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Hydrophobic copper nanowires for enhancing condensation heat transfer

Rongfu Wen12 Qian Li1 Jiafeng Wu13 Gensheng Wu14 Wei Wang15 Yunfei Chen6 Xuehu

Ma2 Dongliang Zhao1 and Ronggui Yang17

1Department of Mechanical Engineering University of Colorado Boulder CO 80309-0427

USA

2Liaoning Key Laboratory of Clean Utilization of Chemical Resources Institute of Chemical

Engineering Dalian University of Technology Dalian 116024 P R China

3Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education School of

Energy and Environment Southeast University Nanjing 210096 P R China

4 School of Mechanical and Electronic Engineering Nanjing Forestry University Nanjing 210037 P R China

5Advanced Li-ion Batteries Engineering Lab Ningbo Institute of Material Technology and

Engineering Chinese Academy of Sciences Ningbo 315201 P R China

6Jiangsu Key Laboratory for Design amp Manufacture of MicroNano Biomedical Instruments and

School of Mechanical Engineering Southeast University Nanjing 210096 P R China

7Materials Science and Engineering Program University of Colorado Boulder CO 80309-0596

USA

These authors contribute equally

Corresponding author RongguiYangColoradoEdu

1

Supplementary Information

S1 Surface Fabrication

S2 Experimental System for Condensation Heat Transfer

S3 Data Reduction

S4 Droplet Growth and Distribution at Different Surface Subcooling

S5 Theoretical Model for Droplet Jumping in Different Wetting States

Supplementary Videos

1 Droplet behaviors on the nanowired hydrophobic surface at Pv = 60kPa ΔT = 1 K




5 Droplet behaviors on the plain hydrophobic surface at Pv = 60kPa ΔT = 5 K

2


High purity copper (999 purity) is used to fabricate the condensing block (see

Supplementary Section 2) The condensing surface on the condensing block is polished by 2000

grit sandpaper cleaned in an ultrasonic bath with acetone for 10 minutes and then rinsed with

isopropyl alcohol ethanol and deionized water For comparison both plain hydrophobic surface

and nanowired hydrophobic surface has been fabricated as the condensing surface on the block

The plain hydrophobic surface is fabricated by dipping the condensing surface in a 25 mM

n-octadecanethiol (96 n-octadecyl mercaptan Acros Organics) in ethanol solution for 60

minutes at 70 A self-assembly monolayer (SAM) hydrophobic coating forms on the plain

copper surface

To fabricate nanowired hydrophobic surfaces copper nanowires are fabricated on the

condensing surface of the copper condensing block by a two-step porous anodic alumina (PAA)

template-assisted electro-deposition method as shown in Fig S1 The commercial PAA template

(nominal pore size 200 nm from GE Healthcare) formed by electrostatic oxidization is used [1]

Fig S2a shows the schematic of the PAA template used in this work The template has

hexagonal distributed holes with the diameter of ~220 nm and center-to-center spacing of ~380

nm on average (Fig S2b)

The first step of the electrodeposition process is to bond the PAA template onto the copper

condensing block For the bonding process the PAA template is first placed on the clean copper

condensing block The electrolyte solution composed of cupric pyrophosphate (Cu2P2O7xH2O

Sigma-Aldrich) potassium pyrophosphate (K4P2O7 Sigma-Aldrich) ammonium citrate tribasic

3

(C6H17N3O7 Sigma-Aldrich) and DI water (6252100 wt) is pipetted on top of the template

After the template is sufficiently wetted a filter pater wetted with electrolyte solution is placed

on the template which provide a conductive channel for the copper ions from the anode to

cathode (condensing block) Another copper plate is then placed on the filter paper as the counter

electrode Fig S1a shows the stacking structure consisting of the condensing block a PAA

template a filter paper wetted with electrolyte solution and another copper plane on the top of it

(Fig S1a) Uniform pressure is exerted to make sure that the PAA template adhere tightly on the

copper plate by a fastening device (Fig S1c) A constant voltage of -08 V (Electrochemical

Workstation CH Instrument CHI760C) is applied between the counter electrode (copper plane)

and the condensing block During this first-step bonding process copper nanowires are grown on

the copper substrate to serve as the screws that bonds PAA template on top of the copper sample

After 15 minutes of the bonding step the copper sample along with PAA template is released

from the stacking structure

4

Fig S1 Fabrication of nanowired surfaces a-b Schematic illustrating the two-step porous anodized

alumina (PAA)-templated electrodeposition process c Photographs of the fastening device for the first

electrodepostion step ie bonding

Fig S2 The structure of PAA a Schematic showing PAA template size feature b SEM image of the PAA

template

During the second electro-deposition step the condensing block along with PAA template

on the top is placed in a 3-electrode electroplating cell (Fig S1b) A constant voltage of -08 V

versus reference electrode (AgAgCl) is applied for the deposition of copper nanowires The

length of copper nanowires is controlled by the electro-deposition time Here the nanowires with

an average height (length) of 20 microm and 30 microm are fabricated after the electro-deposition in the

3-electrode electroplating cell for 150 and 240 minutes respectively By immersing the sample

in 2 molL NaOH solutions for 180 minutes the PAA template is released from the copper

nanowires grown on copper condensation block The sample is then washed with deionized

water to remove the residual solutions and dried in the vacuum chamber SAM hydrophobic

coating is then applied on copper nanowire surfaces by putting the sample into the 25 mM n-

octadecanethiol (96 n-octadecyl mercaptan Acros Organics) in ethanol solution which is

maintained at 70 for 60 minutes While the SAM hydrophobic coating thickens the diameter

5

of nanowires by ~3 nm due to the deposition of n-octadecyl mercaptan the general morphology

of nanowired surfaces remains unchanged [2]

Fig S3 shows the typical surface morphologies of both plain and nanowired hydrophobic

surfaces using a field-emission scanning electron microscope (FE-SEM JEOL JSM-7401F) For

the plain hydrophobic surface there is no obvious hierarchical and geometrical features except

some polished traces Nanowires on nanowired hydrophobic surfaces are hexagonal distributed

with a diameter (d) and center-to-center spacing (w) of ~220 nm and ~380 nm respectively

which is a replica of the PAA template Based on the nanowire distribution and geometry the

solid fraction is calculated as φ= π d2

2radic3 w2 to be 0282 The roughness factor r f=1+ 2 π dhradic3 w2 of the

nanowired hydrophobic surfaces are calculated to be 54 and 81 for nanowires with the length of

20 microm and 30 microm respectively Here d h and w are the diameter the length and the center-to-

center spacing of nanowires

The apparent contact angles of both plain and nanowired hydrophobic surfaces are

measured by the sessile droplet method with the values as 1146 plusmn 26deg (plain) 1392 plusmn 35deg (20-

μm long nanowires) and 1436 plusmn 13deg (30-μm long nanowires) respectively The images are

obtained using a high-speed camera (Photron FASTCAM SA4) with 5 μl droplets at atmospheric

pressure and room temperature

6

Fig S3 SEM images showing the surface morphology of (a) plain hydrophobic surface and (b)

nanowired hydrophobic surface (20 μm long nanowires) The insets show the apparent contact angle of

droplet on the plain and nanowired hydrophobic surfaces are 1146 plusmn 26deg and 1392 plusmn 35deg respectively


Fig S4a shows the schematic of our custom-built setup for dropwise condensation heat

transfer measurements with in-situ visualization capability which consists of a steam generator

a condensation chamber a vacuum pump a chilled water bath and a data acquisition subsystem

The steam generator is a Ф76 mm times 900 mm vertical cylinder with an electric heater inside the

chamber The electric heater is designed to heat non-uniformly the larger heating power is

applied under the water level to boil the water and the upper part of the heater functions as a

super-heater The heating power is adjusted by a direct-current regulator (Agilent N5771A) The

steam temperature (Tse) at the outlet of the steam generator is always maintained to be 02~03 K

higher than the saturated water vapor temperature (Tv) measured in the condensing chamber The

superheated steam leaves the steam generator and enters the condensing chamber through a

connecting pipe (20 mm in diameter) To prevent condensation at the inside walls the

connecting pipe is heated by an adjustable heating tape (Omega HTWC 101-004) and covered

with fiberglass for the insulation

7

Condensation occurs in the condensing chamber which is a stainless steel cylinder with the

inner dimensions of Ф263 mm times 50 mm (Fig S4b) Flanges are used for sealing the end faces of

the condensing chamber A heating tape is wrapped around the exterior of the chamber walls to

prevent condensation at the inside walls where the exterior walls are insulated except a

transparent window for visualization The steam connection pipe is installed on the cover flange

and the condensing block is located below the inlet of steam At the bottom of the condensing

chamber a backflow pipe returns the condensate (water in this study) to the steam generator Fig

S4c shows the condensing block which is machined as two co-axial copper cylinders in different

diameters the smaller one (40 mm in diameter) is used as the condensing surface while the

larger one (90 mm in diameter) is designed to connect with the chiller (Thermo Electron

Corporation HAAKE Phoenix II) for dissipating the latent heat from the condensing surface A

flow meter (Proteus Industries 08004SN1) with an accuracy of plusmn 3 is integrated along the

cooling water inflow line to measure the flow rate G so that the heat transfer rate can be

calculated with the inlet (Ti) and outlet (To) temperatures measured for the cooling water loop

The condensing block is installed vertically at the center of condensing chamber Three holes (2

mm in diameter) are drilled in parallel on condensing block to measure the temperature

distribution in the condensing block during condensation (Fig S4c) All thermocouple holes

have the same distances of 35 mm to the condensing surface A transparent window (100 mm in

diameter) is installed about 50 mm in front of the condensing surface for the visualization using

high speed camera (Photron FASTCAM SA4)

T-type thermocouples and a pressure transducer (Omega PX409-050AI plusmn 008 accuracy)

are installed to monitor the temperature and pressure inside the chamber The thermocouple

bundles flow meter and pressure transducer are all connected to a data acquisition (Agilent

8

34970A) which is interfaced to a computer for data recording A vacuum pump (Edwards RV8)

is integrated into the vacuum line to pump down the experimental system to vacuum conditions

before water is filled into the steam generator

9

10

Fig S4 Experimental system a Schematic showing the custom-built setup for condensation heat

transfer with in-situ visualization capability b Photograph of the experimental setup (refrigeration

unit is not shown) c Photographs of the condensing block

S3 Data Reduction

Based on the energy balance the condensation heat flux q on the surface is calculated by

the temperature rise in the chilled water loop

q=cG (T ominusT i )

A (S1)

where c is the specific heat of cooling water (4200 Jmiddotkg-1K-1) A is the area of condensing surface

(1257 cm2) G is the mass flow rate of cooling water measured by the flow meter Ti and To are

the inlet and outlet temperatures of cooling water respectively Here the inlet temperature (Ti) of

cooling water is controlled by the chilled water tank with the fluctuation less than plusmn 01 K The

steady state of condensation is maintained for more than 40 minutes for each data point

The wall temperature (Tw) of condensing surface is calculated by assuming one-dimensional

heat conduction through the condensing block as

(S2)

where Tm is the average temperature measured by the three thermocouple in the condensing

block δ is the distance (35 mm) between the condensing surface and the measurement position

of thermocouples and k is the thermal conductivity of copper (398 Wm-1K-1 measured)

The surface subcooling ΔT is defined as the temperature difference between the steam

temperature (Tv) in condensing chamber and the wall temperature (Tw)

(S3)

Heat transfer coefficient h of condensation is defined as the ratio of heat flux to surface

subcooling which can be expressed as

11

(S4)

Table S1 summarizes the uncertainties of the measured quantities including the temperature

T the steam pressure Pv in condensing chamber the mass flow rate of cooling water G the

distance between condensing surface and the bottom of thermocouple holes δ the thermal

conductivity of condensing block k

Table S1 Parameters and uncertainties

Parameters Uncertainty (plusmn)

Temperature T (K) 015

Pressure P (kPa) 008

Flow rate G (kg) 03

Distance δ (mm) 025

Thermal conductivity k (Wm-1K-1) 1

Based on the error propagation the uncertainty of heat flux σ(q) is determined by

(S5)

The uncertainty of the mass flow rate (σ(G)) is plusmn 03 according the specifications of the

flow meter (Proteus Industries 08004SN1) The uncertainty of the inlet and outlet temperature of

cooling water (σ(Ti) and σ(To)) are both plusmn 015 K according the specifications of the

thermocouples (Omega T-type) The uncertainty of heat flux can then be obtained by the

measure quantities

The uncertainty of surface subcooling σ(ΔT) is determined by

(S6)

12

The uncertainty of the temperature of steam and condensing surface (σ(Tv) and σ(Tm)) are

both plusmn 015 K according the specifications of the thermocouples (Omega T-type) The

uncertainty of heat flux σ(q) is determined by equation (S5) The uncertainty of distance between

condensing surface and the bottom of thermocouple hole σ(δ) due to the mechanical processing

is plusmn 025 mm The uncertainty of the thermal conductivity of copper due to the change of

temperature in condensation experiments is plusmn 1

The uncertainty of heat transfer coefficient of condensation σ(h) is then determined by

(S7)

The uncertainty of heat flux σ(q) and surface subcooling σ(ΔT) are calculated by equation

(S5) and equation (S6) The derived quantities including heat flux q and surface subcooling ΔT

can be obtained by equation (S1) and equation (S3)

In the experiment all values of the temperature pressure and flow rate are collected by the

data acquisition simultaneously with the video capturing Error bars in Fig 2 indicate the

propagation of error associated with the temperatures pressure and flow rate measurements The

heat transfer error bars at small surface subcooling are largest due to the relatively low heat

fluxes measured corresponding to the small temperature difference between the outlet and outlet

of cooling water


Representative droplet images at various times after the onset of condensation on both plain

(Fig S5a-c) and nanowired (Fig S5d-f) hydrophobic surfaces at different surface subcooling are

shown in Fig S5 Fig S5a-c show dropwise condensation on the plain hydrophobic surface

where discrete droplets form and grow to the sizes approaching the capillary length (~1 mm) 13

before being removed by gravity Despite that the growth rates of condensed droplets are

different at different surface subcooling the condensation mode is independent of the surface

subcooling In contrast the condensation on nanowired hydrophobic surfaces shows significant

dependence on the surface subcooling (Fig S5d-f) At low surface subcooling (ΔT = 3 K)

droplets on the nanowired hydrophobic surface are highly efficiently removed by the

coalescence-induced jumping mechanism with numerous microscale droplets populating on the

surface (Fig S5d) However as the surface subcooling is increased to 11 K the droplet

morphology transitions from highly mobile jumping droplets to the pinned wetting droplets (Fig

S5e) With the surface subcooling further increased to 28 K (Fig S5f) a large number of pinned

droplets stay on the surface until the gravity-induced removal leading to a flooding condensation

mode

14

Fig S5 Sequential images of droplet growth and distribution a-c Time-lapse images of droplet growth

and distribution on the plain hydrophobic surface at the surface subcooling of 3 K 14 K and 25 K

respectively d-f Time-lapse images of droplet growth and distribution on the nanowired hydrophobic

surface (20 μm long) at the surface subcooling of 3 K 11 K and 28 K respectively Scale bar 800 μm


The above discussion clearly shows that the nucleation-induced wetting transition of

condensed droplets plays a crucial role in condensation heat transfer To gain further insight of

how the dynamic behavior of droplets is controlled by the wetting states we proposed a simple

model based on energy balance to quantify the jumping behaviors of condensed droplets in

15

different wetting states As shown in Fig S6 when the mobile state droplets coalesce on

nanostructured hydrophobic surfaces at small surface subcooling (ΔT = 05 K) the merged

droplet can jump away from the surface in a process that is termed coalescence-induced droplet

jumping In general the coalesced jumping droplets caused by coalescence range from several

microns to hundreds of microns [3] Droplet jumping is a process governed by the conversion of

excess surface energy into kinetic energy when droplets coalesce

Fig S6 Coalescence-induced droplet jumping High-speed time-lapse images capturing coalescence-

induced droplet jumping Conditions Pv = 60 kPa ΔT = 05 K The red line shows trajectory of droplet

Several studies have attempted to explain the underlying physical mechanisms governing

coalescence-induced droplet jumping based on the balance of surface energy kinetic energy

and energies dissipated by viscous and surface-adhesion effects before and after coalescence [3-

7] Boreyko and Chen [4] were the first to report droplet jumping in condensation on

superhydrophobic surfaces They developed a simple capillary-inertial scaling to assess the

droplet jumping velocity by assuming that all of the surface energy of spherical droplets released

was converted into kinetic energy Wang et al [8] included the additional viscous dissipation

caused by the flow during coalescence on a superhydrophobic surface which showed that

droplet jumping can occur only for coalescence of droplets within a certain range of size

16

Subsequently Lv et al [9] considered the additional surface adhesion-induced energy dissipation

caused by contact angle hysteresis in the analysis and showed that surface adhesion limits the

critical size range for jumping droplets Recently the expression for adhesion-induced energy

dissipation was modified for the coalescence of multiple droplets and the results showed that the

jumping velocity increases with the number of coalescing droplets [3] None of the previous

models includes the effect of droplet wetting states caused by surface subcooling on the droplet

dynamic behaviors Here we develop a model to investigate the coalescence of condensed

droplets with different wetting states

Accounting for viscous dissipation energy Evis and work of adhesion between liquid and

nanostructures ΔEw after releasing the droplet interfacial surface free energy ΔEs the kinetic

energy of the coalesced droplet Ek can be expressed as [4 10]

(S8)

To simplify the mathematical derivation it is assumed that the coalescence occurs between

two droplets with the same radius Here the surface free energy difference of droplet before and

after the coalescence is given by ΔEs = σlgΔAlv + σslΔAsl where A is the interfacial surface area

before and after coalescence σ is the interfacial tension and subscripts s l and v denote the

solid liquid and gas phase respectively

Considering the high aspect ratio nanowires it is assumed that the nucleation position

extends from the top to bottom of the separation with the increase of surface subcooling Here

we define the immersion factor ξ as the ratio of immersion depth hw to the height of nanowires h

as shown in Fig S7 to describe the different wetting states of droplets The immersion factor ξ is

the percentage of immersion height hw within nanostructures over the height of nanowires h ξ =

0 corresponds to a Cassie state while ξ = 1 refers to a Wenzel state

17

Fig S7 Schematic illustrating droplet wetting state on nanowired hydrophobic copper surfaces

The surface free energy difference ΔEs can now be estimated as

(S9)

where r Rc σlv and θ are the radius of droplets before coalescence the radius of droplet after

coalescence surface tension and apparent contact angle of water Here f(ξ) is related to the

immersion depth of condensed droplets on nanowired hydrophobic surfaces and is obtained as

(S10)

where θw and θc are contact angle of droplets in Wenzel state and Cassie state θY is the

equilibrium contact angle on a nanowired hydrophobic surface rf and φs are the roughness factor

and the fraction of solid-liquid contact area

The viscous dissipation energy for each droplet is obtained as[8]

(S11)

where μ and ρl are the viscosity and density of condensed droplets

The work of adhesion between droplet and nanowires can be shown as [10]

(S12)

18

where Asl is obtatin by Asl = 2πr2sin2θ[ξrf + (1 - ξ)φs]

The kinetic energy of the coalescent droplet after merging tow identical droplets can then be

obtained as

(S13)

Then the jumping velocity can be found to be

(S14)

The jumping velocity obtained from equation (S14) can quantitatively describe the dynamic

behavior of condensed droplets in different wetting states on nanowired hydrophobic surfaces

When a kinetic energy (jumping velocity) is larger than zero droplets can jump from the

condensing surface after coalescence Otherwise droplet remains on the surface after

coalescence until growing to a size that is removed by gravity Fig S8a shows that the droplet

jumping velocity increases to a maximum and then decreases with the increase of droplet size for

various immersion depth A too small or too large droplet cannot jump because of viscous

dissipation and the work needed to acount for adhesion With the increase of immersion depth

from 0 nm to 600 nm the maximum of droplet jumping velocity decreases from 027 to 002 ms-1

and the smallest size of droplets that can jump increases from 10 μm to 230 μm More

importantly when the immersion depth is larger than 600 nm the released surface energy after

the coalescence of two droplets is not sufficient to overcome the dissipative forces resulting in

no jumping Fig S8b shows that the available jumping velocity of coalesced droplets is inversely

19

proportional to the degree of droplet immersion and the size range of available jumping droplets

increases with the increase of immersion factor Based on the assumption that the nucleation

position extends from the top to bottom of the separation with the increase of surface subcooling

a smaller immersion factor can be achieved at small surface subcooling which facilitates droplet

jumping Large surface subcooling could lead to the increase of immersion factor as well as the

decreased droplet jumping velocity which results the failure of of nanowired hydrophobic

surfaces

Fig S8 Dynamic behavior of condensed droplets in different wetting states a Droplet jumping velocity

as a function of droplet size with different immersion depth b Available velocity range and size range of

jumping droplets as a function of immersion factor for condensed droplets

20

References

[1] M Tian W Wang Y Wei R Yang J Power Sources 211 (2012) 46-51[2] MD Porter TB Bright DL Allara CED Chidsey J Am Chem Soc 109 (1987) 3559-3568[3] X Chen RS Patel JA Weibel SV Garimella Sci Rep 6 (2016) 18649[4] JB Boreyko CH Chen Phys Rev Lett 103 (2009) 184501[5] KM Wisdom JA Watson XP Qu FJ Liu GS Watson CH Chen Natl Acad Sci USA 110 (2013) 7992-7997[6] R Enright N Miljkovic J Sprittles K Nolan R Mitchell EN Wang ACS Nano 8 (2014) 10352-10362[7] BL Peng SF Wang Z Lan W Xu RF Wen XH Ma Appl Phys Lett 102 (2013) 151601[8] FC Wang FQ Yang YP Zhao Appl Phys Lett 98 (2011) 053112[9] C Lv P Hao Z Yao Y Song X Zhang F He Appl Phys Lett 103 (2013) 021601[10] GQ Li MH Alhosani SJ Yuan HR Liu A Al Ghaferi TJ Zhang Langmuir 30 (2014) 14498-14511

21

Supplementary Information



S3 Data Reduction



Supplementary Videos





5 Droplet behaviors on the plain hydrophobic surface at Pv = 60kPa ΔT = 5 K

2










copper surface












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S3 Data Reduction



q=cG (T ominusT i )

A (S1)








(S2)






(S3)



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(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

12








(S7)









of cooling water
















mode

14










15


















16












(S8)












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(S9)




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(S11)



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20

References


21










copper surface












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template













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7
























8




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10




S3 Data Reduction



q=cG (T ominusT i )

A (S1)








(S2)






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(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

12








(S7)









of cooling water
















mode

14










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16












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(S9)




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20

References


21














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template













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10




S3 Data Reduction



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A (S1)








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(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

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(S7)









of cooling water
















mode

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20

References


21





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S3 Data Reduction



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Flow rate G (kg) 03




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Flow rate G (kg) 03




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measure quantities


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Flow rate G (kg) 03




(S5)





measure quantities


(S6)

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mode

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References


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S3 Data Reduction



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References


21




9

10




S3 Data Reduction



q=cG (T ominusT i )

A (S1)








(S2)






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Flow rate G (kg) 03




(S5)





measure quantities


(S6)

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(S7)









of cooling water
















mode

14










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(S8)












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(S11)



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obtained as

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20

References


21

10




S3 Data Reduction



q=cG (T ominusT i )

A (S1)








(S2)






(S3)



11

(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

12








(S7)









of cooling water
















mode

14










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16












(S8)












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(S9)




(S10)





(S11)



(S12)

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obtained as

(S13)


(S14)














19







surfaces




20

References


21

S3 Data Reduction



q=cG (T ominusT i )

A (S1)








(S2)






(S3)



11

(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

12








(S7)









of cooling water
















mode

14










15


















16












(S8)












17



(S9)




(S10)





(S11)



(S12)

18



obtained as

(S13)


(S14)














19







surfaces




20

References


21

(S4)









Flow rate G (kg) 03




(S5)





measure quantities


(S6)

12








(S7)









of cooling water
















mode

14










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20

References


21








(S7)









of cooling water
















mode

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References


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obtained as

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surfaces




20

References


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15


















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obtained as

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obtained as

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References


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17



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(S11)



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18



obtained as

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surfaces




20

References


21



(S9)




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(S11)



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18



obtained as

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surfaces




20

References


21



obtained as

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surfaces




20

References


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surfaces




20

References


21

References


21

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