1.5 (3.17)

Eq. (3.18) defines the porosity of the membrane as the volume of pores with ion clusters

divided by the total volume.

1

e

e e ee

etot

m e

W

V ff

WV

(3.18)

We and ρe which are the weight fraction and the density of the adsorbed electrolyte is

estimated based on the water uptake of the membrane (Wo in Eq. (3.15)) and the density of the

water. fe is the fraction of electrolyte in the pores with ion cluster; it is estimated based on the

work of Yeo et al. [42] to be 0.76. This gives an estimation of the membrane porosity as a

constant parameter in the model. Also, the membrane is assumed to have stationary fixed

charges and to consist of homogenous cylindrical channels. The concentration of the

stationary fixed charges in the membrane is calculated from Eq. (3.19). It takes into account

the density and weight fraction of the adsorbed electrolyte, equivalent weight (EW); which is

defined as the weight of polymer in gram per mole of sulfonic acid groups; fraction of ionic

groups and electrolyte in the ion cluster [17,42].

1000( )e m

m

e e

fC

EW W f

(3.19)

It has been discussed in literature that a Nafion membrane swells when hydrated [4–6,8,43].

After the model simulation with constant porosity and channel diameter, the ion transport

through the membrane at high current densities is assumed to follow a similar trend as when

the hydration level increases in the membrane. Apparently, increasing the current density

results in opening up of the pore clusters and opening of the dead-end pores [6]. According to

Takahashi et al. [44], the channel size should be dependent on the relationship between the

inner stress due to the pressure inside the channel and the elasticity of the polymer matrix.

Thus, due to higher mass flux under high current density the inner stress increases and results

Chapter 3

49

in opening up of the pore channels [44]. This change in the pore size and opening of the dead-

end pores is depicted by Figure 3.2.

Here the assumption of the membrane swelling based on the work of Tiss et al. is used when

performing the sensitivity analysis of the model. They assumed that the channels are oriented

in the same direction in the membrane and are perpendicular to the membrane-liquid

interface. The membrane porosity, which is the occupied volume fraction of the membrane by

liquid, is assumed to have N number of cylindrical channels (Ntot) per cross sectional area. By

taking into account the tortuosity effect, the total porosity can be calculated with Eq. (3.20):

2tot tot

pN r (3.20)

Combining Eqs (3.17) and (3.20), the total and active porosity of the membrane are defined as

a function of the total number of pores (Ntot) and the pore radius (rp) in Eqs (3.21) and (3.22).

Figure 3.2. Simplified sketch of the membrane cross sectional area consisting of homogenous

cylindrical channels with open (active) pores and closed (inactive) pores of a (a) non-swollen

membrane and (b) swollen membrane at high current densities.

2

2 5( )tot tot

pN r (3.21)

(a)

(b)


50

2

2 5( )act act

pN r (3.22)

The transport number presented in Eq. (3.23) is the fraction of current carried by a certain ion.

It is an indication of the membrane permselectivity.

ii

J Ft

I

(3.23)

Model input parameters:

Table 3.1 presents the input parameters used in the model based on the experimental condition

and also the model assumptions. The outputs of the model are the concentration of ions in the

membrane, fluxes, the membrane voltage drop and the sodium transport number.

Table 3.1. Input parameters of the model.

Parameter Value Reference

Temperature [°C] 40

Sodium diffusivity in free water [m2.s-1] 1.33x10-9 [45]

Hydroxide diffusivity in free water [m2.s-1] 5.27x10-9 [45]

Water diffusivity in membrane [m2.s-1] 2.8x10-10 [46]

Mass transfer coefficient in solution* [m.s-1] 1x10-4

Sodium hydroxide viscosity [kg.m-1.s-1] 1.44x10-3 [17]

Dry membrane thickness [m] 2.54x10-4 [36]

Wet membrane thickness **[m] 2.7x10-4

Dry membrane density [kg.m-3] 2x103 [47]

EW [-] 1100 [36]

Membrane porosity [m3void/m

3m] 0.27 [48,49]

Sodium hydroxide concentration in both anolyte and

catholyte [wt%]

15

Membrane water content [wt. % dry polymer] Correlation [17]

/m ef f 1 [42]

*Measured in a rotor-stator spinning disc reactor [50]

** Measured with a digital caliper

Results and discussion

Figure 3.3 shows the profiles of concentration change for sodium, hydroxide and water in the

membrane over a dimensionless length of the membrane at the steady-state. The identical

concentrations in the anolyte and catholyte bulk solution are shown as straight lines followed

by the gradient in the boundary layer thickness. The concentration inside the membrane

Chapter 3

51

stands between the two vertical lines. Increasing the current density results in a lower

concentration of ions in the membrane on the anode side and a higher concentration on the

cathode side.

(a) (b)

(c)

Figure 3.3 Concentration profiles of (a) sodium ions (b) hydroxide ions and (c) water inside the N-

1110 membrane at the steady-state for current density range of 0 – 20 kA.m-2 in 15 wt% sodium

hydroxide solution as both anolyte and catholyte.

Figure 3.4 shows that the voltage drop and sodium transport numbers calculated for the model

with constant porosity and active number of pores do not fit with the measured values in the

experiment. The experiments were carried out on the mono layer Nafion N-1110 in an

identical solution of 15 wt% sodium hydroxide at 40 ºC [12]. The model shows a linear

increase of the membrane voltage drop with current density and no dependence of sodium

transport number on the current density. Since the model is unable to predict the membrane

performance as a function of current density, the membrane swelling assumption as described

in section 3.2 is used to describe the membrane behavior at high current densities.

Figure 3.5a and Figure 3.5b presents the sensitivity analysis of the model over a range of

membrane pore diameters, and active numbers of cylindrical pores at 10 kA.m-2 and 20 kA.m-

2 respectively for 2x1016 total number of pores. The total number of pores was calculated from

the properties presented in Table 3.1. It shows that for a certain total number of pores there is


52

a unique set of channel diameter and active number of pores that fits to the experimental

values of the membrane voltage drop and sodium transport number.

The optimized pore diameter and number of active pores used in the model to match the

experimental values of the voltage drop are presented in Figure 3.4. The transport number is

only fitted at the two available values of 10 kA.m-2 and 20 kA.m-2. Figure 3.4a shows how the

pore diameter increases with increasing current density. Figure 3.4b shows the opening of the

dead-end pores and activation of more cluster channels in transporting the ions though the

membrane as a function of current density. This shows that increasing the current density

results in swelling of the membrane due to an increase in channel diameter. Also, it predicts

that with an increase in the current density the number of active pores that participate in the

ion transport increases and possibly some of the dead end pores open at high current densities.

This way the model is able to give a better prediction of ion transport inside the membrane.

The proposed values of the channel diameter for a swollen membrane by others [7,8] is an

average of 20 nm for solutions other than sodium hydroxide which could be the reason of the

different obtained optimized channel diameter here. It is worth mentioning that using the

optimized channel diameters and the number of active pores at different current densities did

not change the concentration profiles of the ions and water in the membrane.

(a) (b)

Figure 3.4. Membrane (a) voltage drop and (b) sodium transport number at the steady-state and current

density range of 0.3 kA.m-2 to 20 kA.m-2 measured experimentally [12] and calculated for the base

model.

Chapter 3

53

(a) (b)

Figure 3.3. Sensitivity analysis of membrane voltage drop and sodium transport number over a range

of pore diameters (― dp, nm) and numbers of active pores (- - Nactx10-15) for a given 2Χ1016 total

number of pores. The experimental membrane voltage drop and sodium transport number (●) at (a) 10

kA.m-2 (b) 20 kA.m-2 [12].

(a) (b)

Figure 3.4. The effect of current density on the membrane swelling and opening up of (a) the pore

clusters and (b) the dead-end pores.

Conclusion

The transport of ions and water through a cation-exchange membrane has been

mathematically modeled using the Nernst-Planck equation. For a single layer Nafion N-1110

membrane, the model has been validated by fitting the membrane voltage drop and sodium

transport number at high current densities up to 20 kA.m-2. With increasing current density


54

more charged ions rush into the membrane. Therefore, the membrane conductivity increases

with current density. The qualitative swelling model can explain the behavior of the

membrane pore clusters at high current density.

We conclude that at high current densities the diameter of the pore channels is likely to

increase due to the membrane swelling. This results in a higher number of active pores

participating in transport of the ions through the membrane. It is believed that the membrane

structure i.e. channel size and porosity has a high impact on the performance of this

membrane in sodium hydroxide solution. Furthermore, it shows that there is a unique set of

pore diameters and number of active pores that satisfies the experimental sodium transport

number at a certain membrane voltage drop. This suggests that having a more in depth

knowledge of the membranes structure in a molecular level helps better understanding the ion

transport in extreme operating conditions such as high current density.

Nomenclature

Latin symbols

a Activity coefficient

A Membrane cross sectional area [m2]

C Concentration [mol.m-3]

dh Hydrodynamic permeability [kg.s.m-3]

dp Pore diameter [m]

D Diffusion coefficient [m2.s-1]

Dij Effective diffusion coefficient [m2.s-1]

f Fraction in cluster [-]


hf Hydration factor [-]

I Current density [A.m-2]

J Flux [mol.m-2.s-1]

K Donnan equilibrium constant [-]

Kanolyte Mass transfer coefficient in anolyte [m.s-1]

N Number of pore channels [-]

P Pressure [Pa]

r Radius [m]

R Gas constant [J.mol-1.K-1]

t Time [s]

ti Ion transport number [-]

T Temperature [K]

W Weight percentage [wt%]

x Length [m]

x’ Dimensionless length [-]

Chapter 3

55

V Volume [m3]

V̄ Partial molar volume [m3.mol-1]

zi Valence [-]

z Dimensionless length [-]

Greek symbols

δ Membrane thickness [m]

φ Electrical potential [V]

Δ Difference [-]

∇ Gradient [-]

κ Conductivity [ohm-1.m-1]

ρ Density [g.cm-3]

μ Chemical potential [J.mol-1]

η Dynamic viscosity [Pa.s]

ν Convective volume flux [m3.m-2.s-1]

ε Porosity [-]

τ Tortuosity [-]

<λ> Actual pore length [m]

Superscript and subscript

act active

A anode

Am Anolyte-membrane

c Centigrade

Cm Catholyte-membrane

Don Donnan

e electrolyte

i Species

int Interface

L Left

m Membrane

p pore

R Right

s Solution phase

tot total

w water


56

Bibliography

[1] F.S. Rohman, N. Aziz, Mathematical Model of Ion Transport in Electrodialysis

Process, Chem. React. Eng. Catal. 3 (2008) 3–8.

[2] S.T.P. Psaltis, T.W. Farrell, Comparing Charge Transport Predictions for a Ternary

Electrolyte Using the Maxwell–Stefan and Nernst–Planck Equations, J. Electrochem.

Soc. 158 (2011) A33.

[3] E.E. Graham, J.S. Dranoff, Application of the Stefan-Maxwell Equations to Diffusion

in Ion Exchangers. 1. Theory, Am. Chem. Soc. 21 (1982) 360–365.

[4] M. Fujimura, T. Hashimoto, H. Kawai, Small-Angle X-ray Scattering Study of

Perfluorinated Ionomer Membranes. 2. Models for Ionic Scattering Maximum, Am.

Chem. Soc. 15 (1982) 136–144.

[5] H. Haubold, T. Vad, H. Jungbluth, P. Hiller, Nano structure of NAFION : a SAXS

study, Electrochim. Acta. 46 (2001) 1559–1563.

[6] K.A. Mauritz, R.B. Moore, State of understanding of Nafion, Chem. Rev. 104 (2004)

4535–85.

[7] K. Schmidt-Rohr, Q. Chen, Parallel cylindrical water nanochannels in Nafion fuel-cell

membranes, Nat. Mater. 7 (2008) 75–83.

[8] G. Gebel, Structural evolution of water swollen perfluorosulfonated ionomers from dry

membrane to solution, Polymer (Guildf). 41 (2000) 5829–5838.

[9] M.W. Verbrugge, R.F. Hill, Ion and Solvent Transport in Ion-Exchange Membranes I.

A macrohomogeneous mathematical model, Electrochem. Soc. 137 (1990) 886–893.

[10] V. Fila, K. Bouzek, A mathematical model of multiple ion transport across an ion-

selective membrane under current load conditions, J. Appl. Electrochem. 33 (2003)

675–684.

[11] V. Fíla, K. Bouzek, The effect of convection in the external diffusion layer on the

results of a mathematical model of multiple ion transport across an ion-selective

membrane, J. Appl. Electrochem. 38 (2008) 1241–1252.

[12] S. Moshtarikhah, M.T. de Groot, J.T.F. Keurentjes, J.C. Schouten, J. van der Schaaf,

Cation-exchange membrane performance under high current density, In Prep. (2016).

Chapter 3

57


Amsterdam, 2004.

[14] T. Sata, Ion Exchange Membranes; preparation, characterization, modification and

application, The royal society of chemistry, 2004.

[15] R. Schlӧgal, Membrane Permeation in Systems far from Equilibrium, 1 (1965) 400–

414.

[16] R. Schlӧgl, Stofftransport durch membranen, 1964.



[18] T. Okada, G. Xie, O. Gorseth, S. Kjelstrup, Ion and water transport characteristics of

Nafion membranes as electrolytes, Electrochim. Actamica Acta. 43 (1998) 3741–3747.

[19] R.J. Stewart, W.F. Graydon, Ion-exchange membranes. III. Water transfer, J. Phys.

Chem. 61 (1955).

[20] C. Bourdillon, M. Demarty, E. Selegny, Transport of water in cation exchange

membranes II. Influence of polarization layers in natural convection, J. Chim. Phys. 71

(1974) 819–827.

[21] N. Lakshminarayanaiah, Electroosmosis in Ion-Exchange Membranes, J. Electrochem.

Soc. 116 (1969) 338.

[22] J.J. Krol, Monopolar and Bipolar Ion Exchange Membranes: Mass Transport

Limitations, University of Twente, 1969.

[23] G. Khedr, A. Schmitt, R. Varoqui, Electrochemical Membrane Properties in Relation to

Polarization at the Interfaces during Electrodialysis, Colloid Interface Sci. 66 (1978).

[24] Y. Fang, Q. Li, M.E. Green, Noise Spectra of Sodium and Hydrogen Ion Transport at a

Cation Membrane-Solution Interface, Colloid Interface Sci. 88 (1982) 214–220.

[25] B.A. Cooke, Concentration Polarization in Electrodialysis-I. The Electrometric

Measurment of Interfacial Concentration, Electrochim. Acta. 3 (1961) 307–317.

[26] M. Taky, G. Pourcelly, C. Gavach, Polarization phenomena at the interfaces between

an electrolyte solution and an ion exchange membrane Part II . Ion transfer with an

anion exchange membrane, Electroanal. Chem. 336 (1992) 195–212.


58

[27] T. Yamabe, M. Seno, The concentration polarization effect in ion exchange membrane

electrodialysis, Desalination. 2 (1967) 148–153.

[28] R. Simons, The origin and elimination of water splitting in ion exchange membranes

during water demineralisation by electrodialysis, Desalination. 28 (1979) 41–42.

[29] I. Rubinsten, L. Shtilman, Voltage against Current Curves of Cation Exchange

Membranes, Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 75 (1978) 231–246.

[30] N.W. Rosenberg, C.E. Tirrell, limiting Currents in Membrane Cells, Ind. Eng. Chem.

49 (1957) 780–784.

[31] M. Block, J.A. Kitchener, Polarization Phenomena in Commercial Ion-Exchange

Membranes, Electrochem. Soc. 113 (1966) 947–953.

[32] Y. Tanaka, Mass transport in a boundary layer and in an ion exchange membrane:

Mechanism of concentration polarization and water dissociation, Russ. J. Electrochem.

48 (2012) 665–681.

[33] P.C. Ho, D.A. Palmer, Electrical conductivity measurements of aqueous electrolyte

solutions at high temperatures and high pressures, in: 12. Int. Conf. Prop. Water Steam,

1995.

[34] M. Higa, A. Tanioka, K. Miyasaka, Simulation of the transport of ions against their

concentration gradient across charged membranes, J. Memb. Sci. 37 (1988) 251–266.

[35] M. Meeuwse, Rotor-Stator Spinning Disc Reactor, Eindhoven University of

Technology, 2011.

[36] P. Majsztrik, A. Bocarsly, J. Benziger, Water permeation through Nafion membranes :

The role of water activity, Phys. Chem. 112 (2008) 16280–16289.

[37] J.A. Wesselingh, P. Vonk, G. Kraaijeveld, Exploring the Maxwell-Stefan description

of ion exchange, Chem. Eng. 57 (1995) 75–89.

[38] T.J. Marshal, Permeability and the Size Distribution of Pores, Nature. 180 (1957) 664–

665.

[39] R.J. Millington, Gas Diffusion in Porous Media, Science. 130 (1959) 100–102.

[40] H.L. Weissberg, Effective Diffusion Coefficient in Porous Media, J. Appl. Phys. 34

(1963) 2636.

Chapter 3

59

[41] G.H. Neale, W.K. Nader, Prediction of Transport Processes within Porous Media:

Diffusive Flow Processes within an Homogeneous Swarm of Spherical Particles,

AIChE J. 19 (1973) 112–119.

[42] R.S. Yeo, Ion Clustering and Proton Transport in Nafion Membranes and Its

Applications as Solid Polymer Electrolyte, J. Electrochem. Soc. 130 (1983) 533–538.

[43] N.P. Berezina, N.A. Kononenko, O.A. Dyomina, N.P. Gnusin, Characterization of ion-

exchange membrane materials: properties vs structure., Adv. Colloid Interface Sci. 139

(2008) 3–28.



Ltd, London, 2001.

[45] E. Samson, J. Marchand, K.A. Snyder, Calculation of ionic diffusion coefficients on

the basis of migration test results, Mater. Struct. 36 (2003) 156–165.

[46] G. Suresh, Y. Scindia, A. Pandey, A. Goswami, Self-diffusion coefficient of water in

Nafion-117 membrane with different monovalent counterions: a radiotracer study, J.

Memb. Sci. 250 (2005) 39–45.

[47] DuPont Fuel Cells, Technical information, n.d.

[48] F. Tiss, R. Chouikh, A. Guizani, A numerical investigation of the effects of membrane

swelling in polymer electrolyte fuel cells, Energy Convers. Manag. 67 (2013) 318–324.

[49] P.H. Chi, S.H. Chan, F.B. Weng, A. Su, P.C. Sui, N. Djilali, On the effects of non-

uniform property distribution due to compression in the gas diffusion layer of a

PEMFC, Int. J. Hydrogen Energy. 35 (2010) 2936–2948.

[50] P. Granados Mendoza, Liquid solid mass transfer to a rotating mesh electrode, Heat

Mass Transf. Submitt. (2016).


60

Appendix A. Non-linear potential gradient

The electroneutrality condition (A3.1) should hold in the membrane. Moreover,

electroneutrality should be valid on either side of the membrane as well, Eq. (A3.2).

Furthermore, because the fixed group concentration is constant in the membrane, the

summation of diffusional flux of positive charges equals the summation of diffusional flux of

negative charges (A3.3). This means that the total summation of diffusional fluxes is zero

(A3.4).

1

0n

i i m m

i

z C z C

(A3.1)

1 1

( ) ( )n n

L R

i i i i

i i

z C z C

(A3.2)

1 1

L Rn n

i i i i i i

i i

z D C z D C

(A3.3)

1

0n

i i i

i

z D C

(A3.4)

Also, the flux on right and left sides of the membrane should be equal at steady-state (A3.5).

Eq. (A3.6) is derived by writing the flux equations for the left and right sides and using Eq.

(3.7). The convective term is neglected in the flux equations.

L R

i iJ J (A3.5)

2 2

1 1 1 1

( ) ( )n n n n

L R

i i i i i i i i i i i i

i i i i

I F Fz D C z D C z D C z D C

F RT RT

(A3.6)

By omitting the diffusional term (based on Eq. (A3.3)) Eq. (A3.7) is derived after a few

rearrangements and assuming that the potential gradient is constant Eq. (A3.7) contradicts

from electroneutrality condition (A3.2).

2 2

1 1i i

L Rn n

i i i i

i i

z D C z D C

(A3.7)

Chapter 3

61

Appendix B. Transport equations

The material balance is needed (B3.1) to describe the transport of ions due to diffusion,

electro-migration and convection inside the membrane. As explained, these three transport

terms are described with the Nernst-Planck equation. Eq. (B3.1) can be made dimensionless

by substituting Eq. (B3.2) in Eq. (B3.1).

ii

dCJ

dt (B3.1)

xz

(B3.2)

( )( )

1( )i

i i i ii

i

dC F dD z DC C

d RT

dC d

dt d z z dz

(B3.3)

hm mC

dv z F P

(B3.4)

1 1

2

1

n n

i i i i i

i i

n

i i i

i

Iz D C v z C

d F

Fdz D C

RT

z

(B3.5)

Appendix C: Donnan equilibrium at the interface

Derivation of the solution interface concentration as a function of the membrane

interface concentration:

Recalling the Donnan equilibrium in which the osmotic contribution is neglected, Eq. (3.13),

one can obtain (C3.1) and (C3.2) for the positive and negative species, respectively.

,int

, , .1A M

i pos i posC CK

(C3.1)

,int

, , .A M

i neg i negC C K (C3.2)

By combining the electroneutrality in the solution with (C3.1) and (C3.2), (C3.3) is obtained.

After rearrangement of Eq. (C3.3), an expression for Donnan constant K is presented in

(C3.4).


62

, ,

1. .

ions ions

M M

i pos i ne

i

g

N N

i

C KCK (C3.3)

,

,

ions

ions

M

i pos

M

i

i

N

neg

N

i

K

C

C

(C3.4)

Substitution of (C3.4) in (C3.1) and (C3.2) results in (C3.5) and (C3.6), respectively. For a

system of only sodium and hydroxide, (C3.5) and (C3.6) reduce to (C3.7).

,,int

, ,

,

ions

ions

M

i negA M

i p

N

i

N

i

os i pos

M

i pos

C

C C

C

(C3.5)

,,int

, ,

,

ions

ions

M

i posA M

i n

N

i

N

i

eg i neg

M

i neg

C

C C

C

(C3.6)

,int .A M M

Na Na OHC C C (C3.7)

Derivation of the membrane interface molality as a function of the solution interface

molality:

From Eq. (3.13), (C3.8) and (C3.9) is obtained for the positive and negative species,

respectively.

,int

, , .M A

i pos i posC C K (C3.8)

,int

, ,

1.M A

i neg i negC CK

(C3.9)

By combining the electroneutrality in the membrane with (C3.8) and (C3.9), (C3.10) is

derived. After rearrangement of (C3.10), a quadratic expression for K is obtained, see (C3.11)

. This quadratic expression can be solved resulting in (C3.12).

Chapter 3

63

,int ,int

, ,

1. .

ion ion

A A

i pos m i neg

N N

i i

C K CK

C (C3.10)

,int ,int2

, , 0.ion ion

A A

i pos m i neg

N N

i i

C KC CK (C3.11)

,int ,int

, ,

,in

2

t

,2

4ion ion

ion

A A

m m i pos i neg

A

i pos

N N

i i

N

i

C C C C

C

K

(C3.12)

Substitution of (C3.12) in (C3.8) and (C3.9) results in (C3.13) and (C3.14), respectively. For

a system of only sodium and hydroxide, (C3.13) reduces to (C3.15).

,int ,int

, ,

,int

, ,

,int

,

2 4

2

ion ion

ion

N NA A

m m i pos i neg

M A

i pos i pos

A

i po

i i

i

s

N

C C C C

C C

C

(C3.13)

2

,int

,,int

, ,

,int ,int

, ,

2

4

ion

ion ion

A

i posM A

i neg i neg

A A

m m i pos

N

i

N N

i i

i neg

C

C C

C C C C

(C3.14)

22

,int4

2

A

m m NaM

Na

C C CC

(C3.15)

Prove that (C3.7) and (C3.15) are equal:

Substitution of the electroneutrality condition in the membrane in (C3.15), (C3.7) is obtained

with (C3.16) as an intermediate result.

2

,intA M M

mNa Na NaC C C C (C3.16)

Multicomponent ion transport in a

mono and bilayer cation-exchange

membrane at high current density

Abstract

This chapter describes a model for bilayer cation-exchange membranes used in the chlor-

alkali process. The ion transport inside the membrane is modeled with the Nernst-Planck

equation. A logistic function is used at the boundary between the two layers of the bilayer

membrane to describe the change in the properties of each membrane layer. The local

convective velocity is calculated inside the membrane using the Schlӧgl equation and the

equation of continuity. The model calculates the ion concentration profiles inside the

membrane layers. Modeling results of mono- and bilaye membranes are compared. The

changes in membrane voltage drop and sodium selectivity are predicted. The concentration

profile of sodium ions in the bilayer membrane is significantly different from the mono layer

membrane. Without applied current a linear change in the sodium concentration is observed in

the mono layer membrane, and in each layer of the bilayer membrane. With an increase in

current density the stronger electromotive force in the carboxylate layer causes a decrease in

the sodium concentration in the sulfonate layer, down to the fixed ionic group concentration.

This significant decrease of sodium ion concentration in the sulfonate layer results in low

concentrations of counter ions and as a consequence a higher permselectivity of the bilayer

membrane is obtained when compared to the single layer membrane. As a drawback, the

resistance in the bilayer membrane increases.

4

Comparison of multicomponent ion transport in a mono and bilayer cation-exchange

66

Introduction

Bilayer cation-exchange membranes have a wide range of applications in current industrial

applications than mono layer membranes. The focus of this work is on the membranes used in

the chlor-alkali process in which sodium chloride and sodium hydroxide are used as the

anolyte and catholyte solutions respectively. Perfluorinated membranes have been modified to

increase the permselectivity of the membrane and the overall current efficiency of the process.

The replacement of mono layer by bilayer membranes in the chlor-alkali process increased the

current efficiency from 85 % to 97 % [1]. Bilayer cation-exchange membranes are made by

modifying the catholyte side of the membrane or adding an extra layer to that side. In the

chlor-alkali technology the extra layer on the cathode side is either a sulfonate layer with a

different equivalent weight or a carboxylate layer. The carboxylate layer typically has a lower

conductivity compared to the sulfonate layer, and it has a lower water content. The bilayer

membrane is made either by laminating or co-extrusion [1].

In spite of a number of literature studies on the structure of cation-exchange membranes [2–

7], there have been few studies looking into the structure and performance of bilayer

membranes individually [8–10]. Also, virtually no data exists in the literature that compares

the performance of mono and bilayer cation-selective membranes especially at high current

densities. There are various methods to model ion transport in ion-exchange membranes, and

these have been reviewed and modeled by several authors [11–13]. In our earlier paper [14]

we developed a Nernst-Planck model of multicomponent ion transport through a cation-

exchange membrane for a mono layer membrane. The model was validated with experiments

using same electrolyte solutions with identical anolyte and catholyte concentrations. In this

paper, the ion transport in the mono and bilayer membranes is compared using the Nernst-

Planck equation. The bilayer membrane is assumed to be with the sulfonic/carboxylic

polymers.

The concentration profiles of the charged species and water in the boundary layer and inside

the mono and bilayer membranes are calculated by solving the Nernst-Planck equation. The

concentration profiles of the ions and water are compared. The potential drop over the

membrane and the membrane permselectivity are determined for current densities up to 20

kA.m-2.

Model approach and assumptions

To model the ion transport inside the membrane a one dimensional Nernst-Planck equation is

used for both mono and bilayer membranes. The molar flux density in each layer of the

membrane is defined with Eq. (4.1). The current density is an important parameter when

investigating high current density operation. It is directly related to the flux of charged species

Chapter 4

67

as presented in Eq. (4.2). The convective velocity is described using the Schlӧgl equation (Eq.

(4.3)) The mass continuity should hold which is presented by Eq. (4.4). The local electrolyte

composition inside the membrane changes, which results in a change of density locally in the

membrane. The mixture density (Eq. (4.5)) is used to calculate the local density of the

electrolyte in the membrane [1]. The local electrolyte concentration in the membrane is

calculated based on the estimation method used by Bouzek et al. [15]. The local voltage drop

is calculated from Eq. (4.6), which is derived from Eq. (4.2). Eq. (4.7) describes the material

balance to solve the system of Eqs (4.1) to (4.6).

i i i i i i i

FJ D C z DC C v

RT (4.1)

1

n

i i

i

I F z J

(4.2)

( )h m md z C F P (4.3)

( ) 0v (4.4)

3 4 2 3 5 210 1.006 0.001 0.17 10 0.35 10 0.21 10 0.007NaOH NaOH c c NaClW W T T W (4.5)

1 1

2

1

n n

i i i i i

i i

n

i i i

i

Iz D C v z C

F

Fz D C

RT

(4.6)

ii

dCJ

dt (4.7)

A logistic function is implemented for describing the change in properties of the membrane

from the anolyte side layer to the catholyte side layer. This is to avoid a discontinuity when

solving the partial differential equations with MATLAB. The general logistic function is

shown in Eq. (4.8) in which A and B are the lower and upper asymptote values respectively, k

defines the slope of the curve and x0 is the midpoint of the curve.

0k(x x )( )

1

B Af x A

e

(4.8)


68

The fixed ionic group concentration is the property that changes most significantly between

the two layers of the membrane. The concentration of fixed ionic groups is defined with Eq.

(4.9). In this equation the electrolyte uptake and the equivalent weight of each layer in the

membrane are different. The electrolyte uptake is assumed to be equal to the water uptake of

each layer and is calculated based on Eqs (4.10) and (4.11) for the sulfonated and

carboxylated layers, respectively [1].

1000( )e m

m

e e

fC

EW W f

(4.9)

3 20.0052 (0.001 ) 0.1655 (0.001 ) 2.7085 (0.001 ) 36.682s

e e e eW C C C (4.10)

3 20.0033 (0.001 ) 0.1157 (0.001 ) 1.7809 (0.001 ) 18.618c

e e e eW C C C (4.11)

The fixed ionic group concentration is defined with the logistic function as presented in Eq.

(4.12) in which x0 is zero and the slope of the curve is chosen 120. The slope of the curve

defined the thickness of the transition state in the logistic function. It is 11% of the total grid

length which is calculated based on 5% and 95 % of the lower and upper asymptote values

respectively. The schematic of the logistic function for the fixed ionic group concentration

inside the membrane is shown in Figure 4.1.

0k(x x )

( )(x)

(1 )

c ss m m

m m

C CC C

e

(4.12)

Figure 4.1. Schematic of the logistic function expressing the fixed ionic group concentration in the

bilayer membrane. Cms and Cm

c are the fixed ionic group concentrations in the sulfonate and the

carboxylate layers, respectively. X0 is the midpoint of the curve which is the transition point between

the sulfonate and the carboxylate layers.

Chapter 4

69

The boundary conditions at the membrane-solution interface are summarized in Eqs (4.13)

and (4.14) [14]:

Am,int,e ,int ,int Am,i

'

nt Am,int

'

1( ) ( D )

eA A Ai ii i i i i i i i

diff

D dC F dC C vC z DC C

d RT dx x

(4.13)

,0 ,0

, ,,int ,0 ,int ,0

, , , ,

,0 ,0

, ,

;

ions ions

ions ions

m m

i neg i posAm m Am m

i pos i pos i neg i neg

m m

i pos i ne

N N

i i

N N

g

i i

C C

C C C C

C C

(4.14)

Constant pressure and temperature are assumed. Electrolyte solutions are assumed to be ideal.

The electrolytes are sodium chloride as anolyte and sodium hydroxide as catholyte. A very

high mass transfer at the membrane is assumed to avoid steep concentration gradients in the

boundary layers. The spinning disc technology which works based on high-shear forces

induced with high velocity gradient or high-gravity situations has proven [16–19] to have

high mass transfer rate from the gas phase to the liquid film and from the liquid film to the

solid phase. For this, the thickness of the diffusion layer is calculated based on the assumption

of having a high mass transfer rate in the spinning disc reactor [19,20]. For a proper bi-layer

model, reliable data for diffusivities of each membrane layer are required. However, in the

literature there is not enough data on diffusivities of all sodium, hydroxide and chloride ions

in the sulfonate and carboxylate layers [9,10,21]. The sodium self-diffusion coefficient in both

sulfonate and carboxylate membranes has been reported in a sodium chloride and sodium

hydroxide solution by Ames [21]. He reported the sodium self-diffusion coefficient to be one

order of magnitude higher in the sulfonate layer in both sodium chloride and sodium

hydroxide solutions [8,9]. On the other hand, Yeager et al. and Twardowski et al. have

measured a slightly higher sodium diffusion coefficient in the sulfonate compared to the

carboxylate membranes in sodium chloride solution [8,21]. For sake of simplicity, here the

self-diffusivities are assumed to be equal in both layers. The diffusivities are calculated based

on the temperature dependent diffusivity in free water [22]. The calculation of the diffusion

coefficients inside the membrane taking into account the effect of tortuosity and porosity,

together with the calculation of the total porosity of the membrane has been elaborated in our

previous paper [1,14,23]. The membrane permselectivity as represented by the sodium

transport number is calculated from the ionic fluxes:

ii

J Ft

I

(4.15)


70

Modeling conditions and membrane properties

Table 4.1 presents the general operating conditions and the membrane characteristics in both

mono and bilayer membranes. Table 4.2 presents the properties of each membrane layer in the

bilayer membrane. The equivalent weights and thickness of each layer is estimated based on

the available data for Nafion 954 as an example of a sulfonate/carboxylate bilayer membrane

[24].

Table 4.1. General modelling conditions for both mono and bilayer membranes.



Pressure [atm] 1

Sodium hydroxide [wt%] 32 [1]

Sodium chloride [wt%] 24 [1]

Sodium diffusivity in free water [m2.s-1] Correlation [22]

Hydroxide diffusivity in free water [m2.s-1] Correlation [22,25]

Chloride diffusivity in free water [m2.s-1] Correlation [22]

Water diffusivity in membrane [m2.s-1] Correlation [22]

Mass transfer coefficient in solution [m.s-1] 1x10-4 [26]

Diffusion layer thickness [m] 8.3x10-6 [26]

Viscosity in the membrane [kg.m-1.s-1] Correlation [1]

Total wet membrane thickness *[m] 2.4x10-4



3m] 0.27 [14,28,29]

/m ef f 1 [23]

x0 (midpoint of the logistic curve) 0

k (slope of the logistic function) 120

* Measured with a digital caliper after equilibration in sodium hydroxide solution

Table 4.2. Characteristics of sulfonic and carboxylate layers in the bilayer membrane.

Parameter Sulfonate Carboxylate Reference

EW [-] 1080 1050 [24]

Water content [wt. % dry polymer] Eq. (4.10) Eq. (4.11) [1]

Fixed ionic group concentration [M] 3.36 7.4 Eq. (4.9)

Thickness of layers [m] 1.54 x10-4 0.86 x10-4 [24]

Solution strategy

The convective velocity defined by the Schlӧgl equation (Eq. (4.3)) is position dependent

inside the membrane, and is calculated with the continuity equation (Eq. (4.4)). At first, an

Chapter 4

71

initial guess is required for the total potential gradient over the membrane, and the resulting

convective velocity at the anolyte side of the membrane is calculated with this total potential

gradient by Eq. (4.3). The local concentration of the species determines the local density

inside the membrane. The local convective velocity is calculated with the local density and

the equation of continuity (Eq. (4.4)). This is to avoid the violation of the continuity equation.

The general material balance (Eq. (4.7)) for the ions is then solved using the pdepe solver in

MATLAB. By iterating the model over time, new values of the convective velocity at the

anolyte side and the potential gradient are recalculated for each time step. The iteration

continues until a steady-state is achieved.


4.3.1 Concentration profiles inside the membrane

The concentration profiles of the ionic species and water are shown in Figure 4.2 to Figure

4.5. Each figure is divided into anolyte and catholyte bulk solutions, boundary layers and

membrane layers; regions I and VI present the concentration of the electrolyte solutions in the

anode and cathode compartments, respectively. Regions II and V show the concentration

profiles in the anolyte and catholyte boundary layers at different current densities. Region III

presents the sulfonate layer of the membrane and region IV presents the carboxylate layer of

the membrane. The concentrations of ions and water are assumed constant in the electrolyte

bulk solutions. The concentration of the ionic charged species in the boundary layers (regions

I and VI) change linearly. The slope slightly increases with increasing current density. This

could be explained by the convective flux in the boundary layers. Having a stronger

convective flow in the anolyte results in build-up of ion concentration higher than what can be

transferred through the membrane. The counter effect occurs at the catholyte side.

As presented in regions III and IV in Figure 4.2a-b the concentration inside the membrane

shows an enormous difference between the mono and bilayer membrane for sodium ions. In

the monolayer membrane the concentration increases monotonically between the anolyte and

catholyte boundaries. With an increase in current density the concentration profile becomes

more curved. In the bilayer membrane there is a linear concentration gradient in regions III

and IV when no current is applied. As the current density increases the concentration gradient

in region IV becomes steeper, and the sodium ion concentration in region III decreases. At a

very high current density (20 kA.m-2) a concave plateau is observed in region III which shows

that the concentration of sodium ions in this region reaches the limit of the fixed ionic group

concentration.

Regions III and IV in Figure 4.3a-b present the hydroxide ion concentration inside the mono

and bilayer membranes. In the mono layer membrane the concentration decreases linearly

from the catholyte to the anolyte boundary and with increasing current density the


72

concentration profiles become more curved closer to the anolyte boundary. In the bilayer

membrane the concentration gradient is linear in regions III and IV with a steeper change at

the interface between the layers. The concentration gradient becomes steeper and more curved

in the carboxylate layer with increasing current density, and the concentration profile in

region III becomes convex and reaches a plateau value of virtually zero in the membrane with

increasing the current density up to 20 kA.m-2. The chloride ion concentration inside the

membrane is presented in regions III and IV of Figure 4.4a-b. It shows a similar trend of

concentration change in both mono and bilayer membranes. As the current density increases a

very sharp decrease is observed in chloride ion concentration. The water concentration profile

inside the membrane is shown in regions III and IV of Figure 4.5a-b. The water concentration

is calculated based on the local concentration of the other ions inside the membrane. A

decrease in water concentration is observed in the monolayer membrane which is the opposite

of the sodium ion concentration. In region IV of the bilayer membrane a steep decrease in

water concentration is observed with increasing the current density, however, a maximum

plateau is observed in region III in which the sodium ion concentration is very low and close

to the fixed ionic group concentration.

(a) (b)

Figure 4.2. Sodium ion concentration profile over the solution and the membrane. The position is

made dimensionless to only demonstrate different regions: I. Anolyte bulk solution II. Anolyte

boundary layer thickness III. Sulfonate layer IV. Carboxylate layer V. Catholyte boundary layer

thickness V. Catholyte bulk solution for a (a) mono layer (b) bilayer membrane for a current density

range of 0 to 20 kA.m-2. At T=80 ºC, 24 wt% sodium chloride, 32 wt% sodium hydroxide. Cs and Cc

are the fixed ionic group concentrations of the sulfonate and the carboxylate layers, respectively.

Chapter 4

73

(a) (b)

Figure 4.3. Hydroxide ion concentration profile over the solution and the membrane. The position is




range of 0 to 20 kA.m-2. At T=80 ºC, 24 wt% sodium chloride, 32 wt% sodium hydroxide.

(a) (b)

Figure 4.4. Chloride ion concentration profile over the solution and the membrane. The position is




range of 0 to 20 kA.m-2. At T=80 ºC, 24 wt% sodium chloride, 32 wt% sodium hydroxide.


74

(a) (b)

Figure 4.5. Water concentration profile over the solution and the membrane. The position is made

dimensionless to only demonstrate different regions: I. Anolyte bulk solution II. Anolyte boundary

layer thickness III. Sulfonate layer IV. Carboxylate layer V. Catholyte boundary layer thickness V.

Catholyte bulk solution for a (a) mono layer (b) bilayer membrane for a current density range of 0 to

20 kA.m-2. At T=80 ºC, 24 wt% sodium chloride, 32 wt% sodium hydroxide.

4.3.1 Membrane voltage drop and permselectivity

The membrane voltage drop and permselectivity are the most important parameters for

determination of the membrane performance and current efficiency of the process. They have

been calculated up to 20 kA.m-2 current density. Figure 4.6 presents the effect of current

density on the membrane voltage drop and the sodium selectivity for the mono and bilayer

membranes. Figure 4.6a shows that in both the mono and bilayer membranes the voltage drop

increases when increasing the current density. Additionally, it shows that the membrane

voltage drop is higher for the bilayer membrane compared to the mono layer membrane. The

sodium transport number is presented in Figure 4.6b. In the bilayer membrane the sodium

transport number decreases up to 3 kA.m-2 and then increases. There is a general increasing

trend of sodium transport number for both mono and bilayer membranes with increasing the

current density, however, it is higher in the bilayer membrane.

Chapter 4

75

(a) (b)

Figure 4.6. (a) Membrane voltage drop (b) Sodium transport number over a current density range of 2

to 20 kA.m-2 for a mono and bilayer membrane. At T=80 ºC, 24 wt% sodium chloride and 32 wt%

sodium hydroxide.

Discussion

The calculated concentration profiles in mono and bilayer membranes show a large difference

in the ion transport between the mono and bilayer membranes. A lower concentration region

in the sulfonate layer is caused because with increasing current density a strong electromotive

force in the carboxylate layer dominates the electromotive force in the sulfonate layer.

Consequently, the carboxylate layer pulls the ions from the sulfonate layer and reduces the

concentration in the sulfonate layer. This way, the diffusive transport in the sulfonate layer

increases and compensates for the lower electromotive force. The reduction in sodium

concentration between the sulfonate and carboxylate membrane was explained by Takahashi

et al. [30]. They used a three compartment cell: a first compartment with anolyte separated

with a sulfonate membrane from a second compartment, which is separated with a

carboxylate membrane from a third compartment that contains the catholyte. The second

compartment was used to represent the interface between a sulfonate and a carboxylate layer

in a bilayer membrane. It was shown that the steady state concentration in the second

compartment was significantly lower than the concentration in the first compartment. The

current efficiency decreased with decreasing concentration in the second compartment. In our

modeling work we observe that with increasing current density the sodium concentration in

the sulfonate layer decreases to the concentration of fixed ionic groups which is in line with

the work presented by Takahashi et al. This suggests that at very high current density the

fixed ionic groups and the sodium counter ions balance each other and as a consequence the

presence of hydroxide and chloride ions decreases in the sulfonate layer. This results in higher

sodium selectivity of the bilayer membrane, and unfortunately also an increase in the

membrane resistance. In addition, the sharp decrease of the hydroxide ions in the carboxylate

layer confirms that the carboxylate layer at the cathode side prevents the back transport of


76

hydroxide ions in the bilayer membrane especially at high current densities. This results in

higher sodium selectivity of the bilayer membrane compared to the mono layer membrane.

Furthermore, a steep decrease of the chloride ion concentration at high current densities

makes the contribution of transport of chloride ions inside the membrane lower compared to

the other ions. The increase of sodium selectivity with increasing current density is not in line

with the observed decreasing trend in chapter 2 [14] in a system with identical sodium

hydroxide solution as both anolyte and catholyte. However, it is in line with the observed

increasing trend of selectivity in the chlor-alkali experiment carried out in the spinning disc

membrane electrolyzer explained in our paper elsewhere [31]. The low concentration of water

in the carboxylate layer helps the prevention of hydroxide back transport. The high

concentration of water in the sulfonate layer with increasing current density should decrease

the membrane resistance, however, a decrease of the sodium ion concentration in the

sulfonate layer below the anolyte concentration has a higher effect on increasing the overall

bilayer membrane resistance.

Conclusion

Multicomponent ion transport in mono and bilayer cation-exchange membranes has been

compared. The concentration profiles of ions inside the membrane show how the extra layer

at the catholyte side with a higher electromotive force draws sodium ions from the sulfonate

layer. This increases the membrane efficiency in terms of selectivity by decreasing the back

transport of hydroxide ions to the anolyte side especially at a high current density of 20 kA.m-

2, at which the hydroxide concentration in the sulfonate layer is virtually zero. Also, the

membrane voltage drop in the bilayer membrane is higher than the mono layer membrane

because of the lower sodium concentration. In conclusion, it is shown that the extra

carboxylate layer at the cathode side improves the efficiency of the bilayer membranes

compared to the mono layer membranes. The slightly increase and decrease in concentration

of sodium ions at the anolyte and catholyte boundary layers is unexpected.

Nomenclature

Latin symbols

A Membrane cross sectional area [m2]

C Concentration [mol.m-3]

dh Hydrodynamic permeability [kg.s.m-3]

D Diffusion coefficient [m2.s-1]

f Fraction in cluster [-]


I Current density [A.m-2]

J Flux [mol.m-2.s-1]

Chapter 4

77

P Pressure [Pa]

R Gas constant [J.mol-1.K-1]

t Time [s]

ti Ion transport number [-]

T Temperature [K]

Tc Temperature [C]

V Volume [m3]

V̄ Partial molar volume [m3.mol-1]

W Weight fraction [%]

We Weight fraction of adsorbed electrolyte [%]

Wes Weight fraction of adsorbed electrolyte in sulfonate layer [%]

Wec Weight fraction of adsorbed electrolyte in carboxylate layer[%]

x’ Dimensionless lenght [-]

z Valence [-]

Greek symbols



Δ Difference [-]

∇ Gradient [-]

ρ Density [g.cm-3]


ε Porosity [-]

Superscript and subscript

A Anolyte

Am Anolyte/membrane

c Carboxylate

diff Diffusion layer

e Electrolyte

i Species

int Interface

m Membrane fixed group

m,0 Membrane interface

s Sulfonate


78

Bibliography



[2] K.A. Mauritz, R.B. Moore, State of understanding of Nafion, Chem. Rev. 104 (2004)

4535–85.

[3] G. Gebel, Structural evolution of water swollen perfluorosulfonated ionomers from dry

membrane to solution, Polymer (Guildf). 41 (2000) 5829–5838.

[4] K. Schmidt-Rohr, Q. Chen, Parallel cylindrical water nanochannels in Nafion fuel-cell

membranes, Nat. Mater. 7 (2008) 75–83.

[5] M. Fujimura, T. Hashimoto, H. Kawai, Small-Angle X-ray Scattering Study of

Perfluorinated Ionomer Membranes. 2. Models for Ionic Scattering Maximum, Am.

Chem. Soc. 15 (1982) 136–144.

[6] H. Haubold, T. Vad, H. Jungbluth, P. Hiller, Nano structure of NAFION : a SAXS

study, Electrochim. Acta. 46 (2001) 1559–1563.

[7] L. Rubatat, A.L. Rollet, O. Diat, Evidence of Elongated Polymeric Aggregates in

Nafion, Am. Chem. Soc. (2002) 4050–4055.

[8] Z. Twardowski, H.L. Yeager, B.O. Dell, A comparison of perfluorinated carboxylate

and sulfonate ion exchnage polymers: ll. Sorption and transport properties in

concentrated solution environments, Electrochem. Soc. 129 (1982) 328–332.

[9] H.L. Yeager, Z. Twardowski, L.M. Clarke, A Comparison of Perfluorinated

Carboxylate and Sulfonate Ion Exchange Polymers I. Diffusion and water sorption,

Electrochem. Soc. (1982) 324–327.

[10] P.N. Pintauro, D.N. Bennlon, Mass Transport of Electrolytes in Membranes. 2.

Determination of NaCl Equilibrium and Transport Parameters for Nafion, Ind. Eng.

Chem. Fundam. 23 (1984) 234–243.

[11] F.S. Rohman, N. Aziz, Mathematical Model of Ion Transport in Electrodialysis

Process, Chem. React. Eng. Catal. 3 (2008) 3–8.



Soc. 158 (2011) A33.

Chapter 4

79



[14] S. Moshtarikhah, N.A.W. Oppers, M.T. de Groot, J.T.F. Keurentjes, J.C. Schouten, J.

van der Schaaf, Nernst-Planck modeling of multicomponent ion transport in a Nafion

membrane at high current density, In Prep. (2016).

[15] V. Fíla, K. Bouzek, The effect of convection in the external diffusion layer on the

results of a mathematical model of multiple ion transport across an ion-selective

membrane, J. Appl. Electrochem. 38 (2008) 1241–1252.



[17] R.J. Jachuck, C. Ramshaw, K. Boodhoo, J.C. Dalgleish, Process intensification: the

opportunity presented by spinning disc reactor technology, in: ICHEME, 1997: pp.

417–424.


CHP. 13 (1993) 493–513.

[19] M. Meeuwse, Rotor-Stator Spinning Disc Reactor, Eindhoven University of

Technology, 2011.



[21] R.L. Ames, Nitric Acid Dehydration Using Perfluoro Carboxylate and Mixed Sulfonate

/ Carboxylate Membranes, University of California, 2004.

[22] T. Baştuğ, S. Kuyucak, Temperature dependence of the transport coefficients of ions

from molecular dynamics simulations, Chem. Phys. Lett. 408 (2005) 84–88.

[23] R.S. Yeo, Ion Clustering and Proton Transport in Nafion Membranes and Its

Applications as Solid Polymer Electrolyte, J. Electrochem. Soc. 130 (1983) 533–538.

[24] W. Grot, Fluorinated Ionomers, William Andrew, Oxford, 2011.

[25] E. Samson, J. Marchand, K.A. Snyder, Calculation of ionic diffusion coefficients on

the basis of migration test results, Mater. Struct. 36 (2003) 156–165.




80









Ltd, London, 2001.

[31] P. Granados Mendoza, S. Moshtarikhah, M.T. de Groot, J.T.F. Keurentjes, J.C.

Schouten, J. van der Schaaf, Intensification of the chlor-alkali process by using a

spinning disc membrane electrolyzer, In Prep. (2016).

Chapter 4

81

Appendix

The effect of temperature on membrane performance is investigated as well. Operating at

higher temperatures is desirable in the chlor-alkali process because the conductivity of the

solution and the membrane increases with temperature. Finally, the model is used to

investigate the possibility of producing of highly concentrated sodium hydroxide (~ 50 wt%)

directly, thereby eliminating the step of sodium hydroxide processing.

Temperature effect

The effect of temperature on the membrane voltage drop and sodium permselectivity are

presented in Figure A4.7. Figure A4.7a shows that increase in temperature results in lower

membrane voltage drop for both mono and bilayer membranes. This is because at higher

temperature the ion mobility increases inside the membrane. It is observed that the bilayer

membrane has a steeper decreasing trend with increasing temperature compared to the mono

layer membrane. The sodium transport number presented in Figure A4.7b does not seem to

depend on the temperature. It shows that at the operating temperature of T= 80 ºC the bilayer

membrane has a maximum selectivity (~1) and the mono layer membrane selectivity is 0.73.

(a) (b)

Figure A4.7. (a) Membrane voltage drop (b) Sodium transport number over a temperature range of 10

ºC to 80 ºC for a mono and bilayer membrane. At 20 kA.m-2, 24 wt% sodium chloride and 32 wt%

sodium hydroxide.

Catholyte concentration effect

The effect of catholyte concentration on the membrane voltage drop and sodium transport

number is presented in Figure A4.8. Figure A4.8a shows that an increase in the catholyte

concentration results in decrease of the voltage drop for both mono and bilayer membranes. A

more pronounced decrease in the voltage drop is observed for the mono layer membrane at

sodium hydroxide concentration of higher than 15 wt%. However, in practice [1] it is

expected that the membrane voltage drop increases with increasing catholyte concentration.

This opposite prediction by the model could be because of the assumption of ideal solution


82

which is not valid for high concentration condition. Figure A4.8b shows a decreasing trend of

the sodium transport number from 0.85 to 0.6 for the mono layer and from 0.99 to 0.77 for the

bilayer membrane when increasing the concentration from 10 wt% to 40 wt% of sodium

hydroxide at current density of 6 kA.m-2.

(a) (b)

Figure A4.8. (a) Membrane voltage drop (b) Sodium transport number over a sodium hydroxide

concentration range of 10 wt% to 40 wt% for a mono and bilayer membrane. At T=80 ºC, 6 kA.m-2

and 24 wt% sodium chloride.

Diffusion coefficients in solution as a function of temperature

The temperature dependent diffusion coefficients in the free solution which are used to

estimate the self-diffusion coefficients inside the membrane are as follow [22,25]:

9 210 0.0001 0.019 0.699

c cNaD T T

(A4.1)

9 210 0.0001 0.0261 0.894

c cClD T T

(A4.2)

9 210 0.0006 0.1231 0.567

c cOHD T T

(A4.3)

2

9 210 0.0004 0.0365 0.871H O c c

D T T (A4.4)

Maxwell-Stefan modeling of

multicomponent ion transport

inside a cation-exchange

membrane

Abstract

A model has been developed using the Maxwell-Stefan equation to describe the mass

transport inside a cation-exchange membrane used in the chlor-alkali process. In order to

calculate the concentration profiles of the species inside the membrane the pdepe solver of

MATLAB has been used to iterate over time until the steady-state is reached. The Differential

Algebraic Equations (DAEs) in this system have an index of two which cannot be solved by

the pdepe solver. Therefore, an augmented matrix is used by including the membrane

potential drop into the vector of unknown fluxes. The lack of reliable data for Maxwell-Stefan

diffusion coefficients is the main bottleneck of the Maxwell-Stefan approach for describing

the ion transport inside a membrane. Here, three sets of diffusion coefficients reported in

literature for different membranes are used to study the effect and importance of the diffusion

coefficients on the outputs of the model.

5

Maxwell-Stefan modeling of multicomponent ion transport inside a membrane

84

Introduction 5.1

For prediction of ion and water transport inside a membrane appropriate mass transport and

equilibrium models are required. The mass transfer can be modeled using either the Nernst-

Planck or the Maxwell-Stefan equations [1]. The Nernst-Planck equation neglects the

interactions of ions and therefore is only believed to be valid for systems of dilute

concentrations [1–3]. The Maxwell-Stefan equation takes the interaction of different species

into account. However, it requires reliable data for diffusion coefficients [3]. The difference

between Nernst-Planck and Maxwell-Stefan is schematically depicted in Figure 5.1.

(a) (b)

Figure 5.1. Schematic drawing of ion transport inside a cation-exchange membrane with fixed sulfonic

groups in the chlor-alkali process. The interaction and transport of ions and water are depicted as

arrows based on the principles of the (a) Maxwell-Stefan and (b) Nernst-Planck equations.

The general theory of Maxwell-Stefan modeling of multicomponent mass transport is

available in text books [1,4], and applications of the modeling are discussed in a number of

papers. There have been a few studies in the literature [5–11] on the Maxwell-Stefan approach

for multicomponent diffusion in gas and liquid systems. Bothe et al. have developed

Maxwell-Stefan diffusion equations in concentrated solutions and gas mixtures [6]. Leonardi

et al. [8] have studied a numerical approach for Maxwell-Stefan diffusion equations. Leonardi

et al. have developed two approaches in a computational code. In the first method they used

the second-order accurate in time Crank-Nicolson finite difference approach and in the second

method backward differentiation was used. They focused on the numerical resolutions of the

methods and they concluded that both methods give stable and robust results. Silva et al. [9]

have investigated external and intra-particle mass transfer resistances using the Maxwell-

Stefan equation to describe diffusion transport in microporous materials. They fitted their

model to the experimental data with a higher fitting accuracy compared to the Nernst-Planck

model. Wesselingh et al. [10] have explored the effect of interaction between the ionic

diffusion coefficients in porous media. They estimated the diffusion coefficients in a polymer

matrix based on the free water diffusion coefficients and by making corrections for the

Chapter 5

85

tortuosity inside the matrix. They found the friction of counter-ions with the polymer matrix

to be much larger than the predicted values with tortuosity. Moreover, they found the friction

between the ions to depend on the structure of the porous media. In addition, Psaltis et al. [12]

have modeled charged transport in a ternary electrolyte solution using both Nernst-Planck and

Maxwell-Stefan equations and compared the results. They concluded that the concentration

profiles of ionic species in the electrolyte at equilibrium is similar for both Nernst-Planck and

Maxwell-Stefan approaches.

However, there are only few articles available on the Maxwell-Stefan modeling of mass

transport in ion-exchange membranes. Graham et al. [7] have developed the application of the

Maxwell-Stefan flux equations in ion-exchange membranes. They showed that the self-

diffusion coefficients used in the Nernst-Planck equation are a certain combination of the

Maxwell-Stefan diffusion coefficients.

The only research which has investigated the mathematical modeling of ion transport inside a

cation-exchange membrane under current density and using the Maxwell-Stefan equation is

Van der Stegen et al. [13]. They have neglected the concentration gradients of the liquid phase

to derive a correlation for the potential gradient. Furthermore, they assumed the membrane

ionic fixed groups as one of the components in the aqueous mixture which resulted in

calculating a local membrane ionic fixed group concentration inside the membrane. The

authors concluded that using a set of diffusion coefficients reported by other authors and

based on sensitivity analysis resulted in a difference between the absolute values of the

performance parameters, e.g. current efficiency and potential drop and the industrial

operation. However, their model was able to predict the correct trend of the parameters at

different operating conditions.

In this study, a mass transfer model inside a cation-exchange membrane used in the chlor-

alkali process is developed based on the Maxwell-Stefan theory. The ionic fixed groups are

assumed constant and the potential gradient is included in the vector of unknown fluxes and

solved using an augmented matrix. Furthermore, the importance of having reliable data for

diffusion coefficients as an indication of the friction between different species in the

Maxwell-Stefan model is discussed.

Model approach and assumptions

Maxwell-Stefan equation

The Maxwell-Stefan equation is a steady state force balance between driving forces and

friction forces interacting on the species in a mixture. The generalized Maxwell-Stefan

equation expressed based on mole fraction is presented by Eq. (5.1).


86

,

N Nn

itot i i i j j i

j i i j

dlna d RTC X RT z F X X

dx dx

D (5.1)

The derivation of the driving forces in the Maxwell-Stefan equation is based on irreversible

thermodynamics [4,14]. The driving forces are related to the friction forces of different

species. In a system with charged species and an applied electrical potential, the

electrochemical potential is defined as presented by Eq. (5.2). It has two terms of chemical

and electrical potential. For sake of simplicity here ideal behavior is assumed. The activity of

ions is then given by Eq. (5.3) ( 1i ). The gradient of the electrochemical potential, under

the assumption of one dimensional transport in the x direction, is presented by Eq. (5.4). The

contribution of the pressure gradient compared to the concentration and electrical gradient is

assumed to be negligible [3–5].

i i i i i id d z Fd V dp RTdlna z Fd (5.2)

ii i i

tot

Ca X

C (5.3)

i i tot

i

i tot

d dC dC dRT RTz F

dx C dx C dx dx

(5.4)

From Eq. (5.4), the generalized Maxwell-Stefan equation can be written in the concentration

form (Eq. (5.5)), with di is the driving force for transfer of species.

,

N Nn

i toti i i i j j i

j ii tot tot i j

dC dCRT RT d RTd C z F C C

C dx C dx dx C

D (5.5)

Another important equation for a system with charged species is the electroneutrality

condition (Eq. (5.6)). In the electrolysis system in which the current density is an important

measure for ion transport Eq. (5.7) is used to describe the relation between the ionic fluxes

and the current density.

0i i

i

C z (5.6)

1

n

i i

i

I F z J

(5.7)

Chapter 5

87

Boundary conditions

At steady state the inlet and outlet flux of species should be equal at the membrane and

electrolyte interface. In contrast to the Nernst-Planck model presented in previous chapters

which takes into account the transport in both the membrane and the boundary layer, the

Maxwell-Stefan model only models the ion concentrations inside the membrane.

Concentrations at the membrane boundary are almost equal to the bulk concentrations, by

assuming very high mass transfer (k=1 m.s-1) in the boundary layer. This is because in the

Nernst-Planck model convection transport is represented by the Schlӧgl equation and can be

calculated separately. In the Maxwell-Stefan model this not the case. The convective term is

now part of the equations and can only be incorporated iteratively. This is very time

consuming and therefore infinite high mass transfer coefficients are used here. The equality of

steady state fluxes at the membrane-solution interface is presented by Eq. (5.8). The

concentration at the membrane-solution interface in the membrane is calculated based on the

Donnan Equilibrium theory which is explained in depth in Chapter 3.

,int ,int C membrane solution bulk s s

i i i i iN N k C C (5.8)

Solution strategy

The Maxwell-Stefan equation is a non-linear system of Differential Algebraic Equations

(DAEs) which defines the fluxes in a multicomponent system. The non-linear flux equations

based on the Maxwell-Stefan force balance need to be arranged in a matrix format to be

solved numerically. The system of equations is solved by using the pdepe solver in

MATLAB. The built-in pdepe solver of MATLAB uses ODE15s for solving the DAEs and

can only solve DAEs with index less than 2. The index of DAEs is defined based on the

number of differentiations required for reducing the DAEs to ODEs. In order to calculate the

concentration of species in the membrane by solving Eq. (5.16), double integration of the

DAEs is required which defines an index of 2 for this system. Therefore, it is necessary to

reduce the system with index 2 to 1 to use the pdepe solver of MATLAB. Krishna et al. [15]

have explained that the index 2 of the DAEs in this system can be reduced to 1 by using the

augmented matrix and including the membrane potential drop into the vector of unknown

fluxes. The non-linear flux equations are arranged in an n-dimensional matrix notation

containing the system of Eqs. (5.5) to (5.7). n is the number of species consisting of the ions,

water and the ionic fixed groups of the membrane. The concentration of ionic fixed groups is

known and it has zero flux. Therefore, there are (n-2) independent equations and (n-1) fluxes.

By combining Eqs (5.5) to (5.7) the system of Maxwell-Stefan equations can be brought in

the form of a matrix formulation as presented by Eqs. (5.9) to (5.12). Here, for simplicity the

gradient of the total concentration is neglected. The rearrangement and derivation of the

general matrix formulation is explained in the appendix.


88

1

,11

; 1,2, 1n

i

i j i i ii nj

dC dFb A N C z i n

dx RT dx

(5.9)

,

,

; 1,2, , 1i

i j

tot i j

CA i j n

C

D (5.10)

,1 ,

; 1,2, , 1n

k

i ik tot i ki k

CA i n

C

D

(5.11)

1

1

n

n i ij

Ib z N

F

(5.12)

The general Maxwell-Stefan equation which is formulated into a matrix is defined by Eq.

(5.13) in which vector (J) defines the fluxes and the membrane voltage drop as the unknown

variables. Vector (b) is the augmented vector of driving forces as presented by Eq. (5.14). The

[B] matrix (Eq. (5.15)) is the augmented matrix of friction coefficients combined with matrix

[A] and vector bn (Eqs. (5.10) to (5.12)). The continuity equation as presented by Eq. (5.16) is

used to solve the flux equations and to calculate the steady-state solution.

1

J B b

(5.13)

1

12

2

1 1n n

n

dC

dxb

dCb dx

b dC

dxb

I

F

(5.14)

0

i i

i

FA C z

RTB

z

(5.15)

i idC dN

dt dx (5.16)

Chapter 5

89

5.2.1 Input parameters

Table 5.1 presents the input parameters used in the model. The initial concentrations of the

anolyte and the catholyte solutions are 24 wt% sodium chloride and 32 wt% sodium

hydroxide, typical for the chlor-alkali process. The membrane properties are based on a

monolayer Nafion, N-1110, which has also been used in the Nernst-Planck modeling of a

monolayer membrane as presented in chapter 3.

Table 5.1. Input parameters of the model.


Current density [kA.m-2] 2 – 20

Pressure [atm] 1


Sodium hydroxide [wt%] 32 [16]

Sodium chloride [wt%] 24 [16]

Total wet membrane thickness [m] 2.7x10-4



3m] 0.28 [18–20]

5.2.1 Maxwell-Stefan diffusion coefficients

In the chlor-alkali system there are five main species excluding impurities: sodium,

hydroxide, chloride, the ionic fixed groups of the membrane and water as the solvent.

Therefore, ten binary diffusion coefficients are required. As it was mentioned in the

introduction there is very little information about the binary diffusion coefficients in cation-

exchange membranes or solutions with high concentrations, which is the main bottleneck of

the Maxwell-Stefan model. Since there is no data on the values of the Maxwell-Stefan

diffusivities for the membrane used in this study, only the general trend of the concentration

profiles can be investigated.

In our model we implement different values for the Maxwell-Stefan diffusivities. In the base

case equal diffusion coefficients for all components are used (1.10-10 m2.s-1). This value is

based on the diffusion coefficients in the aqueous solutions and taking into account the effect

of tortuosity and porosity in the membrane as discussed by Van der Stegen et al. [3]. Apart

from the base case values, the reported values of the Maxwell-Stefan diffusion coefficients by

three different authors are implemented in the model [3,11,21]. Table 5.2 presents the

diffusion coefficients of these authors.


90

Van der Stegen et al. have made a sensitivity analysis of the diffusion coefficients used in the

membrane. They ran their model for the given equal diffusion coefficients (1.10-10 m2.s-1), and

changed each of the diffusion coefficients several orders of magnitude to see the effect on the

simulation results. In the end they only incorporated the diffusion coefficients that

significantly changed the simulation results when they were varied and they considered the

rest as unimportant diffusion coefficients. By choosing a high value for the unimportant

diffusion coefficients they excluded their interaction effects. Thereafter, they adopted the

diffusion coefficients determined experimentally by Yeager et al. [22] in a single layer

membrane in such a way that they could obtain the observed fluxes in the DuPont Nafion

which was tested in the chlor-alkali plant. They concluded that having reliable data for

diffusion coefficients inside the membrane plays an important role in the predicted results of

the model.

Visser et al. [21] have reported the fitted values of diffusion coefficients in Nafion 450, a

membrane that is mainly used in electrodialysis application. They have investigated the

diffusion coefficients in different experiments: diffusion dialysis, electro-osmosis, pressure

driven permeation, electrodialysis and resistance experiments. They have investigated the

diffusion coefficients in HCl, H2SO4, NaCl and NaOH electrolyte solutions. They used up to

4 M of sodium hydroxide solution which is lower than the concentration of sodium hydroxide

solution used in the chlor-alkali process (~11 M).

Kraaijeveld et al. calculated the Maxwell-Stefan diffusion coefficients based on the data

collected by Narebska et al. who has studied two systems of (Nafion 120/NaCl and Nafion

120/NaOH) [23,24]. In order to have a positive net flux, Kraaijeveld et al. reported negative

values of diffusion coefficients for the like-like ions.


The concentration profiles of ionic species and water for a current density range of 2 to 20

kA.m-2 are presented in Figure 5.2 for the base case. It is observed that the concentration of

sodium and hydroxide ions decreases with increasing current density especially close to the

catholyte side of the membrane. The concentration profile of chloride ions does not show a

noticeable change with increasing current density. The water concentration increases to a

value higher than the pure water concentration, 55 kmol.m-3 which is impossible. By changing

the values of diffusion coefficients to the values reported by Van der Stegen the concentration

profiles of ions and water change, seen in Figure 5.3. The concentrations of sodium and

hydroxide increase with increasing current density and the concentration of chloride

decreases. The water concentration has the opposite trend compared to the base case.

Chapter 5

91

Table 5.2. Maxwell-Stefan diffusion coefficients reported in literature for different types of

membrane.

Components Membrane phase

(DuPont Nafion) based

on Van der Stegen

[10-10 m2.s-1]

Not concentration

dependent

Membrane phase

(Nafion 450) based on

Visser [10-10 m2.s-1]

Not concentration

dependent

Membrane phase (Nafion

120) based on Narebska et

al. /Kraaijeveld [10-10

m2.s-1]

Concentration dependent

Na+ , H2O 9.0 5.14 2.0

Cl- , H2O 1000 (unimportant) 6.23 1.8

OH- , H2O 10 16.2 8.0

Na+ , Cl- 1000 (unimportant) 0.580 1.0

Na+ , OH- 10 100 1.0

OH- , Cl- 1000 (unimportant) n.a.*(1000) n.a.*(1000)

m , H2O 10 7.92 2.0

m , Na+ 1.17 2.26 0.3

m , Cl- 1.0 0.169 -25

m , OH- 1000 (unimportant) 1.58 -1

*not available

Figure 5.2. Concentration profiles of sodium, hydroxide, chloride and water inside the membrane as a

function of position in a current density range of 2 kA.m-2 to 20 kA.m-2 for the base case. The equal

values of diffusion coefficients, 1.10-10 m2.s-1, are used.

The concentration profiles of ions and water using the diffusion coefficients reported by other

authors were also calculated. The model convergence was sensitive to the selected values of


92

diffusion coefficients. The model with the values of negative diffusion coefficients suggested

by Kraaijeveld et al. did not converge at high current densities. The concentration profiles at 2

kA.m-2 are presented in Figure 5.4 for the base case and for the other cases with the diffusion

coefficients suggested by Van der Stegen et al., Visser et al. and Kraaijeveld et al. It can be

seen that the concentration profiles for sodium, hydroxide and water for the base case are

significantly different than for the other cases.


function of position in the membrane at current density range of 2 kA.m-2 to 15 kA.m-2 based on the

diffusion coefficients suggested by Van der Stegen, et al.


function of position in the membrane at 2 kA.m-2 current density for the base case with all equal

diffusion coefficient values of 1.10-10 m2.s-1, and diffusion coefficients reported by Van der Stegen et

al., Visser et al. and Kraaijeveld et al.

Chapter 5

93

Figure 5.5 shows results for comparison of the different diffusivity values, at 10 kA.m-2

.

Similar to Figure 5.4 it can be observed that the concentration profiles of ions and water have

a different trend as a function of the diffusion.

In addition to concentration profiles of ions and water in the membrane the membrane

voltage drop and sodium selectivity has been calculated for different cases, and it is presented

in Figure 5.6.


function of position in the membrane at 10 kA.m-2

current density for the base case with all equal

diffusion coefficient values of 1.10-10

m2.s

-1, and for the other cases with diffusion coefficients

reported by Van der Stegen et al. and Visser et al.

(a) (b)

Figure 5.6. (a) Membrane voltage drop (b) sodium transport number, as a function of current density

for the base case with all equal diffusion coefficient values of 1.10-10

m2.s

-1, and for the other cases

with diffusion coefficients reported by Van der Stegen et al. and Visser et al.


94

Figure 5.6a presents the membrane voltage drop as a function of current density for the three

different cases. In all cases the membrane voltage drop increases with increasing current

density. However, there is a significant increase in the membrane voltage drop in the base

case. Figure 5.6b presents the values of sodium transport number as an indication of the

membrane permselectivity. It is observed that for the base case the sodium selectivity reaches

1 with increasing current density. For the Van der Stegen case there is a decreasing trend of

sodium transport number with increasing current density up to 5 kA.m-2 followed with an

increase up to 0.3 with increasing the current density up to 15 kA.m-2. The sodium transport

number value of lower than 0.5 indicates that the membrane is not selective to sodium ions. In

the Visser case the sodium transport number has an increasing trend with increasing current

density. The value of the diffusion coefficient for hydroxide ion is ten times lower in the base

case compared to the Van der Stegen and Visser cases. This results in lower ion conductivity

of the membrane which is observed in Figure 5.6a. However, the low value of diffusion

coefficient of hydroxide ion results in a very high value of the sodium transport number (see

Figure 5.6b). The results of the membrane voltage drop and sodium selectivity shows the

importance of having reliable data for binary diffusion coefficients for the Maxwell-Stefan

modeling.

Conclusion

The transport of multicomponent ions and water inside a cation-exchange membrane used in

the chlor-alkali process has been described with Maxwell-Stefan equations. The solution

strategy was based on the augmented matrix formulation of the fluxes and the membrane

voltage drop as the unknown variables. The pdepe solver of MATLAB has been used to solve

the system of Algebraic Differential Equations (DAEs) to determine the steady-state solution.

The biggest challenge of the Maxwell-Stefan approach is the lack of experimentally validated

diffusion coefficients. An arbitrary choice may lead to physically unrealistic solutions. The

diffusion coefficients reported by other authors are used to investigate the influence of the

diffusion coefficients on the results of the model. The calculated concentration profiles show

that the values of Maxwell-Stefan diffusion coefficients strongly influence the model results

in terms of the membrane permselectivity and voltage drop.

Nomenclature

Latin symbols


iV Partial molar volume [m3.mol-1]

p Pressure [pa]

R Gas constant [J.mol-1.k-1]

T Temperature [K]

Chapter 5

95

zi Ionic charge [-]

ai Activity of ions [-]

Di,j Maxwell-Stefan diffusion coefficient [m.s-1]

Ni Molar flux of species [mol.m-2.s-1]

Ctot Total concentration [mol.m-3]

Cs,int Concentration in the solution and at the interface with membrane [mol.m-3]

k Mass transfer coefficient in the boundary layer [m.s-1]

Nimembrane Maxwell-Stefan flux in the membrane [mol.m-2.s-1]

Nisolution Maxwell-Stefan flux in the solution boundary layer [mol.m-2.s-1]

di Driving force for transfer of species

x Length [m]

X Mole fraction [-]

Greek symbols



μ Chemical potential [J.mol-1]

η Electrochemical potential [J.mol-1]

γ Activity coefficient [-]

Ɛ Porosity [-]


Bibliography

[1] R. Taylor, R. Krishna, Multicomponent mass transfer, John Wiley & Sons, Inc., 1993.


Amsterdam, 2004.

[3] J.H.G. van der Stegen, The state of the art of modern chlor alkali electrolysis with

membrane cells, 2000.

[4] J.A. Wesselingh, R. Krishna, Mass transfer in multicomponent mixtures, Delft

University Press, Delft, 2000.

[5] R. Krishna, J. a. Wesselingh, The Maxwell-Stefan approach to mass transfer, Chem.

Eng. Sci. 52 (1997) 861–911.

[6] D. Bothe, On the Maxwell-Stefan approach to multicomponent diffusion, Prog.

Nonlinear Differ. Equations Their Appl. 80 (2011) 1–13.


96



[8] E. Leonardi, C. Angeli, On the Maxwell-Stefan Approach to Diffusion : A General

Resolution in the Transient Regime for One-Dimensional Systems, Phys. Chem. 114

(2010) 151–164.

[9] C.M. Silva, P.F. Lito, Application of the Maxwell–Stefan approach to ion exchange in

microporous materials. Batch process modelling, Chem. Eng. Sci. 62 (2007) 6939–

6946.

[10] J.A. Wesselingh, P. Vonk, G. Kraaijeveld, Exploring the Maxwell-Stefan description

of ion exchange, Chem. Eng. 57 (1995) 75–89.

[11] G. Kraaijeveld, The Maxwell-Stefan description of mass transfer in ion-exchange and

electrodialysis, Rijksuniversiteit Groningen, 1994.



Soc. 158 (2011) A33.

[13] J.H.G. Van Der Stegen, A.J. Van Der Veen, H. Weerdenburg, J.A. Hogendoorn, G.F.

Versteeg, Application of the Maxwell-Stefan theory to the transport in ion-selective

membranes used in the chloralkali electrolysis process, Chem. Eng. Sci. 54 (1999).

[14] K.S. Forland, T. Forland, S.K. Ratkje, Irreversible Thermodynamics. Theory and

Applications, John Wiley & Sons Ltd., 1988.

[15] R. Krishna, Diffusion in multicomponent electrolyte systems, Chem. Eng. 35 (1987)

19–24.

[16] T.F. O’Brien, T. V. Bommaraju, F. Hine, Handbook of Chlor-Alkali Technology,

Springer US, Boston, MA, 2005.







Chapter 5

97

[20] S. Moshtarikhah, N.A.W. Oppers, M.T. de Groot, J.T.F. Keurentjes, J.C. Schouten, J.

van der Schaaf, Nernst-Planck modeling of multicomponent ion transport in a Nafion

membrane at high current density, In Prep. (2016).

[21] C.R. Visser, Electrodialytic Recovery of Acids and Bases. Multicomponent mass

transfer description, Rijksuniversiteit Groningen, 2001.

[22] H.L. Yeager, Z. Twardowski, L.M. Clarke, A Comparison of Perfluorinated

Carboxylate and Sulfonate Ion Exchange Polymers I. Diffusion and water sorption,

Electrochem. Soc. (1982) 324–327.

[23] A. Narebska, S. Koter, W. Kujawski, Irreversible thermodynamics of transport across

charged membranes. I: Macroscopic resistance coefficients for a system with Nafion

120 membrane, J. Memb. Sci. 25 (1985) 153–170.

[24] A. Narebska, W. Kujawski, S. Koter, Ireversible thermodynamics of transport across

charged membranes. II: Ion-water interaction in permeation of alkali, J. Memb. Sci. 30

(1987) 125–140.


98

Appendix

The components contributing to the transport inside the membrane excluding the impurities

are sodium, hydroxide, chloride, the ionic fixed groups and water. This is based on the

friction forces and interactions between different species. Every species is defined with a

number:

2 3Na 1, OH 2, H O 3, Cl 4, SO 5

The total concentration of ions is defined as the summation of all species presented by Eq.

(A5.1). The electroneutrality equation for charged species and the relation of the current

density with fluxes are defined by Eq. (A5.2) and Eq.(A5.3), respectively. The Maxwell-

Stefan equations can be rearranged as presented by Eq. (A5.4).

1 2 3 4 51

n

tot ii

C C C C C C C

(A5.1)

1 1 2 2 4 4 5 51

0n

i ii

z C z C z C z C z C

(A5.2)

1 1 2 2 3 2 4 41

0n

i ii

I z N z N z N z N z N

F (A5.3)

,

1b N N

ni i tot i i

i i j j ij itot tot i j

dC C dC C z F dC C

dx C dx C RT dx

D

(A5.4)

By using Eqs. (A5.1) to (A5.3) in the Maxwell-Stefan equation (A5.4) and writing it for every

component this system of equations is obtained:

3 51 1 2 4 1 1

1 1 2 3 4

1,2 1,3 1,4 1,5 1,2 1,3 1,4

1 1 1 1N N N Ntot

tot tot tot tot tot

dC C CdC C C C C z F db

dx C dx C C C C RT dx

D D D D D D D

3 52 2 1 4 2 2

2 1 2 3 4

2,1 2,1 2,3 2,4 2,5 2,3 2,4

1 1 1 1N N N Ntot

tot tot tot tot tot

dC C CdC C C C C z F db


D D D D D D D

3 3 5 3 31 2 4

3 1 2 3 4

3,1 3,2 3,1 3,2 3,4 3,5 3,4

1 1 1 1N N N Ntot

tot tot tot tot tot

dC C dC C C z FC C C db


D D D D D D D

3 5 3 34 4 1 2

4 1 2 3 4

4,1 4,2 4,3 4,1 4,2 4,3 4,5

1 1 1 1N N N Ntot

tot tot tot tot tot

dC C C C z FdC C C C db


D D D D D D D

5 1 1 2 2 3 3 4 4 z N z N z N z N 0

Ib

F

Chapter 5

99

This system of equations is then formulated in the matrix form as presented by Eqs. (A5.5) to

(A5.7). The vector (b) which is the driving forces, matrix [B] is the augmented matrix of

friction coefficients and vector (J) gives the unknown fluxes and membrane voltage drop.

1 1

12 2

2

1 1 1

tot

tot

tot

tot

n n n tot

totn

dCdC C

dx C dx

b dCdC Cb dx C dx

b dC C dC

dx C dxb

I

F

(A5.5)

0

i i

i

FA C z

RTB

z

(A5.6)

1

J B b

(A5.7)

Gas bubble removal from a gauze

surface in a thin film spinning disc

reactor

Abstract

The efficiency of the gas removal from a mesh surface in a thin film spinning disc reactor has

been investigated as a method for intensification of gas evolving processes. The

heterogeneously catalyzed decomposition of hydrogen peroxide in a thin film spinning disc

reactor has been carried out. The removal of oxygen gas bubbles from a thin film formed on a

nickel gauze surface coated with palladium is studied by determining the overall reaction rate

parameter. The overall reaction rate parameter is obtained by solving mass balances over the

thin film spinning disc reactor as a plug flow model and the liquid vessel as a CSTR model.

The overall reaction rate parameter increases from 0.014 m3L.m-3

R.s-1 to 0.028 m3L.m-3

R.s-1 at

40 °C and a pH of 6.9 and 8, respectively. Also, it increases from 0.0087 m3L.m-3

R.s-1 to 0.045

m3L.m-3

R.s-1 when increasing the temperature from 30 °C to 60 °C at a pH of 3.6. The overall

reaction rate parameter increases ten times higher when increasing the pH from 3.6 to 8. This

indicates that at pH=3.6 the reaction is kinetically limited. Therefore the increase of the

overall reaction rate parameter with increasing the rotation speed can be only because of the

increased removal of gas bubbles and creation of a clean active surface for reaction.

6

Gas bubble removal from a gauze surface in a thin film spinning disc reactor

102

Introduction

Process intensification of electrochemical cells appears promising in terms of reduced capital

costs and improved safety. The size of plant equipment is significantly reduced and special

corrosion resistive materials can be used that are too expensive for large scale equipment. The

productivity of electrochemical cells can be increased by applying a higher current at a higher

potential. However, the formation of gas bubbles often prevents this route to process

intensification. These gas bubbles reduce the accessibility of the electrodes for electrolyte

which leads to an increase in potential drop and correspondingly higher power consumption.

In extreme gas evolution cases the contact between electrodes might even completely

disappear periodically. The removal of gas bubbles is thus a key challenge for intensifying

electrochemical processes. The thin film spinning disc reactor has been proven to intensify

heat and mass transfer [1–4]. Due to the rotation of the disc a thin liquid film with high shear

stresses is formed which can also enable fast removal of gas bubbles from the surface.

Hydrodynamic studies of the thin film liquid on a smooth surface disc and a clothed disc is

complex and has been studied by several authors [5–12]. Thin film formation on smooth and

grooved surfaces in a spinning disc reactor has been presented in previous work of Ramshaw

and Jachuk [13,14]. They showed that grooved surfaces lead to enhancement of the mass

transfer rate [1]. In this work we have studied gauze surfaces. A gauze has the benefit of a

larger electrode area than a smooth disc.

The decomposition of hydrogen peroxide is chosen as the reaction model for studying the

efficiency of gas removal from a thin film spinning disc reactor. A thin layer of palladium is

coated on the rotating gauze of a 13 cm diameter as a catalyst. Hydrogen peroxide

decomposition depends on temperature and pH. To know whether or not we are in the kinetic

or mass transfer limited region, the reaction is studied at different temperatures and pHs.

From these data the overall reaction rate parameter is determined for rotation speeds from 1 –

150 rad.s-1 and flow rates of 2.8x10-6 m3.s-1 – 8.1x10-6 m3.s-1.

6.1.1 Hydrogen peroxide decomposition

The decomposition of hydrogen peroxide in presence of palladium catalyst is given by:

2 2 2 22 2H O H O O

The kinetics of the hydrogen peroxide decomposition are complex and they change with the

temperature, pH and concentration. Kinetics have been reported in the literature mainly for

fine powder catalysts per gram of catalyst powder. [15–19]. The main conclusions were that

increasing the pH, concentration and temperature increases the reaction rate, and the

temperature dependency is described with Arrhenius behavior. Variation of temperature and

pH can therefore be used to investigate the mass transfer rate and the surface coverage with

gas bubbles.

Chapter 6

103

There are three different parameters affecting this gas evolving reaction in the thin film

spinning disc reactor, i.e. the kinetic rate and mass transfer rate together with the available

surface area for reaction. The effect of different parameters i.e. pH, temperature, flow rate and

rotation speed on the overall reaction rate parameter (kov) has been studied. This is to find out

whether the reaction is in the kinetic or the mass transfer limited region. Change of the overall

reaction rate parameter due to variation of the pH and the temperature is expected to be

mainly related to kinetics. However, the flow rate and rotation speed of the reactor affect the

external mass transfer and the bubble coverage. This is because the residence time and the

mixing in the liquid film is a function of the flow rate and the rotation speed [2,7,9,20].

Experimental

6.2.1 Material

Hydrogen peroxide of 50 wt% in water (AlfaAesar®) was used to prepare 2 to 4 M hydrogen

peroxide solutions. A ceric sulfate solution of 0.05 N and 0.01 N (AlfaAesar®), a ferrion

solution (Fluka®), and a 95 % sulfuric acid solution (SIGMA-ALDRICH) were used for

titration of the hydrogen peroxide samples.

6.2.2 Palladium coated nickel gauze

A nickel gauze, 100 mesh woven with a wire diameter of 0.1 mm and an opening width of

0.15 mm from AlfaAesar® was used. In order to make the gauze surface catalytically active

for hydrogen peroxide decomposition it was coated with palladium. The mesh was cut in a

circular form of 13 cm diameter. Hereto, 0.15 µm electrolytic nickel strike for adhesion is

followed by electroplating of 0.2 µm palladium layer (CZL Tilburg BV, The Netherlands).

(a) (b)

Figure 6.1. Magnification of (a) Nickel gauze coated with palladium with wire diameter of 0.1 mm

and opening width of 0.15 mm. (b) PMMA disk with two sets of 24 holes of 0.5 mm diameter and

three central holes to fix the disk on the spinning disc reactor shaft.


104

The palladium coated nickel gauze was fixed on a poly methyl methacrylate (PMMA) disk as

depicted in Figure 6.1. This was done by sewing the gauze with nylon thread through 0.5 mm

holes of the PMMA disk.

6.2.3 Experimental technique

A schematic drawing of the experimental setup is presented in Figure 6.2. The fixed

palladium coated nickel gauze on the PMMA disk is mounted on the shaft of the spinning disc

reactor. The disk is enclosed in a cylindrical housing with 2 mm gap distance between the

disk and the stator. A rotation speed of 1 – 150 rad.s-1 is used. The liquid is pumped through

the reactor using a Tuthill magnetic coupled external gear pump. The liquid enters from the

top of the stator and leaves the reactor from the bottom. The flow rate is in the range of

2.8x10-6 m3s-1 – 8.1x10-6 m3.s-1. The diameter of the opening of the reactor inlet is 3.17 mm

which allows the flow of a liquid forming a jet from the nozzle on the center of the disk. At

first the gas was pushed to the center due to rotation of the disk until it made a gas cap on top

of the liquid film filling the top section of the reactor housing. Then the gas was pushed to the

rim of the reactor and left from the bottom exit. The temperature of the liquid was controlled

with a cooling unit connected to a jacketed vessel. The temperature was recorded in the vessel

and in the line where it left the reactor. These temperatures were monitored with two VWR®

Figure 6.2. Schematic drawing of the experimental set-up. The hydrogen peroxide is pumped from the

liquid vessel through the reactor with a gear pump. It enters from the top of the stator flowing over the

palladium coated nickel gauze. It forms a thin film due to the rotation of the disk. Then the formed gas

and the liquid leave the reactor from the bottom.

Chapter 6

105

electronic thermometers. Samples were taken from the solution vessel at fixed time intervals.

The hydrogen peroxide samples were titrated using ceric sulfate solution. The titration method

was followed from the procedures described by USP TechnologiesTM. It is interesting to see

whether the gravitational force has an effect on the formation of the thin film in the spinning

disc reactor as a function of rotation speed. This is why two configuration of the thin film

spinning disc reactor was studied by operating the reactor in vertical and horizontal

orientations. The observations showed that in the vertical position the film was also formed

and pushed to the disc surface without falling from the walls. The experiments were

performed in the vertical and horizontal orientations to see whether there will be an effect of

the position of the reactor on the results.

Mathematical description

6.3.1 Overall reaction rate parameter and residence time

To model the thin film spinning disc reactor a one dimensional model for the reaction

occurring in the reactor is used. As it was shown by Ramshaw et al. [4,21] a thin film of

liquid in the spinning disc reactor behaves as a plug flow which is presented in Eq. (6.1). The

overall reaction rate parameter is defined based on first order reaction rate kinetics with mass

transfer limitation in Eq. (6.2).

RV ov R

R

dCk C

dV (6.1)

L L r Lov

L L r L

k a k ak

k a k a

(6.2)

Integrating Eq. (6.1) over the reactor volume and assuming a constant reactor volume results

in Eq. (6.3) in which RR

V

V

.

ov Rkout

R VC C e

(6.3)


106

The liquid in the vessel is very well mixed using a magnetic stirrer. By writing a mole balance

over the liquid vessel as a CSTR model [22] Eq. (6.4) is obtained. Substituting Eq. (6.3) in

Eq. (6.4) and integrating over time results in Eq. (6.5) in which tottot

V

V

.

( )outVtot V V R

dCV C C

dt (6.4)

1ln(1 )

ov Rk

tot

eX t

(6.5)

The experimental data are fitted to Eq. (6.5) and the overall reaction rate parameter is

determined from the slope of the fitted trend line.

6.3.2 Analysis of the liquid film on the rotating gauze

As the liquid flow enters the spinning disk reactor, a liquid film is formed on the disk surface.

At first the film accelerates tangentially and when it reaches the angular velocity it moves

outward under the centrifugal acceleration [4]. From Eq. (6.5) it is apparent that the

estimation of the residence time in the reactor is required. Because of the presence of the thin

film with unknown thickness this is difficult to determine. Hydrodynamics of a liquid film on

a gauze surface is more complex than on a smooth surface. The volume of the reactor is

typically small, which prevents the use of classical residence time measurements. A typical

film thickness on a smooth surface has been reported to be between 50 to 250 μm which is

dependent on the rotation speed of the disk [3,6]. The change in the wetting of a gauze surface

based on the film thickness is depicted in Figure 6.3.

(a) (b) (c)

Figure 6.3. Schematic drawing of a (a) fully wetted, (b) partially wetted, and (c) poorly wetted gauze

surface

Here it is chosen to model the film as a regular thin film on top of a gauze. To estimate the

film thickness on a gauze surface the open volume of the gauze is assumed to be always fully

wetted (Figure 6.3a). The open mesh area is calculated based on Eq. (6.6). O is the opening

Chapter 6

107

width, D is the wire diameter and A is the percentage of the open area. The open volume of

the gauze is calculated by multiplying the open area by the gauze thickness. The gauze

thickness is twice the wire diameter [23].

2( ) 100O

AO D

(6.6)

The liquid film thickness on top of the gauze has been estimated using Eq. (6.7). This is a

correlation proposed by Aoune et al. [20] based on the Nusselt model. Several authors have

used the same correlation as an estimation of a Newtonian liquid film thickness on a rotating

surface [2,3,7,9,20,24,25]. Thus, the volume of the liquid in the reactor has been estimated

using Eq. (6.8).

1/3

2 2 2

3( ) ( )

2

Mrr

(6.7)

0

( ).2 .

i

r

open

R gauze

r

V r r dr V (6.8)

Results

The effect of pH and temperature on the hydrogen peroxide decomposition is presented in

Figure 6.4 and Figure 6.5, respectively. The slope of the plot of ln (1-X) versus time is used to

determine the overall reaction rate parameter, kov, based on Eq. (6.5). Figure 6.4 shows that

for a fixed temperature and flow rate and at 1 rad.s-1 rotation speed (considered as almost a

non-rotating reactor) the overall reaction rate parameter is 0.028 m3L.m-3

R.s-1 for pH=8 and

0.014 m3L.m-3

R.s-1 for pH=6.9. This means that an increase in the pH from 6.9 to 8 increases

the overall reaction rate with a factor two. Figure 6.5 shows how kov changes with increasing

the temperature at 60 rad.s-1 rotation speed, pH=3.6 and flow rate of 6x10-6 m3.s-1. kov

increases from 0.0087 m3L.m-3

R.s-1 to 0.026 m3L.m-3

R.s-1 and 0.045 m3L.m-3

R.s-1 by increasing

the temperature from 30 °C to 50 °C and 60 °C, respectively.

Figure 6.6 shows that for two different flow rates at 60 rad.s-1 rotation speed, kov increases

from 0.45 m3L.m-3

R.s-1 to 0.92 m3L.m-3

R.s-1 by increasing the flow rate from 2.8x10-6 m3.s-1 to

3.7x10-6 m3.s-1, respectively. The modeled residence time in the reactor as a function of

rotation speed for two different flow rates of 3.7x10-6 m3.s-1 and 6x10-6 m3.s-1 is calculated

from Eq. (6.8), and it is assumed that the gauze surface is fully wetted as described in section


108

4.2. Results are presented in Figure 6.7. It is observed that the residence time decreases with

increasing the rotation speed.

Figure 6.4. Effect of pH on conversion at ω=1 rad.s

-1 rotation speed, T=40 °C and Փ=6x10

-6 m

3.s

-1.

The initial concentration at pH=6.9 is 3.2 M, and at pH=8 is 2.85 M. The trend lines are calculated

with a polyfit function of MATLAB. The error bars are an indication of the accuracy of every

measurement point in three times titration.

Figure 6.5. Effect of temperature on conversion at ω=60 rad.s

-1 rotation speed, pH=3.6 and Փ=6x10

-6

m3.s

-1. The initial concentration at T=30 ºC, 50 ºC and 60 ºC is 1.35 M. The trend lines are calculated

with a polyfit function of MATLAB. The error bars are an indication of the accuracy of every

measurement point in three times titration.

kov is presented for different temperatures of 30 °C and 60 °C for a flow rate of 2.7x10-6

m3.s

-1

and pH=3.6 as a function of rotation speed in Figure 6.8. At 30 °C, kov increases from 0.001

m3

L.m-3

R.s-1

to 0.01 m3

L.m-3

R.s-1

. At 60 °C it increases from 0.005 m3

L.m-3

R.s-1

to 0.051 m3

L.m-

3R.s

-1. There is a decrease in kov when increasing the rotation speed from 60 rad.s

-1 to 80 rad.s

-

1.

Chapter 6

109

Figure 6.6. The effect of flow rate on the hydrogen peroxide decomposition at T=60 °C and pH=8 and

ω=60 rad.s-1 rotation speed. The initial concentration is 1.35 M. The trend lines are calculated with a

polyfit function of MATLAB. The error bars are an indication of the accuracy of every measurement

point in three times titration.

Figure 6.7. Modelled residence time in the reactor as a function of rotation speed for two different

flow rates of Փ=3.7x10-6 m3.s-1 with initial concentration of 3.5 M and Փ=6x10-6 m3.s-1 with initial

concentration of 1.35 M at T=60 ºC.


110

Figure 6.8. Overall reaction rate parameter as a function of rotation speed at two temperatures of T=30

°C and T=60 °C and at pH=3.6, Փ=6x10-6 m3.s-1 and initial concentration of 1.35 M.

Figure 6.9 presents kov at 40 °C, pH=8 and flow rate of 6x10-6 m3.s-1 as a function of rotation

speed. kov increases from 0.041 m3L.m-3

R.s-1 to 0.56 m3L.m-3

R.s-1 when increasing the rotation

speed from 1 rad.s-1 to 60 rad.s-1; however further increase of rotation speed to 80 rad.s-1

decreases the overall reaction rate parameter to 0.42 m3L.m-3

R.s-1. The decrease in the kov with

increasing the rotation speed from 60 rad.s-1 to 80 rad.s-1 was observed in Figure 6.8 as well.

Hence, this cannot be a measurement error. The overall reaction rate parameter is compared

for two horizontal and vertical orientation of the spinning disk reactor in Figure 6.10. The

results show that the same kov for both horizontal and vertical orientations is obtained. This

suggests that the centrifugal force is the dominant force in both horizontal and vertical

positions of the reactor and more effective than the gravitational force.

Figure 6.9. Overall reaction rate parameter as a function of rotation speed at pH=8, 40 °C and Փ=6x10-

6 m3.s-1 and initial concentration of 1.35 M.

Chapter 6

111

Figure 6.10. Overall reaction rate parameter for horizontal and vertical positioned spinning disc

reactor as a function of rotation speed at pH=3.6, T=30 °C and Փ=2.8x10-6 m3.s-1 and initial

concentration of 2.8 M in vertical orientation and 1.35 M for horizontal orientation.

Discussion

It is shown in the results that the change of the pH and the temperature only affect the kinetics

of the reaction. The kinetics of the reaction increase at higher pH and temperature and as a

consequence the kov increases. An increase of 30 °C in temperature results in a factor five

higher overall reaction rate parameter. Furthermore, changing the flow rate varies the

residence time of the liquid in the reactor. This suggests that kov is affected by the residence

time of the liquid besides the temperature and the pH. The decrease of the residence time with

increasing the rotation speed is because the liquid film gets thinner which results in a decrease

of the liquid volume in the reactor. A ten times higher overall reaction rate parameter in

Figure 6.9 compared to Figure 6.8 shows that whether the reaction at pH=8 is mass transfer

limited or not, it is certain that at pH=3.6 the reaction is kinetically limited. It is worth

mentioning that there is a 20 ºC temperature difference between the reaction conditions

presented in Figure 6.8 and Figure 6.9, however, we showed that a 30 ºC increase in the

temperature results in maximum five times higher increase in kov. Therefore, the change of the

overall reaction rate parameter with respect to rotation speed can mainly be due to the clean-

up of the surface from gas bubbles. This means that gas removal is more efficient when higher

shear forces help clean-up the surface and create more catalyst surface available for the

reaction. This is valid based on our assumption of fully wetted gauze surface and estimation

of the liquid volume in the reactor as explained in section 4.2. Any change in this assumption

for calculating the liquid volume should be applied to all rotation speeds. Therefore, the effect

of increase in kov with increasing rotation speed still remains valid. On the other hand, the

decrease of kov with increasing the rotation speed higher than 60 rad.s-1 in Figure 6.8 and

Figure 6.9 suggests that there might be poor wetting of the gauze surface at higher rotation

speed. This could result in the loss of active surface area for the reaction. Increase in kov with


112

increasing the rotation speed above 80 rad.s-1

in Figure 6.8 suggests that increasing the

rotation speed further could help improving the gas removal efficiency from the surface and

as a consequence increase the kov higher. In addition, based on Eq. (6.2) the ratio between the

overall reaction rate parameters at two different rotation speeds is an indication of the surface

coverage with gas bubbles. This is because the interfacial area is a hidden parameter in the

kov. This ratio is 7.1 when increasing the rotation speed from 2 rad.s-1

to 30 rad.s-1

, and it

decreases to 1.4 when increasing the rotation speed from 30 rad.s-1

to 80 rad.s-1

in Figure 6.8.

This indicates that the coverage of the gauze surface decreases with increasing the rotation

speed.

Conclusion 6.6

The decomposition of hydrogen peroxide on an active palladium coated nickel gauze was

studied in a thin film spinning disc reactor. Production of oxygen gas allowed the study of gas

removal from a thin liquid layer formed on the gauze surface as a function of different

parameters, i.e. temperature, pH, flow rate and the rotation speed. The kinetics of hydrogen

peroxide decomposition play an important role in the overall reaction rate. A one order of

magnitude higher overall reaction rate parameter resulted from increasing the pH from 3.6 to

8. This means that at pH=8 the increase of the overall reaction rate parameter with increase in

rotation speed can be only due to efficient gas removal from the surface. In fact, at higher

rotation speed the higher shear forces help cleaning the surface by shear-induced gas removal

and prevent the blockage of the catalyst site. Additionally, in the thin film spinning disc

reactor with increasing the rotation speed the produced gas is removed more efficiently from

the surface and the liquid film becomes thinner. This favors gas evolution reactions in the thin

film spinning disc reactor. However, the thinner liquid film on a gauze surface has a risk of

making dry spots or poor wetting of the surface. Also, we concluded that the orientation of the

rotating disk does not affect the overall reaction rate parameter and as a result efficiency of

the reaction.

Nomenclature

Latin symbols

aL Interfacial area [m2]

CR Concentration in the reactor [mol.m-3

]

CRout

Outlet reactor concentration [mol.m-3

]

CV Concentration in the vessel [mol.m-3

]

D With opening of the gauze [mm]

kL Reaction rate constant [m.s-1

]

kr Mass transfer coefficient [m.s-1

]

kov Overall reaction rate parameter [m3.m

-3.s

-1]

Chapter 6

113

O Gauze wire thickness [mm]

r Disc radius [m]

t Time [S]

VR Liquid volume in the reactor [m3]

Vtot Total liquid volume [m3]

Vopengauze The open volume of the gauze [m3]

X Conversion [-]

Greek symbols

δ Liquid film thickness [m]

M Mass flow rate [kg.s-1]

V molar flow rate [m3.s-1]

ρ Density [kg.cm-3]

μ viscosity [kg.m-1.s-1]

τ Residence time in the reactor [s]

τtot Total residence time [s]

ω Rotation speed [rad.s-1]

Bibliography



[2] G. Peev, D. Peshev, A. Nikolova, Gas absorption in a thin liquid film flow on a

horizontal rotating disk, Heat Mass Transf. 43 (2007) 843–848.

[3] J.R. Burns, R.J.J. Jachuck, Determination of liquid–solid mass transfer coefficients for

a spinning disc reactor using a limiting current technique, Int. J. Heat Mass Transf. 48

(2005) 2540–2547.

[4] D. Reay, C. Ramshaw, A. Harvey, Process intensification: engineering for efficiency,

sustainability and flexibility, Elsevier Ltd, Oxford., 2008.

[5] S. Basu, B.M. Cetegen, Analysis of Hydrodynamics and Heat Transfer in a Thin Liquid

Film Flowing Over a Rotating Disk by the Integral Method, J. Heat Transfer. 128

(2006) 217–225.


114

[6] T. Gambaryan-Roisman, M. Freystein, P. Stephan, Hydrodynamics and Heat Transfer

in a Liquid Film Flowing Over a Spinning Disk With Wall Topography, Heat Transf.

Eng. 34 (2013) 266–278.

[7] G.M. Sisoev, O.K. Matar, C.J. Lawrence, Modelling of film flow over a spinning disk,

J. Chem. Technol. Biotechnol. 78 (2003) 151–155.

[8] N. Brauner, D.M. Maron, characteristics of inclined thin films, waviness and the

associated mass transfer, Int. J. Heat Mass Transf. 25 (1982) 99–110.

[9] O.K. Matar, C.J. Lawrence, G.M. Sisoev, The flow of thin liquid films over spinning

disks: Hydrodynamics and mass transfer, Phys. Fluids. 17 (2005) 052102–1–052102–

20.

[10] W.P. Woods, The hydrodynamics of thin liquid films flowing over a rotating disc,

Newcastle, 1995.

[11] X. Feng, D.A. Patterson, M. Balaban, E.A.C. Emanuelsson, Characterization of liquid

flow in the spinning cloth disc reactor: residence time distribution, visual study and

modeling, Chem. Eng. J. 235 (2014) 356–367.

[12] I. Boiarkine, S. Norris, D. Patterson, Investigation of the effect of flow structure on the

photocatalytic degradation of methylene blue and dehydroabietic acid in a spinning

disc reactor, Chem. Eng. J. 222 (2013) 159–171.

[13] R.J.J. Jachuck, C. Ramshaw, Process intensification: Heat transfer characteristics of

tailored rotating surfaces, Heat Recover. Syst. CHP. 14 (1994) 475–491.

[14] R.J. Jachuck, C. Ramshaw, K. Boodhoo, J.C. Dalgleish, Process intensification: the

opportunity presented by spinning disc reactor technology, in: ICHEME, 1997: pp.

417–424.

[15] V.R. Choudhary, A.G. Gaikwad, Kinetics of hydrogen peroxide decomposition in

aqueous sulforic acid over palladium/carbon: Effect of acid concentration,

React.Kinet.Catal.Lett. 80 (2003) 27–32.

[16] I.W. Mckee, Catalytic Decomposition Metals and Alloys of Hydrogen of the Platinum

Peroxide Group, J. Catal. 14 (1969) 355–364.

[17] V.S. Shivankar, N. V Thakkar, Decomposition of hydrogen peroxide in presence of

mixed ligand cobalt ( II ) and nickel ( II ) complexes as catalysts, J. Sci. Ind. Res.

(India). 64 (2005) 496–503.

Chapter 6

115

[18] Y. Voloshin, J. Manganaro, A. Lawal, Kinetics and Mechanism of Decomposition of

Hydrogen Peroxide over Pd / SiO2 Catalyst, Ind. Eng. Chem. 47 (2008) 8119–8125.

[19] R. Javaid, U.Y. Qazi, S.-I. Kawasaki, Efficient and continuous decomposition of

hydrogen perxoide using a silica capillary coated with a thin palladium or platinum

layer, Bull. Chem. Soc. Jp. 88 (2015) 976–980.

[20] A. Aoune, C. Ramshaw, Process intensification: heat and mass transfer characteristics

of liquid films on rotating discs, Int. J. Heat Mass Transf. 42 (1999) 1432–1445.


CHP. 13 (1993) 493–513.

[22] H. Scott Fogler, Elements of Chemical Reaction Engineering, Prentice Hall PTR, 2006.

[23] G.H. Sedahmed, M.A. Darwish, Liquid-solid mass transfer behaviour of rotating screen

discs, Chem. Eng. 76 (2000) 247–252.

[24] I. Tsibranska, D. Peshev, G. Peev, A. Nikolova, Modelling of mass transfer in film

flow of shear thinning liquid on a horizontal rotating disk, Chem. Eng. Process. Process

Intensif. 48 (2009) 823–827.

[25] D. Peshev, G. Peev, A. Nikolova, Dissolution in film flow of shear thinning liquid on a

horizontal rotating disk, Chem. Eng. Process. Process Intensif. 49 (2010) 616–621.

Intensification of the chlor-alkali

process by using a spinning disc

membrane electrolyzer

Abstract

A zero gap spinning disc membrane electrochemical reactor (SDMER) is presented for the

intensification of the chlor-alkali process. The SDMER is especially designed for chlor-alkali

production at high current densities. Two configurations, namely the rotor-stator (RS) and the

thin film (TF) configuration, are presented and compared with a conventional parallel plate

cell. The cell voltage as a function of current density is virtually identical for the RS-SDMER

and the TF-SDMER. The cell voltage is lower when compared to parallel plate cell.

The effect of the rotational speed on the cell voltage shows that a decrease of 0.9 V in the cell

voltage at 6 kA/m2 when the rotational speed increases from 40 to 60 rad/s in the RS-

SDMER. Results show that at high current densities the effect of an increase in rotation speed

is more pronounced in cell voltage reduction. This is because at high rotation speed the

produced gas is removed from the reactor more efficiently. Additionally, increasing the

temperature from 40 ºC to 80 ºC at 20 kA/m2 results in a decrease of the cell voltage from 6.5

V to 5.5 V. Increasing the sodium chloride concentration decreases the cell voltage. At a low

concentration of sodium chloride, at which mass transfer is important, it is shown that

increasing the rotation speed decreases the cell potential. The highest sodium hydroxide

concentration corresponding to the lowest conductivity, results in the highest cell voltage.

Finally, the membrane permselectivity is estimated from measurements of the acid addition.

The permselectivity increases with increasing current density to values between 0.95 and

0.98. The intensification of the chlor-alkali process was successful with the spinning disc

membrane electrochemical reactor by obtaining an approximately three times higher

production compared to the parallel plate cell when increasing the current density from 6

kA/m2 to 20 kA/m2.

NOTE: This chapter is the joint work of P. Granados Mendoza and S. Moshtarikhah within the framework of the

SPINCHAL project. Both authors contributed to the design of the reactor and carried out jointly the experimental

work here described. Sections noted with (1) are primarily authored by Granados Mendoza. Sections noted with

(2) are primarily authored by S.Moshtarikhah. The sections marked with (3) are the result of joint authorship.

7

Intensification of chlor-alkali process by using a spinning disc membrane electrolyzer

118

Introduction (1)

The chemical industry is continuously striving for the development of substantially smaller,

cleaner, and more energy efficient technologies, in other words: process intensification [1,2].

For energy-intensive industries it is highly desired to decrease the energy consumption of the

processes. The chlor-alkali is an example of an energy intensive industry [3] with an average

energy consumption per tonne of chlorine produced of ~3.4 MWh [4]. The chlor-alkali

process is the electrolysis of aqueous sodium chloride (brine) to yield chlorine, sodium

hydroxide and hydrogen. This process is one of the major electrochemical processes rendering

an annual chlorine production of 9612 ktonnes in Europe in 2014 [5] that supports the

production of about 55% of the chemicals and pharmaceuticals [6]. A schematic chlor-alkali

cell is depicted in Figure 7.1 where the following electrochemical reactions occur:

Anode:2( )

1

2gCl Cl e (7.1)

Cathode: 2 2( )

1

2gH O e OH H e (7.2)

Figure 7.1. A typical membrane cell for chlor-alkali process.

In the past years industrial and academic chlor-alkali research has focused on decreasing the

cell voltage (Ecell) and increasing the current efficiency (ηeff) in order to decrease the power

consumption (PCl2) per tonne of chlorine produced. These quantities are related by:

2

-1756.1kW h tonnecell

Cl

eff

EP

(7.3)

The development of novel electrode materials [7–10], the design of more efficient and durable

membranes [7,11] and the implementation of zero-gap cells [12,13] have been the major

breakthroughs of the chlor-alkali process in the last decades contributing to a significant

Chapter 7

119

decreases in the power consumption. Typical current densities are now in the range of 5-7

kA/m2 [7,12].

Working at higher current densities inherently decreases the electrode area, and therefore

reactor volume, needed to achieve a given production capacity. Thus, ideally the power

consumption in Eq. (7.3) can be lowered if the cell voltage is decreased. However operation at

higher current densities is associated with several challenges, for instance: 1) increased bubble

generation causing larger ohmic drops and increased power consumption (bubble effect), 2)

more pronounced concentration gradients in the boundary layer leading to undesired side-

reactions and current efficiency losses and 3) an increase in membrane voltage drop and the

possibility of loss in permselectivity of the membrane.

In order to achieve the intensification of the chlor-alkali process it is necessary to design an

electrochemical reactor that allows operating at high current densities while dealing with the

above-mentioned challenges. The spinning disc reactor (SDR) is a type of rotating equipment

that is suitable for this purpose. Essentially there are two types of SDR [14] namely the rotor-

stator spinning disc reactor (RS-SDR) [15,16] and the thin-film spinning disc reactor (TF-

SDR) [17].

(1) The RS-SDR consists of a rotating disc in a cylindrical housing, with a typical gap

distance between the rotor and the stator in the order of 1-5 mm [14]. The high

velocity gradient between the rotor and the stator and the high shear forces cause high

turbulence that intensifies the liquid-solid mass transport and therefore decrease the

concentration gradients in the boundary layer. Our previous research regarding the

liquid-solid mass transfer to a rotating mesh electrode [16] indicates that the liquid

solid mass transfer coefficient can be one order of magnitude higher than non-rotating

configurations. Furthermore, the centrifugal forces generated from the rotation of the

disc facilitate the bubble disengagement resulting in a decrease of the bubble effect.

For these reasons, the RS-SDR is a promising process intensification technology for

the brine electrolysis.

(2) The TF-SDR consists of a rotating disc in a cylindrical housing in which the two

fluids are mixed due to centrifugal acceleration of the liquid film. At first, the film

tangentially accelerates due to formation of shear stresses at the disc-liquid interface.

When reaching the local angular velocity the liquid moves outward forming a film

with a typical thickness of 50 microns for liquids with similar properties as water [17].

The very thin film provides a very high mass, heat and momentum transfer between

the gas and liquid and also between the mesh electrode surface and the electrolyte. The

supersaturation is kept low by this high mass transfer, which suppresses the formation

of gas bubbles.

In this work we present the experimental results of a zero-gap spinning disc membrane

electrolyzer suitable for the chlor-alkali process that allows both rotor-stator and thin-film


120

configurations [18]. Results of the cell voltage for current densities up to 20 kA/m2 are

presented as a function of rotational speed, electrolyte concentrations and temperatures.

Experimental results are compared to a laboratory scale parallel plate cell with a finite gap.

Finally, the membrane selectivity is also reported and compared to previous literature [19].

7.1.1 Spinning disc membrane electrochemical reactor (SDMER)

The proposed spinning disc membrane electrochemical reactor (SDMER) is depicted in

Figure 7.2 and consists of two compartments mounted on a common horizontal rotation axis

and placed back to back where the rotor of each compartment is the respective electrode. The

cation exchange membrane is placed between the compartments, forming a rotating stack of

anode-membrane-cathode. In this way a zero-gap configuration is obtained. A stator is placed

inside each rotating cavity. Each stator consists of a flat disc that is connected at its center to a

double concentric cylinder that serves as axis of the reactor. Current is fed to the electrodes

through slip rings (type SRH038-2, Gileon B.V.) located at the edges of the rotating axis. The

rotating housing is connected to a motor (SEW-Eurodrive) by means of a timing belt.

Rotational speeds up to 1000 RPM were investigated.

Figure 7.2. Spinning disc membrane electrochemical reactor for chlor-alkali process.

The anode compartment’s body material is stainless steel with an inner thin jacket of titanium

(grade 2, 99+% purity, Salomons Metalen). All metal parts in contact with the electrolyte are

Chapter 7

121

made of titanium. The anode consists of a titanium (grade 1, 99+% purity, UNIQUE Wire

Weaving Co., Inc.) plain weaved mesh of 80 wires/inch woven from 0.13 mm wires and a

width opening of 0.2 mm. A triangular area of 10 cm2 of the mesh was coated with a Ru/Ir/Ti-

mixed metal oxide (MMO) catalyst (coating by MAGNETO Special Anodes B.V.). The

cathode compartment’s body material is stainless steel with an inner thin jacket of nickel

(99+% purity, Salomon’s Metalen). All metal parts in contact with the catholyte are made of

nickel. The cathode is a nickel (purity 99+%, Alfa Aesar) plain weaved gauze of 100

wires/inch woven from 0.1 mm wires and a width opening of 0.15 mm. The cation exchange

membrane is Nafion NX-982 (Dupont). Two reactor configurations of the SDMER are

possible and are explained below. For clarity, the description below corresponds to one

compartment of the reactor, but applies to both compartments as they are symmetrical.

7.1.1.1 Rotor-stator SDMER

The rotor-stator configuration is depicted in Figure 7.3a. The electrolyte enters the reactor

through the outermost concentric cylindrical cavity of the stator axis. The flow path of the

electrolyte in each compartment is such that it flows past the rotating electrode in a radially

inwards manner. During the electrolysis, a dispersion of bubbles from the gas produced at the

electrode is formed in the electrolyte that fills the cavity between the rotating electrode and

the stator. This electrolyte mixture exits the reactor through the innermost cylindrical cavity

of the stator axis.

(a) (b)

Figure 7.3. Comparison of the flow paths in the Rotor-Stator (a) and (b) Thin-Film configurations.


122

7.1.1.2 Thin film SDMER (2)

The thin-film configuration is depicted in Figure 7.3b. The electrolytes enter the reactor

through the innermost concentric cylindrical cavity of the stator axis forming a jet of liquid on

the rotating electrode. Due to its rotation, a thin film of liquid flowing radially outwards is

formed on the rotating electrode. The gas produced at the rotating electrode is collected in the

gas pocket formed between the stator and the electrolyte thin film. The liquid and the gas

collected at the rim of the rotating electrode exit the reactor by flowing radially inwards past

the counter side of the stator and through the outermost concentric cylindrical cavity of the

stator axis.

Experimental (1)

7.2.1 Experimental setup

The experimental set-up is depicted in Figure 7.4 and consists of three parts: the

electrochemical reactor, the anolyte circuit and the catholyte circuit. Three reactor

configurations are used in this study: 1) the rotor-stator SDMER described in 7.2.1.1, 2) the

thin-film SDMER described in 7.2.1.2 and 3) a parallel plate cell (PP cell). The later was used

as comparison of the performance of the SDMER and consisted of an Electrocell® Micro

Flow Cell [20] with Ir/Ru-MMO on the Ti anode and a nickel cathode, both of 10 cm2 of

electrode area, an electrode membrane gap of 4 mm and fitted with the same membrane as

described in 7.2.1. For all cases the electrochemical reactor is connected to a power supply

(TDK-Lamba Gen 30-50).

Each electrolyte (anolyte and catholyte) circuit consists of feed, water and waste vessels, a gas

cooler and its respective pumps, flow controllers and other sensors. Additionally, the anolyte

circuit includes a chlorine removal section and an acid unit. The entire setup is placed in a

closed Item® rack which for safety reasons remained closed during operation. An in-house-

designed Labview® interface allowed the remote control and operation of the experimental

setup via a programmable logic computer (PLC). All sensors, instruments and equipment in

the setup are connected to the PLC. For additional safety, the Item® rack is connected to two

ventilation points with gas detection sensors (Buveco).

All vessels are made of insulated glass and are designed to be leak tight. Both feed vessels are

stirred and heated by a tracing cable. Prior to the experiments the anolyte and catholyte feed

tanks are filled with aqueous NaCl (VWR Chemicals) and aqueous NaOH (Sigma Aldrich)

solutions respectively at the desired experimental condition. Anolyte pH is controlled by

addition of 1 M HCl (VWR Chemicals) based on the measurement of the pH (Metrohm);

when necessary additional acid solution is fed with the aid of a micropump dosing unit

(Burkert). The anolyte and catholyte are circulated to the respective compartments of the

Chapter 7

123

electrochemical reactor in separate hydraulic circuits by two gear pumps (Gather) regulated

with their respective mass flow controllers (Bronkhorst). Unless otherwise noted the

electrolyte flowrates were 7 ml/s. Three-way solenoid valves (Burkert) connected to the PLC

are used to control the direction of the flow during the experiments and during the rinsing

procedure. Pressure sensors (Huba Control) and temperature sensors (Metatemp) are located

at the inlet of the reactor, at the exit of the reactor and after the gas coolers.

The outflows of the electrolysis reactor consist of mixtures of electrolyte-gas and they can be

re-circulated to the respective feed tanks for further re-use or the waste tanks for their

disposal. The produced gases (Cl2 and H2) are separated from the top of their respective tanks.

Before the gases are further processed or vented they are cooled in their respective gas

coolers. The Cl2 gas is absorbed by contact with NaOH solution using washing bottles to form

Figure 7.4. Schematic drawing of the experimental set-up. In the center the electrochemical reactor is

shown; the anolyte circuit is on the left and the catholyte circuit is on the right. The electrolyte from

the eletrolyte vessels enters the electrochemical reactor through a pump. The temperature and pressure

are monitored before and after the reactor. The outlet leaves the reactor back to the electrolyte vessels

during operation and it goes to the waste vessel during the rinsing procedure with water. The outlet

chlorine and oxygen gas pass through the cooler and enters the bleach bottles to absorb the chlorine.

The oxygen and hydrogen leave through the ventilation.


124

NaOCl+NaCl. For safety reasons and to minimize corrosion issues, at the end of each

experimental procedure the reactor and all lines are flushed with nitrogen and water. Due to

this rinsing procedure, a small, but unknown amount of water remains present in the lines,

which for practical reasons is not removed in between experiments. Therefore some variations

in the concentrations occurred between experiments. To make sure that the concentrations of

the electrolytes during the experimental procedure are known, sampling valves are located at

the outlets of the reactor. Samples of the anolyte and catholyte were taken during the

experimental procedure and analyzed offline as explained in section 7.2.3.

7.2.2 Analytical techniques

The experimental procedures for the quantification of the concentrations of the electrolytes

and the active chlorine content in the brine is explained below. For all cases, each titration

was repeated three times and the average concentration is determined.

7.2.2.1 Determination of the brine concentration

The chloride (Cl-) concentration was determined via the Volhard Method [21] which consists

of back titration of silver nitrate with potassium thiocyanate. The end point of the titration is

determined by using Fe(NO3)3 as indicator in an acidic environment as proposed by Swift et

al. [22].

Samples of 100 µl of the anolyte were added to 5 ml 4 M HNO3 (Sigma Aldrich) and allowed

to stir while 5 ml of 0.1 M AgNO3 (VWR Chemicals) and 5 ml of 2.2 M Fe(NO3)3 (VWR

Chemicals) were added. Back titration of the mixture with 0.1 M KSCN (VWR Chemicals)

was performed until the solution turned red.

7.2.2.2 Determination of the active chlorine content

The active chlorine content in the brine was determined by its reaction with iodide in acid

solution forming an equivalent quantity of iodine [21]. The liberated iodine was titrated with

thiosulphate and the end point was determined with the aid of starch as indicator.

A brine sample of approximately 20-30 ml was added to a flask containing 5 ml 1M HCl

(VWR Chemicals) and 5 ml 1.2 M KI (Sigma Aldrich) and allowed to react while stirring for

two minutes. Then the sample volume was determined in a graduated cylinder and transferred

to a beaker. The titration with 0.1 M Na2S2O3 (Merck) was performed adding 5 ml of 0.2%

starch solution (VWR Chemicals) near the end point.

Chapter 7

125

7.2.2.3 Determination of the caustic concentration

The caustic concentration was determined by titration with HCl. A sample of 200 µl from the

catholyte was titrated with 0.1 M HCl (VWR Chemicals) using phenol red as indicator of the

equivalence point.


7.3.1 Rotor-stator spinning disc membrane electrolyzer

7.3.1.1 Effect of the rotational speed (1)

Results presented in this section correspond to the rotor-stator configuration as described

above in section 7.2.1.1. The effect of the rotational speed in the cell voltage is shown in

Figure 7.5 for two cases: 1) Figure 7.5a shows measurements at a constant rotational speed

while the current density is increased stepwise from 2 to 20 kA/m2 and 2) Figure 7.5b shows

measurements at constant current density while the rotational speed was increased stepwise

from 400 to 1000 RPM. For both cases, measurements of the cell voltage during each current

density step are taken every 1 second for a period of 180 seconds. The standard deviation of

the cell voltage σEcell is defined as:

2

1Ecell

x x N

where x is the measured cell voltage data at every second, x is the averaged cell voltage, and

N is the number of measurements. The standard deviation of the average cell voltage (σEcell) is

presented in Figure 7.5 as error bars. A decrease in the cell voltage is observed when

increasing the rotational speed, particularly at current densities higher than 6 kA/m2. The

effect is less pronounced at lower current densities, for instance at 2 kA/m2 the cell voltage

decreased 0.2 V when increasing the rotational speed from 40 to 60 rad/s (Figure 7.5b). At the

current density typically used in the chlor-alkali industry (i.e. 6 kA/m2) the cell voltage

decreased 0.9 V when increasing the rotational speed from 40 to 60 rad/s (Figure 7.5b). These

results can be compared to the work presented by Cheng et al. [23] who reported the

intensification of the chlor-alkali process in a centrifugal field. The authors reported a

decrease of 0.6 V in the cell voltage at 6 kA/m2 in their rotary cell at 190 g of relative

acceleration.

At low current densities, both bubble generation and concentration gradients have a relatively

small impact on the cell voltage. It is at higher current densities when these become of

importance. The higher standard deviation shown in Figure 7.5 at low rotational speeds,

particularly for current densities higher than 6 kA/m2, can be attributed to the bubble effect.

When the gas formed is not efficiently removed from the reactor, bubbles remain attached to


126

the electrode decreasing its available area and increasing the cell voltage. In practice this was

identified by unstable readings of the cell voltage, leading to larger standard deviations.

Results shown in Figure 7.5 indicate that at high gas production rates, i.e. high current

densities, there is a minimum rotational speed that is required to allow a stable operation of

the reactor. In other words, a minimum rotational speed is required to efficiently release the

gas produced at the electrode, leading to a small variation in the measured cell voltage as

reflected in the standard deviation. This is explained in Figure 7.6 where the standard

deviation of the cell voltage data presented in Figure 7.5 is plotted as a function of the

rotational speed. From Figure 7.6a it can be observed that the standard deviation of the

measured cell voltage decreases as a function of the rotational speeds for all current densities

investigated. An arbitrary threshold of σEcell<0.1 V is defined as the limit for the stable

operation. Measurements with σEcell>0.1 are considered as unstable operation. The data

presented in Figure 7.5b are analyzed accordingly and the results are shown in Figure 7.6b

where the flow map of the stable operation of the reactor is presented.

7.3.1.2 Comparison with parallel plate cell and literature data (3)

The cell voltage obtained from the rotor-stator spinning disc membrane electrochemical

reactor (RS-SDMER) is compared in Figure 7.7 with the results of a conventional parallel

plate cell (PP cell) described in section 7.2.2. As expected, the cell voltage increases as a

function of current density in all cases, however the slope at which this increase occurs is

different for each case. Results obtained in this work are comparable to those reported by

Chandran et al. [24] for a similar PP cell but with a higher electroactive area (34.3 cm2). It is

worth mentioning that the material of the electrodes and the cation-exchange membrane used

by Chandran et al. [24] are different from the ones used in this work (see details in Figure

7.7). However, results for both PP cells are virtually the same. The RS-SDMER shows a

comparably lower cell voltage especially at currrent densities above 2 kA/m2. This difference

increases at higher current densities and it is mainly attributed to a decrease in the bubble

effect due to the rotational speed (ω=84 rad/s) and the zero-gap configuration of the RS-

SDMER. The error bars in Figure 7.7 correspond to the standard deviation of the experiments

as explained in the previous section. It can be observed that for the case of the PP cell studied

here at current densities higher than 6 kA/m2 the standard deviation is larger than that of the

RS-SDMER. This result indicates that using the RS-SDMER allows a more stable operation

at higher current densities. O’Brien et al. [7] reported a cell potential of 3.5 V for the

electrolysis at 3.5 kA/m2 for similar operating conditions and electrodes as used here. This is

in line with our measured value of 3.4 V at 3.5 kA/m2 (see line RS-SDMER – 80oC in Figure

7.7). Newer industrial cell designs with activated cathodes and improved membranes can

achieve lower cell voltages. For instance, an industrial manufacturer reports a cell voltage of

3.1 V for electrolysis at 7 kA/m2 [25], which is 0.15 V lower than the voltage measured for

Chapter 7

127

(a) (b)

Figure 7.5. Effect of rotational speed (ω) on the cell voltage (ECell) of a rotor-stator spinning disc

membrane electrolyzer for chlor-alkali. (a) Cell voltage as a function of the current density (i) for

various rotational speeds. Measurements taken at constant rotational speed and stepwise increase of

current density. Operating conditions: T=24±3oC, Anolyte: 3.5±0.1 M NaCl pH=2.5±0.2, Catholyte

4.0±0.1 M NaOH. (b) Cell voltage as a function of the rotational speed for various current densities.

Measurements taken at constant current density and stepwise increase of the rotational speed.

Operating conditions: T=40±2oC, Anolyte: 2.4±0.1 M NaCl pH=2.5±0.2, Catholyte 3.4±0.1 M NaOH.

(a) (b)

Figure 7.6. Stable operation of the rotor-stator spinning disc membrane electrochemical reactor (RS-

SDMER) as a function of the rotational speed and current density. (a) Standard deviation (σEcell) of the

cell voltage data presented in Figure 7.5b as a function of the rotational speed for various current

densities. Operating conditions: T=40±2oC, Anolyte: 2.4±0.1 M NaCl pH=2.5±0.2, Catholyte 3.4±0.1

M NaOH. The dashed area marks the limits of stable operation according to the definition of σEcell <0.1

V. (b) Flow map of the stable operation of the RS-SDMER. The line denotes the minimum rotational

speed needed to achieve stable operation (σEcell <0.1 V) as a function of the applied current density

according to (a).

0 2 4 6 8 10 12 14 16 18 20 22

3.0

4.0

5.0

6.0

7.0

8.0E

Cel

l (V

)

i (kA/m2)

42 rad/s

63 rad/s

84 rad/s

105 rad/s

40 50 60 70 80 90 100

3.0

4.0

5.0

6.0

7.0

8.0

EC

ell (

V)

(rad/s)

2 kA/m2

6 kA/m2

10 kA/m2

14 kA/m2

20 kA/m2

40 50 60 70 80 90 1000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

E

cell (

V)

(rad/s)

2 kA/m2

6 kA/m2

10 kA/m2

14 kA/m2

20 kA/m2

2 4 6 8 10 12 14 16 18 2030

40

50

60

70

80

Unstable operation

Ecell

>0.1V

Stable operation

Ecell

<0.1V

i (kA/m2)

st

able(

rad/s

)


128

the RS-SDMER. It is expected that with these new materials a significant improvement in cell

potential can be obtained.

Figure 7.7. Comparison of the experimental cell voltage as a function of current density for the rotor-

stator spinning disc membrane electrochemical reactor (RS-SDMER), the parallel plate cell (PP cell)

studied here, and a PP cell reported in the literature. Operating conditions: = PP cell (reported by

Chandran et al. [24]), T=90oC, saturated NaCl, 10 M NaOH, RuO2-TiO2 anode, steel cathode,

membrane: Nafion 901, 34.3 m2 electroactive area. = PP cell (this work), T=53±2oC, Anolyte:

5.0±0.1 M NaCl pH=2.5±0.2, Catholyte 10.0±0.1 M NaOH, 10 m2 electroactive area. = RS-

SDMER (this work), T=42±2oC, Anolyte: 3.0±0.1 M NaCl pH=2.5±0.2, Catholyte 10.4±0.1 M NaOH,

ω=84 rad/s. = RS-SDMER (this work), T=80±2oC, Anolyte: 5.0±0.1 M NaCl pH=2.5±0.2,

Catholyte 10.4±0.1 M NaOH, ω=84 rad/s.

7.3.1.3 Temperature and concentration effect (1)

In addition to the effect of the rotational speed on the cell voltage, the effects of temperature

and concentration have also been investigated. Results of the temperature effect are shown in

Figure 7.8 for various current densities at 80 rad/s. It can be observed that lower cell voltages

are obtained at the highest temperature of 80o C as expected from the Nernst equation [26]. At

20 kA/m2 the cell voltage decreased from 6.5 V at 42oC to 5.5 V at 81oC. This can be

explained by the increase in the conductivity of the membrane and the decrease of the

thermodynamic potential at higher temperatures. The effect of the NaCl concentration is

shown in Figure 7.9 where it is observed that increasing NaCl leads to lower cell voltages.

Figure 7.9a shows the cell voltage as a function of the NaCl concentration at 80 rad/s for three

current densities. At the highest current density (20 kA/m2) the cell voltage decreased from

7.2 V at 1.6 M NaCl to 6.3 V at 3.5 M NaCl. The NaCl has an effect on various components

of the cell voltage. Primarily on the thermodynamic potential, which increases with

decreasing NaCl concentration. Also, the chlorine current efficiency is linked to the NaCl

concentration [27] which in turn has an effect on the overpotential. Results in Figure 7.9b

0 2 4 6 8 10 12 14 16 18 20 22

3.0

4.0

5.0

6.0

7.0

8.0

9.0

EC

ell (

V)

i (kA/m2)

PP cell 34.3 cm2- 90

oC (Chandran et al.)

PP cell 10 cm2- 53

oC (this work)

RS-SDMER - 42oC (this work)

RS-SDMER - 80oC (this work)

Chapter 7

129

show the effect of the rotational speed at various NaCl concentrations at 20 kA/m2. At lower

concentrations the mass transfer effects play a more significant role, and therefore it is

expected that the rotational speed has a higher impact than at high concentrations. However

only a slightly more pronounced effect of the rotational speed is observed at the lowest

concentration, hence no strong mass transfer dependency. This is an indication of the decrease

of the bubble coverage at higher rotation speeds which has been shown in our previous work

[28]. For instance, at the lowest concentration studied here of 1.6 M NaCl, the cell voltage

decreased 0.3 V from 0.73 rad/s to 105 rad/s, whereas a decrease of 0.2 v from 0.73 rad/s to

105 rad/s was observed at 3.5 M NaCl. The effect of the NaOH concentration is shown in

Figure 7.10 for experiments at 84 rad/s and at three current densities. A slight increase in the

cell voltage at the highest NaOH concentration of 10.4 M for all current densities can be

observed. The cell voltage is virtually the same for 3.1 and 4.5 M NaOH for all current

densities, and an average increase of 0.35 v is observed from 4.5 M to 10.4 M. The increase in

the cell voltage at highest concentration of sodium hydroxide is similar to the trend of sodium

hydroxide and cation-exchange membrane conductivity as reported in the literature [7].

Figure 7.8. Effect of temperature on the cell voltage of the rotor-stator spinning disc electrochemical

reactor for chlor-alkali. Cell voltage (ECell) as a function of the temperature (T) for various current

densities. Operating conditions: T=40±2oC, Anolyte: 4.0±0.5 M NaCl pH=2.5±0.2, Catholyte 10.4±0.5

M NaOH, ω=84 rad/s.

40 50 60 70 80

3.0

4.0

5.0

6.0

7.0

8.0

EC

ell (

V)

T (oC)

6 kA/m2

10 kA/m2

14 kA/m2

20 kA/m2


130

(a) (b)

Figure 7.9. Effect of NaCl concentration on the cell voltage of the rotor-stator spinning disc

electrochemical reactor for chlor-alkali. (a) Cell voltage (ECell) as a function of the anolyte (NaCl)

concentration (CNaCl) for various current densities at 84 rad/s. Operating conditions: T=24±3oC,

Anolyte: 1.6, 2.4 and 3.5 M NaCl pH=2.5±0.2, Catholyte 4.0±0.1 M NaOH, ω=84 rad/s. (b) Cell

voltage (ECell) as a function of the rotational speed (ω) for various anolyte concentrations at 20 kA/m2.

Operating conditions: T=24±3oC, Anolyte: 1.6, 2.4 and 3.5 M NaCl pH=2.5±0.2, Catholyte 4.0±0.1 M

NaOH.

7.3.1.1 Membrane permselectivity (2)

The membrane permselectivity is an important factor in the efficiency of the chlor-alkali

process. This is why the membrane permselectivity has also been investigated in the RS-

SDMER. The membrane permselectivity (SNa+) is defined as:

Na Nan F

Si A t

Where is the number of moles of sodium, is the Faraday constant, i is the current

density, A is the surface area and t is the time.

The total amount of moles of sodium transferred is calculated from:

Na OHi A t n n

In which OH

n is determined from the acid addition to the anolyte and the oxygen production.

The amount of acid needed to keep the pH stable was used to calculate the consumed number

of proton moles. The measurements were corrected with the pH change and from the the

oxygen production. The change in the pH during operation is caused by the side reaction of

oxygen evolution. The current efficiency due to oxygen evolution is assumed 95% which is

typically reported in literature [27] for this type of anodes. Figure 7.11a-b show the trend of

the estimated proton moles from oxygen production and the number of proton moles based on

1.5 2.0 2.5 3.0 3.5

3.0

4.0

5.0

6.0

7.0

8.0E

Cel

l (V

)

CNaCl

(M)

6 kA/m2

10 kA/m2

20 kA/m2

70 75 80 85 90 95 100 1056.0

6.5

7.0

7.5

8.0

EC

ell (

V)

(rad/s)

NaCl concentration

1.6 M

2.4 M

3.5 M

Nan F

Chapter 7

131

the added acid to keep the pH stable for two different anolyte concentration as a function of

current density respectively.

Figure 7.10. Effect of NaOH concentration on the cell voltage of the rotor-stator spinning disc

electrochemical reactor for chlor-alkali. a) Cell voltage (ECell) as a function of the catholyte (NaOH)

concentration (CNaOH) for various current densities at 84 rad/s. Operating conditions: T=41±3oC,

Anolyte: 3.5±0.2 M NaCl pH=2.5±0.2, Catholyte 3.1, 4.5 and 10.4 M NaOH, ω=84 rad/s.

(a) (b)

Figure 7.11. Number of H+ moles in the anolyte solution from the (a) oxygen production (b) the

amount of acid needed to keep the pH stable as a function of current density. Operating conditions:

T=24±3oC, Anolyte: 1.6 and 3.5 M NaCl pH=2.5±0.2, Catholyte 4.0±0.1 M NaOH, ω=84 rad/s.

The change in the sodium selectivity of the membrane is shown in Figure 7.12 as a function

of current density. A general increasing trend is observed as the current density increases.

Generally a steep increase of sodium transport number from 0.90 at 2 kA/m2 to 0.95 at 8

kA/m2 is observed. The permselectivity increases up to 0.95 and 0.98 at higher current

densities. Sodium permselectivity values between 0.9 and 1 are in line with the values of

membrane permselectivity reported in literature [7,29]. On the other hand, a decrease in

membrane permselectivity at high current densities was observed in the system of sodium

2 4 6 8 10

3.0

4.0

5.0

6.0

7.0

8.0

EC

ell (

V)

CNaOH

(M)

6 kA/m2

10 kA/m2

20 kA/m2


132

hydroxide electrolyte as both anolyte and catholyte [19] for which we do not have a concrete

explanation. Figure 7.12a presents the sodium selectivity as a function of current density for

three different concentrations of anolyte. It is observed that at the lowest concentration of

anolyte, the sodium selectivity is the highest measured. This could be explained based on the

calculated concentration profile of sodium as presented in our previous work [30]. A lower

concentration of anolyte results in decrease of the sodium ion concentration in the membrane

and reaching the limit of fixed group cocnentration. This results in decrease of the co-ion

concentration in the membrane and reching zero concentration which leads to increase in the

permselectivity up to 1 for the lowest concentration of anolyte. Figure 7.12b shows the effect

of NaOH concentration on the permselectivity of the membrane. It can be observed that the

highest concentration of NaOH (10.4M) has the lowest selectivity, ranging from 0.92 at 6

kA/m2 to 0.97 at 20 kA/m2. This is attributed to the higher chance of back transport of

hydroxide ions in more concentrated NaOH environment compared to lower NaOH

concentrations.

7.3.1 Thin-film spinning disc membrane electrolyzer (2)

Besides the rotor-stator configuration of the SDMER the thin film configuration has been

investigated as well. The cell voltage results are presented in Figure 7.13 and compared to the

rotor-stator configuration for two rotation speeds. The cell voltage in the rotor-stator

configuration is comparable with the results of the thin film configuration. It has been shown

by other people that the thin film spinning disc reactor has a high mass transfer [14,31,32].

Additionally, more efficient removal of produced gas from a gauze surface with increase in

rotation speed has been demonstrated previously [28]. Proper wetting by high jet velocity on

the center of the disc is essential. The results show that both configurations have similar

performance efficiency for the cell voltage. Additionally, these results in general suggests that

both configurations seems to give promising lower cell voltage compared to a conventional

parallel plate cell.

Conclusions

The spinning disc membrane electrochemical reactor is a suitable technology for the

intensification of the chlor-alkali process allowing stable operation at high current densities.

Two configurations (rotor-stator (RS) and thin film (TF)) are reported and compared with a

conventional parallel plate cell. Similar voltage vs current density curves are obtained for both

RS and TF configurations. A decrease of 0.9 V in the cell voltage is observed at 6 kA/m2

when increasing the rotational speed from 40 to 60 rad/s in the RS-SDMER. Results show

that the effect of the rotational speed is more pronounced at high current densities, where the

Chapter 7

133

(a) (b)

Figure 7.12. Membrane selectivity towards Na+ ion (SNa+) as a function of the current density for the

chlor-alkali electrolysis in a rotor-stator spinning disc electrochemical reactor. (a) Effect of anolyte

concentration (NaCl) on membrane selectivity. Operating conditions: T=24±3oC, Anolyte: 1.6, 2.4 and

3.5 M NaCl pH=2.5±0.2, Catholyte 4.0±0.1 M NaOH, ω=84 rad/s. (b) Effect of catholyte

concentration (NaOH) on membrane selectivity. Operating conditions: T=41±3oC, Anolyte: 3.5±0.2 M

NaCl pH=2.5±0.2, Catholyte 3.1, 4.5 and 10.4 M NaOH, ω=105 rad/s.

Figure 7.13. Comparison of thin film (TF) and rotor-stator (RS) configurations of the spinning disc

membrane electrochemical reactor (SDMER). Cell voltage as a function of the current density (i) for

two rotational speeds (84 and 105 rad/s) for two reactor configurations (TF-SDMER and RS-

SDMER). Measurements taken at constant rotational speed and stepwise increase of current density.

Operating conditions: T=25±5oC, Anolyte: 4.5±0.2 M NaCl pH=2.5±0.2, Catholyte 6.3±0.2 M NaOH,

ω= 85 and 105 rad/s.

gas production is higher. Lower cell voltages are reported for both RS and TF-SDMER

compared to the parallel plate cell. Therefore the SDMER is likely to allow an increase of the

production capacity while maintaining a low cell voltage. The measured values of cell voltage

0 2 4 6 8 10 12 14 16 18 20 220.85

0.88

0.90

0.93

0.95

0.98

1.00S

Na+

(-)

i (kA/m2)

NaCl concentration

1.6 M

2.4 M

3.5 M

0 2 4 6 8 10 12 14 16 18 20 220.85

0.88

0.90

0.93

0.95

0.98

1.00

SN

a+ (

-)

i (kA/m2)

NaOH concentration

3.0 M

4.5 M

10.4 M

0 2 4 6 8 10 12 14 16 18 20 22

3.0

4.0

5.0

6.0

7.0

8.0

EC

ell (

V)

i (kA/m2)

TF-SDMER - 84 rad/s

TF-SDMER - 105 rad/s

RS-SDMER - 84 rad/s

RS-SDMER - 105 rad/s


134

for the RS and TF-SDMER are slightly higher than those typically reported in industry.

Further optimization of the SDMER, including the use of activated cathodes and improved

membranes, is likely to offer even lower cell voltage at high current densities in the future.

Additionally, the effect of operating conditions such as temperature and concentration is

reported for the RS-SDMER. Results show that increasing the temperature from 40 ºC to 80

ºC at 20 kA/m2 causes the cell voltage to decrease from 6.5 V to 5.5 V. At low sodium

chloride concentrations, at which the mass transfer is important, it is shown that increasing the

rotation speed decreases the cell voltage. Increasing the sodium chloride concentration and

decreasing the sodium hydroxide concentration decreases the cell voltage. The membrane

permselectivity in the RS-SDMER is estimated from the measurements of the acid addition

and it is shown that it increases with increasing current density to values between 0.95 and

0.98 at current densities of 20 kA/m2.

Bibliography

[1] A. Stankiewicz, J. Moulijn, Process intensification: transforming chemical engineering,

Chem. Eng. Prog. (2000) 22–34.

[2] A. Stankiewicz, J.A. Moulijn, Re-Engineering the Chemical Processing Plant: Process

Intensification, CRC Press, 2003.

[3] Questions and answers on the chlor alkali sector and the EU emission trading system

(ETS), 2010.

[4] Eurochlor, The amazing chlorine universe, Brussels, 2014.

[5] Chlorine Industry Review 2014-2015, (n.d.).

[6] The European Chlor-Alkali industry: an electricity intensive sector exposed to carbon

leakage, n.d.



[8] S. Trasatti, Progress in the understanding of the mechanism of chlorine evolution at

oxide electrodes, Electrochim. Acta. 32 (1987) 369–382.

[9] E. Endoh, H. Otouma, T. Morimoto, Advanced low hydrogen overvoltage cathode for

chlor-alkali electrolysis cells, Int. J. Hydrogen Energy. 13 (1988) 207–213.

Chapter 7

135

[10] H.S. Burney, Chlor-alkali and Chlorate Technology: R.B. MacMullin Memorial

Symposium : Proceedings of the Symposium, The Electrochemical Society, 1999.

[11] H. Miyake, The design and development of Flemion membranes, in: T.C. Wellington

(Ed.), Mod. Chlor-Alkali Technol. Vol. 5, Springer Netherlands, Dordrecht, 1992: pp.

59–80.

[12] ThyssenKrupp Uhde GmbH, Chlor alkali electrolysis plants, Dortmund, 2015.

[13] B.B. Johnson, Zero gap cell, PCT/US1983/001871, 1985.



[15] M. Meeuwse, Rotor-stator spinning disc reactor, Technische Universiteit Eindhoven,

2011.



[17] D. Reay, C. Ramshaw, A. Harvey, Reactors, in: Process Intensif. Eng. Effic. Sustain.

Flex., Second edi, Elsevier, 2008: pp. 103–186.

[18] J. van der Schaaf, P. Granados Mendoza, S. Moshtarikhah, D. Bindraban, M.T. de

Groot, Electrochemical cell, 2015.


Cation-exchange membrane performance under high current density, In Prep. (2016).

[20] Micro Flow Cell, Electrocell. (n.d.). http://www.electrocell.com/fileadmin/pdf/MFC-

brochure.pdf.

[21] D.C. Harris, Quantitative Chemical Analysis, 5th ed., W. H. Freeman, 1999.

[22] E.H. Swift, G.M. Arcand, R. Lutwack, D.J. Meier, Determination of Chloride, Anal.

Chem. 22 (1950) 306–308.

[23] H. Cheng, K. Scott, C. Ramshaw, Chlorine evolution in a centrifugal field, J. Appl.

Electrochem. 22 (2002) 831–838.

[24] R.R. Chandran, D.-T. Chin, Reactor analysis of a chlor—alkali membrane cell,

Electrochim. Acta. 31 (1986) 39–50.


136

[25] G.G. Botte, Electrochemical Manufacturing in the Chemical Industry, Electrochem.

Soc. Interface. (2014) 49–55.

[26] A.J. Bard, Electrochemical Methods: Fundamentals and Applications, 1980.

[27] F. Hine, Electrochemical Behavior of the Oxide-Coated Metal Anodes, J. Electrochem.

Soc. 126 (1979) 1439.


Gas bubble removal from a gauze surface in a thin film spinning disc reactor, In Prep.

(2016).

[29] A.A. Gronowski, Factors Which Affect the Permselectivity of Nafion® Membranes in

Chlor-Alkali Electrolysis, I., J. Electrochem. Soc. 138 (1991) 2690.


Multicomponent ion transport in a mono and a bilayer cation-exchange membrane at

high current density, In Prep. (2016).

[31] G. Peev, D. Peshev, A. Nikolova, Gas absorption in a thin liquid film flow on a

horizontal rotating disk, Heat Mass Transf. 43 (2007) 843–848.

[32] J.R. Burns, R.J.J. Jachuck, Determination of liquid–solid mass transfer coefficients for

a spinning disc reactor using a limiting current technique, Int. J. Heat Mass Transf. 48

(2005) 2540–2547.

137

Conclusions and outlook

Conclusion

This thesis describes the efficiency and performance of cation-exchange membranes in an

intensified electrochemical reactor suitable for the chlor-alkali electrolysis. The reactor is a

zero-gap spinning disc membrane electrolyzer, and it works based on the concept of spinning

disc technology. It uses high shear and gravity forces which increase the mass transfer and

mixing toward the electrodes and the membrane in a zero-gap configuration. The cation-

exchange membrane is the core of the electrolyzer, and one of the key contributors to the cell

voltage. Also, the permselectivity of the membrane determines the current efficiency of the

process. In this thesis cation-exchange membranes have been investigated experimentally and

modeled to study their performance especially at high current densities.

In Chapter 2 the conductivities and permselectivities of mono and bilayer perfluorinated

membranes have been measured is a sodium hydroxide system. The effect of various

operating parameters, i.e. sodium hydroxide concentration (10-32 wt%), temperature (40-80

ºC) and current density (0.86-20 kA.m-2) was investigated. It has been found that the

membrane conductivity increases with increasing current density. This is potentially

beneficial for industrial electrolysis processes, since it enables higher production rates without

an excessive increase in energy costs. On the other hand, the permselectivity of the

membranes decreases in the sodium hydroxide system with increasing the current density.

Furthermore, at high concentrations of the sodium hydroxide in the anolyte, the membrane

conductivity, permselectivity and water transport number decrease.

In Chapter 3 the experimental results of the conductivity and permselectivity for the mono

layer membrane, Nafion N-1110, have been used to validate a mathematical model using the

Nernst-Planck equation. A qualitative membrane swelling model has been used to explain the

non-ohmic increase observed experimentally in the membrane voltage drop. It is concluded

that at high current densities the membrane swells and as a consequence pore channels

8


138

become larger, and a higher number of active pores contributes to the ion transport inside the

membrane.

In Chapter 4 the Nernst-Planck model has been extended to a bilayer membrane by using a

logistic function to describe the change of properties between the sulfonate and the

carboxylate layer. The performance of the mono and bilayer membranes in the chlor-alkali

process has been compared especially at high current densities. The model predicts that the

sodium selectivity in the carboxylate layer is higher than the sulfonate layer, which results in

a low sodium concentration region at the interface between the layers. The decrease in

hydroxide concentration is more pronounced in the bilayer membrane, which makes it more

selective to sodium ions. Theoretically, the bilayer membranes proved to be more efficient

than the mono layer membranes especially at high current densities.

In Chapter 5 Maxwell-Stefan modeling of multicomponent ion transport in a membrane for

the chlor-alkali system was developed using an augmented matrix. The diffusion coefficients

reported by different authors were investigated in the model and were found to have a large

influence on the results of the modeling. It was concluded that having reliable data for binary

diffusion coefficients plays a key role in obtaining reliable concentration profiles.

In Chapter 6 the gas removal efficiency from a gauze surface in a thin film spinning disc

reactor was studied by determining the overall reaction rate parameter as a function of

rotation speed. It was shown that increasing the rotation speed results in formation of a

thinner liquid film and improves the removal of produced gas from the gauze surface. This

makes the thin film spinning disc reactor suitable for gas evolving reactions.

In Chapter 7 the performance of two types of spinning disk membrane electrolyzers has been

investigated. Both the thin film and the rotor-stator configurations of the spinning disc

membrane electrolyzer showed a significantly lower cell voltage compared to the

conventional parallel plate cells, especially at high current densities. This clearly shows the

benefits of the spinning disk membrane electrolyzers. Additionally, the effect of current

density, concentration of anolyte and catholyte, temperature and rotation speed were

investigated in the spinning disc membrane electrolyzer. It was observed that especially at

high current densities there is a high impact of rotation speed on reduction of the cell voltage.

This is because at high rotation speeds the removal of the produced gas becomes more

efficient as it was shown in Chapter 6. The effect of rotation speed is clearer at low

concentrations of sodium chloride where mass transfer plays an important role. Increasing the

temperature from 40 ºC to 80 ºC decreased the cell voltage from 6.5 V to 5.5 V. The cell

voltage decreased at higher sodium chloride and sodium hydroxide concentrations,

respectively. The experiments in the spinning disc membrane electrolyzer showed an increase

of the membrane sodium selectivity as a function of current density, which was in contrast

with the decreasing sodium selectivity observed in Chapter 2 . At the moment it is unclear

how this can be explained.


139

Outlook

8.2.1 Membrane performance

This research shows the importance of improving the cation-exchange membranes to enable

process intensification of the chlor-alkali process. High performance membranes, which

increase mixing and turbulence, have been already designed [1]. However, this is no longer a

need in the spinning disc membrane cell electrolyzer. There is room for further improving the

structure of cation-exchange membranes to enable operation at higher current densities. The

swelling model, which helped predicting the non-ohmic increase of the membrane voltage

drop suggests that the pore diameter and structure of the membrane has a large influence on

the membrane resistance. Therefore, having more uniform and larger channel provides an

easier path for the ion transport and as a result lower voltage drop. However, this could lead to

a lower selectivity. Non-uniform and narrow channel structures seem to lose their function

when they are in a dehydration state. Therefore, it is recommended to work on developing

more homogeneous ion clusters in the membranes. Furthermore, the ion transport modeling in

bilayer membranes which was presented in Chapter 4 showed that at high current densities the

concentration of sodium ions reaches the fixed ionic group concentration as presented

schematically in Figure 8.1. This results in high selectivity of the membrane, however, the

whole length of the valley (ds) is not necessary. Therefore, the resistance of the bilayer

membranes can be decreased by reducing ds in the sulfonate layer. Another important aspect

when reducing the membrane thickness is to keep the structural integrity of the membrane.

This is typically attained using the reinforcements in the membrane. Fine mesh electrodes in a

zero-gap configuration of the electrolyzer could play a support role for the mechanical

strength of the membrane and replace the internal reinforcement in the membrane.

Figure 8.1. Sodium ion concentration profile over the membrane layers: sulfonate and carboxylate

layers; current density of 20 kA.m-2. Cs and Cc are the fixed ionic group concentrations of the sulfonate

and the carboxylate layers, respectively. ds is the length of the sulfonate layer in which the

concentration of sodium ions reaches the fixed ionic group concentration.


140

Additionally, the electrode and membrane materials used in the spinning disc membrane

electrolzyer were not the state of the art materials. Therefore, improvements in the design of

the electrodes and the membrane could help to have a more uniform current distribution at the

membrane surface. The sodium transport number is generally higher in the carboxylate layer

in comparison with the sulfonate layer. Therefore, maintaining a high concentration at the

interface of the layers by designing a sulfonate layer that has a high sodium transport number

at high current density is desirable.

All this suggests that having more in depth knowledge of the membrane structure and a better

understanding of the ion transport inside the membrane at extreme operating conditions such

as high current density is beneficial. This is why preliminary experimental research has been

carried out to measure the sodium ion concentration inside the membrane as a function of

position with NMR. The advantage of NMR is that it is selective for certain species.

Furthermore, the concentration profiles of both sodium and proton ions (an indication of

water) can be measured in-situ inside the membrane. The electro-osmotic transport of water in

a hydrated membrane has been investigated by several authors [2–5]. The electro-osmotic

drag coefficient of methanol in Nafion N117 has been studied by Halberg, et al. [6]. They

tried to measure the electrokinetic transport and self-diffusion of methanol and water in a

Nafion membrane.

8.2.2 Concentration visualization of ions in cation-exchange

membranes using NMR technique

In our preliminary work we tried to measure the concentration of sodium ions in a 30 mm

stack of monolayer Nafion. The NMR system used for this experiment consisted of a 1.5 T

magnetic field inside a whole-body medical scanner. The setup has a large experimental space

which allows the measurement of different frequency ranges, a low frequency range for 23Na

and a high frequency range for 1H. A detailed description of the set-up and the experimental

method is explained by Pel, et al. [7] using the same technique to measure the concentration

of 1H, 23Na and 35Cl in cementitious materials. The concentration profiles of 23Na and 1H were

measured with a spatial resolution of 6 mm and 2 mm respectively with a spin-echo

technique. This spatial resolution made measuring the concentration of ions in one piece of

membrane impractical. In the first attempt, circular membrane pieces with a diameter of 12

mm were cut from a monolayer Nafion 1110 membrane sheet, as depicted in Figure 8.2a. The

membrane pieces were then equilibrated in a 6 M sodium hydroxide solution for two days,

and then stacked inside the holder as depicted in Figure 8.2b to make a 30 mm thick

membrane. A cross shape support was placed on each side of the stack holder to push the

membranes in place and prevent the membranes from moving or getting curved due to

swelling. The stack holder was closed with two caps and screwed with an open end on one

side for injecting the solution. On the other side a reference solution with a known

concentration was attached to the membrane holder.


141

Thereafter, the stack holder was placed in the NMR set-up to check the detection of 23Na and 1H signals and get the initial state of the sample. In the next step, sodium chloride in a heavy

water solution of 6 M was injected into the reservoir of the membrane holder. This was to

distinguish the 1H and 2H. The 23Na and 1H signals were measured in time intervals of days.

The profiles of signal intensity as a function of position in the membrane are presented in

Figure 8.3. The signal intensities over four days showed that 1H was replaced by 2H, however

the high concentration of sodium ions in the sample and the reservoir did not allow to observe

a noticeable change in the 23Na signal intensity.

(a) (b)

Figure 8.2. (a) Cutting 12 mm diameter membrane circles and make a 30 mm thick membrane stack

(b) The membrane stack holder with a cross shape support and caps for closing.

(a) (b)

Figure 8.3. Signal intensity of (a) 1H and (b) 23Na in Nafion, N-1110, in different time intervals after

one, two, three and four days (NMR profiles were measured by L. Pel and P.A.J. Donker).

In a different approach a sheet of a bilayer membrane, NX-982, which was already in the

sodium form was covered with Vaseline grease on one side to avoid the capillary effect of

solution. Then the membrane was rolled to make a one continuous sample with a diameter of

20 mm and a length of 100 mm. The sample was placed in the NMR set-up to measure the

initial state. Thereafter, one side of the sample was placed in a solution of 6 M sodium


142

chloride and measured for two days. The results are shown in Figure 8.4. The ingress of 23Na

was observed in Figure 8.4a. Figure 8.4b shows an egress of 1H in the beginning followed by

and ingress of 1H in the sample which is not expected. The non-homogeneous signal intensity

of 1H is difficult to explain. It can be an indication that the membrane might not have a

homogeneous cluster structure. Furthermore, the sample holder contains 1H and can affect the

non-homogeneous signal intensity in Figure 8.4b.

These preliminary results show that measuring the sodium concentration inside a membrane is

challenging but possible with NMR. This research could be continued by carrying out the

measurement during electrolysis operation to have in-situ measurements of the concentration

profiles. This way an experimental validation of the calculated concentration profiles with

either the Nernst-Planck or the Maxwell-Stefan equations can be obtained. A challenge that

remains is the low spatial resolution of NMR, which would need to be improved to also

obtain valuable data for thin membranes.

(a) (b)

Figure 8.4. Signal intensity of (a) 23Na and (b) 1H in a rolled sample of Nafion, NX-982, covered with

Vaseline grease. The signal in the left side of graph (b) before 95 mm shows the membrane section

immersed in the 6 M sodium chloride solution and follows with the solo membrane sample with lower

signal intensity. The arrows indicate that going from black to green lines the signal intensity increases

for sodium and proton (NMR profiles were measured by L. Pel and P.A.J. Donker).

8.2.3 Combined reactor and membrane model for chlor-alkali

process in the spinning disc membrane electrolyzer

NOTE: This section derives from the joint work of P. Granados Mendoza and S. Moshtarikhah within the framework of the SPINCHAL project. Moshtarikhah contributed with the ion-transport model through the

membrane as presented in [8]. Granados Mendoza contributed with the reactor model as presented in [9] and the

implementation of Moshtrarikhah’s membrane model in the reactor model.


143

In our previous work (Chapter 7, [9]) we have presented the approach for modeling the chlor-

alkali spinning disc reactor including material and voltage balances, and considering the

effects of the mass transfer enhancement due to the rotation of the electrodes in the spinning

disc reactor configuration. By solving material balances per compartment in combination with

the electrochemical relations, such as electrode kinetics and electrode potentials, and

considering the effect of the non-ideality of the electrolytes and the dependence of the

physical properties on concentrations and temperatures, the spinning disc membrane

electrolyzer performance has been modeled for a wide range of operating conditions.

However, the previous model [9] does not include a detailed modeling of the ion-transport

inside the membrane and the resulting effect of the operating conditions on the membrane

permselectivity. Especially, the convective transport in the membrane was neglected which is

an important transport term.

Separately, we have also proposed the modeling of the multicomponent ion-transport through

a bi-layer cation-exchange membrane based on the Nernst-Planck equation [8]. The material

balance over the membrane is described by a set of partial differential equations describing

the flux of ionic species. The flux of species is described with the Nernst-Planck equation.

The convective velocity inside the membrane, which is position dependent, is calculated

based on the Schlögl equation and the continuity equation. At first, the convective velocity at

the anolyte side is calculated based on the total potential gradient. Thereafter, the local

convective velocity is calculated based on the equation of continuity and the local density

inside the membrane. The boundary condition is presented based on the Donnan equilibrium

phenomena at the membrane-solution interface. By solving this system of equations the

membrane voltage drop and the membrane permselectivity are calculated as an output [8].

Here, we propose an approach for the mathematical modeling of the chlor-alkali process by

combining the reactor model described in [10] and the membrane model elaborated in [8] in

order to predict the effect of the various process conditions on the performance of a zero-gap

spinning disc electrolyzer with a bilayer membrane. The analysis of the reactor cell voltage,

chlorine current efficiency and membrane efficiency can be achieved by combining the

material and voltage balances of the anolyte and catholyte compartments, and coupling the

concentrations at the membrane with a mass and voltage balance in the bilayer membrane.

The combined model of reactor and membrane is implemented and solved using MATLAB.

The algorithm that is used to solve the model is shown in Figure 8.5. First, the initial

parameters are loaded and an initial guess of the membrane selectivity and voltage drop is

made. Then, the reactor model is solved together with the mass transfer, electrochemical,

activity and physical property sub-models. Next, the concentrations at the membrane surface

are calculated and are used as input for solving the membrane model. The ionic transport

numbers are re-calculated from the Nernst-Planck equation and are compared with the initial

guesses. The iteration continues until the difference between the transport numbers obtained


144

from the current and previous iteration is smaller than the tolerance. At this point the model

terminates and the output is recorded.

Figure 8.5. The flowchart of the solution strategy of the combined reactor and membrane model in the

zero-gap spinning disc membrane electrolyzer.

The preliminary results are presented in Figure 8.6. In this figure we present the concentration

profile of sodium ions inside the membrane and the adjacent anolyte and catholyte solutions.

Regions I and IV present the anolyte and catholyte solutions, respectively and regions II and

III represent the sulfonate and the carboxylate layers of the bilayer membrane. Figure 8.6a

shows the effect of current density on the profile of the sodium ion for two different current

densities of 1 kA.m-2 and 20 kA.m-2. It is observed that the concentration profile inside both

sulfonate and carboxylate layers is linear at 1 kA.m-2. At 20 kA.m-2 the concentration gradient

in the carboxylate layer becomes steeper and the concentration in the sulfonate layer

decreases and reaches the fixed ionic group concentration. Figure 8.6b presents the effect of

rotation speed of the spinning disc membrane electrolyzer on the concentration profiles in the

membrane and the boundary layers of the membrane. The Na+ concentration at the membrane

interface was lower than the bulk concentration at higher rotation speed. In fact, similar

results were found in our previous work with respect to the current density: at increasing

current density the Na+ concentration at the membrane interface decreases on the catholyte

side and increases on the anolyte side. As it was explained in our previous work this could be

caused by the convective flux in the boundary layers. Having a stronger convective flow in

the anolyte results in build-up of ion concentration higher than what can be transferred

through the membrane. The counter effect occurs at the catholyte side.

We observe that high values for the transport number of both anions (OH- and Cl-) are

obtained especially at low rotational speeds. It must be noted that the convective velocity is

iterated during the solution of the membrane module. This iteration procedure should be

examined. A thorough analysis of the model predictions of the different transport

contributions in the Nernst-Planck equation is necessary, unfortunately it is out of the scope

of this work. For future work it is also suggested to model both the electrolyte solution and


145

membrane using the Nernst-Planck approach. In this way we expect to have a more

reasonable account of the transport contributions inside the membrane.

(a) (b)

Figure 8.6. Sodium ion concentration profile over the dimensionless position. Regions: I = Anolyte, II

= Sulfonate layer, III = Carboxylate layer and IV = Catholyte. Left: Concentration profiles for 1 and

20 kA/m2 at ω=100 rad/s. Right: Concentration profiles for 1, 10 and 100 rad/s at 20 kA/m2.

Operating conditions: T=80oC, Anolyte: 25wt% NaCl with pH=2, Catholyte 32wt% NaOH,

QIN=10x10-6 m3/s.

Bibliography

[1] W.C. Theobald, High Current Density Operation of Chlor-Alkali Electrolysers - the

Standard for the New Millennium, in: Mod. Chlor-Alkali Technol. - Vol. 8, London,

2001.

[2] K.D. Kreuer, M. Schuster, B. Obliers, O. Diat, U. Traub, A. Fuchs, et al., Short-side-

chain proton conducting perfluorosulfonic acid ionomers: Why they perform better in

PEM fuel cells, J. Power Sources. 178 (2008) 499–509.

[3] F. Meier, G. Eigenberger, Transport parameters for the modelling of water transport in

ionomer membranes for PEM-fuel cells, Electrochim. Acta. 49 (2004) 1731–1742.

[4] X. Ren, W. Henderson, S. Gottesfeld, Electro-osmotic Drag of Water in lonomeric

Membranes New Measurements Employing a Direct Methanol Fuel Cell, Electrochem.

Soc. 144 (1997) 0–3.


146

[5] T.A. Zawodzinski, C. Derouin, S. Radzinski, R.J. Sherman, V.T. Smith, T.E. Springer,

et al., Water Uptake by and Transport Through Nation® 117 Membranes, Electrochem.

Soc. 140 (1993) 1043–1047.

[6] F. Hallberg, T. Vernersson, E.T. Pettersson, S. V. Dvinskikh, G. Lindbergh, I. Furó,

Electrokinetic transport of water and methanol in Nafion membranes as observed by

NMR spectroscopy, Electrochim. Acta. 55 (2010) 3542–3549.

[7] L. Pel, P.A.J. Donkers, K. Kopinga, J.J. Noijen, 1H, 23Na and 35Cl Imaging in

Cementitious Materials with NMR, Appl. Magn. Reson. (2016).


Multicomponent ion transport in a mono and a bilayer cation-exchange membrane at

high current density, In Prep. (2016).

[9] P. Granados Mendoza, M.T. de Groot, J.T.F. Keurentjes, J.C. Schouten, J. van der

Schaaf, Modeling of the chlor-alkali process using a rotor-stator spinning disc

membrane electrochemical reactor, in prep. (2016).

[10] P. Granados Mendoza, Modeling of the chlor-alkali process using a rotor-stator

spinning disc membrane electrochemical reactor, Prep. (2016).

Acknowledgements

Now that this chapter of my life came to an end, I would like to show my gratitude to all those

people whose help, support and presence made this a journey with so much pleasure.

First, I would like to thank my supervisors, Jos Keurentjes, Jaap Schouten, John van der

Schaaf and Thijs de Groot for their guidance and friendship. I am thankful for the many

fruitful meetings and discussions we had during the project. Jos, thank you very much for

your precise and useful comments during the course of our monthly meetings. Jaap, I am

grateful for the opportunely you gave me to conduct my PhD in the SCR group. I always

appreciated your quick answers to my emails always starting with nice words followed by

detailed professional comments on my writings. John, I am grateful for having you as my

daily supervisor, for your eagerness to discuss problems, for your encouragement and having

faith in me. Your friendly attitude turned these challenging years into a memorable experience

for me. Thijs, thank you for your time and availability and for the productive discussions

during our progress meetings, skype meetings and a lot of other meetings we had.

To the experts from AkzoNobel, Hans Lammers, Marco Waas, Ton Manders, Johan Breugem,

Rob Bergevoet, Willem Koelewijn, Bert Vreman, Jan van de Wetering, Fred Witvliet, Remko

van der Meijden, thank you for your input and help in scientific, practical and experimental

aspects of the project. To Leo and Pim, I appreciate letting me use the NMR set-up and your

eagerness in collaboration.

To the committee members of my defense, Elisabet Ahlberg, Ruud van Ommen and Kitty

Nijmeijer, thank you for dedicating your time to read and evaluate my thesis.

To the SCR group for being my second home place during the past years. To Denise, thank

you for your countless helps for my endless questions. You are really a role model of an

organized and accurate person and the hard core of the SCR.

To Madan, thank you for the challenging design and mechanical drawings of our patented

reactor and your cheerful approach. To all people from the workshops, especially Erik, Dolf,

Frans, Paul and Jan, thank you for your eagerness to help and for your time and effort in

solving all the small and big challenges of my experimental set-up. You are all technical

heroes.

To Carlo, thank you for keeping all of us safe in the lab and for taking care of us with restrict

safety rules. To Peter and Marlies, thank you for your help in the lab, being my chemical

shopping pals and the nice chats during the coffee breaks.

To my SPINCHAL mates, Paola, Slavisa and Michiel. Thank you for all the many beautiful

moments we shared during the amazing trips, after work drinks and many more. Paola, let me

write a separate book on that and say here thanks for being not only my project partner, office

mate, great friend, but also always being there for me. Slavisa, thank you for your concerns

Acknowledgements

148

and being always caring and supportive. Michiel, thanks for always being foozool in the most

positive and helpful way.

To my students, Nicky, Clément, Anne, Jasper and Ria, thank you for your hard work and

enthusiasm during the project and your friendship.

To my office mates, Jack, Shima and Myrto, Thank you for the nice moments we shared in

the office which made STW 1.25 the warmest office of the corridor.

To the ladies, Dulce, for spreading positive energy around, Lara, for giving useful advices and

care taking, Emila, for eagerness to help or discuss at any time, Violeta, for being so precise

and helpful, Fer, for teaching your strong willpower, Anto, for always cheering me up and

Nopi, for your nice smiles and the delicious cakes. Thank you all for all the nice gatherings

we had in and outside the university, during event arrangements, during the nice short trips

and the nice long evening talks after work.

To all the other people in the SCR group, who either finished, started, left or stayed during my

time in there. To Xander, Mart, Martin, Ivana, Lida, Christine, Qi, Jiaqi, Jun, Mamoun,

Faysal, Carlos, Frans, Vitaly, Kevin, Vladan, Leticia, Kathrine, Martijn, Miguel and all other

colleagues of the SCR corridor.

To my friends in Eindhoven, Samaneh & Hossein, Elnaz & Arash, Raheleh & Adam, Maryam

& Pouya, Ellahe & Pouyan, Solmaz & Pouya, Maryam & Behrouz, Azar and Hamid, Miran,

Zeljka, thank you for all the nice times we spent together from the brunch, lunch, dinner,

events to all the small trips. Samaneh, Elnaz and Raheleh, thank you for creating a lot of

beautiful memories for me and being in the four… group with me. To Lida, Arash, Somayeh,

thank you for your encouragements, friendship and the nice chats we had in or outside the

Helix building.

To my friends who are all over the world, Laleh, Mozhgan, Sanaz, Farhang, Mona, Bita,

Mohammad, and many more, thank you for your encouragement and support throughout these

years.

To my family, I would like to say how grateful I am for the fortune of being loved by you.

You mean the whole world to me. Mommy, Dadi, there are no words I could use for thanking

you, for your unconditional love and support. My beloved sisters, Sheri and Shaghayegh, for

always being there for me, no matter how many miles distance there were between us. My

inspiring brother-in law, Vahid, for all the motivational talks we had. My lovely angels, Artin

and Tara for always recharging my batteries with your presence and your beautiful smiles

About the author

Shohreh Moshtarikhah was born on 16th

September 1984 in Tehran, Iran. After graduating

from secondary school she carried out her Bachelors in Chemical Engineering at Sharif

University of Technology in Tehran. She obtained her Bachelors degree in 2008 and moved to

Sweden to follow the Master’s program in Chemical Engineering and Energy at Royal

Institute of Technology (KTH). Her master thesis titled “Multicomponent adsorption for

removal of odour compounds from a toluene stream” was carried out at Delft University of

Technology. After obtaining her Masters degree in 2011, she moved to the Netherlands once

again and started her PhD project at the Laboratory of Chemical Reactor Engineering of the

Eindhoven University of Technology under the supervision of prof.dr.ir. J.T.F. Keurentjes,

prof.dr.ir. J.C. Schouten, and dr.ir. J. van der Schaaf. Her PhD project was one of the

SPINCHAL projects and it was in collaboration with AkzoNobel and Alfa Laval to develop a

spinning disc membrane electrolyzer for the chlor-alkali process.

spinning disc membrane electrolyzer : performance of cation- exchange ... · the membrane cell...

Documents