1

A SEMINAR REPORT ON

“MIXING IN MICROCHANNELS”

Submitted in partial fulfillment of the requirements for the

Degree of Bachelor of Technology

---------- Presented & Submitted-----------

By

HARSHIT KUMAR

(Roll No. U10CH038)

B. TECH. IV (Chemical) 7th Semester

Guided by

Dr. V.N.LAD

Assistant Professor

CHEMICAL ENGINEERING DEPARTMENT

Sardar Vallabhbhai National Institute of Technology

Surat-395007, Gujarat, INDIA

DECEMBER - 2013

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Sardar Vallabhbhai National Institute of Technology

Surat-395007, Gujarat, INDIA

CHEMICAL ENGINEERING DEPARTMENT

CERTIFICATE

This is to certify that the B. Tech. IV (7th Semester) SEMINAR REPORT entitled

“Mixing in Microchannels” presented & submitted by Mr. Harshit Kumar, bearing

Admission No. U10CH038, in the partial fulfillment of the requirements for the award of

degree B. Tech. in CHEMICAL Engineering at Sardar Vallabhbhai National Institute of

Technology, Surat.

He has successfully and satisfactorily completed his seminar work.

Dr. V. N. Lad

(Guide)

Assistant Professor

Chemical Engineering Department.

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DEPARTMENT OF CHEMICAL ENGINEERING

Sardar Vallabhbhai National Institute of Technology,

Surat.

This is to certifiy that Mr.Harshit Kumar, registered in Chemical Engineering Department

of S.V.N.I.T. Surat having Admission No. U10CH038 has successfully presented his Seminar

of B. Tech. (Chemical) 7th Semester, on 11/12/2013 at 04:00 P.M. The seminar is presented

before the following members of the Committee.

Sign Date

1) Examiner-1 ____________ ___________ _________

2) Examiner-2 _____________ ___________ _________

The Seminar entitled “Mixing in Microchannels” is submitted to the Head ( ChED ) along

with this certificate.

Place: Surat

Date: 11/12/2013

Prof. Z. V. P. Murthy

Head,

Chemical Engineering Department,

SVNIT – Surat.

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ACKNOWLEDGEMENT

It gives me great pleasure to present my seminar report on “MIXING IN

MICROCHANNELS”. No work, big or small, has ever been done without the

contributions of others.

I would like to express deep gratitude towards Dr. V. N. LAD, Assistant

Professor at Chemical Engineering Department, SVNIT, who gave me their

valuable suggestions, motivation and direction to proceed at every stage. He

extended towards a kind and valuable guidance, indispensible help and

inspiration at time in appreciation I offer them my sincere gratitude.

In addition, I would like to thanks Department of Chemical Engineering

Department, SVNIT. Finaly, yet importantly, would like to express my heartfelt

thanks to my beloved parents and my brother for their blessings, my

friends/classmates for their help and wishes for the successful completion of

this seminar.

Harshit Kumar

(U10CH038)

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ABSTRACT

The ability to mix efficiently has many uses, particularly in chemistry and biochemistry. A

promising area involves mixing in microchannels—narrow grooves of about 100µm in width.

A microchannel which mixes fluids is called a micromixer.There are two types of mixing

methods in microchannels: active and passive.

In active mixing, fluid is pumped into the channel in such a way that mixing is induced, say

by a time-dependent forcing. However this is difficult to do on such tiny scales as

micrometres, and is also undesirable from a manufacturing standpoint because the design

involves moving parts.

In passive mixing, the shape of the micromixer is designed to create flow patterns that

naturally mix. For example, this is achieved by placing grooves on the walls of the channels

which cause chaotic motions of fluid particles. An alternative approach, used in present work,

is electro-osmosis, where electric fields are used to push the fluid (Ajdari, 1996).

In this seminar we have discussed different types of fabrication of micro channels & flow of

fluids in a microchannels like Crossflow and mixing in obstructed and width-constricted

rotating radial microchannel, Two-fluid mixing in a microchannel, Single-phase fluid flow

and mixing in microchannels, Gas–liquid two-phase flow in microchannel at elevated

pressure, Liquid mixing in gas–liquid two-phase flow by meandering microchannels.

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CONTENTS

PAGE NO.

ACKNOWLEDGEMENT 4

ABSTRACT 5

LIST OF FIGURES 8

1.Introduction 9

2. FABRICATION OF MICROCHANNELS 10

2.1 Fabrication of the microchannels by optical lithography 10

2.2. Wet chemical etching 11

2.3. Reactive ion etching (RIE) 11

2.4 Room Temperature Microchannel Fabrication for Microfluidic System 12

2.5 Cylindrical PDMS Microchannel Fabrication by 16

Sacrificial Molding using Caramel

2.6 One-stage fabrication of sub-micron hydrophilic microchannels on PDMS 17

2.7 Microchannel Fabrication using photomask,SU-8,glass slide 18

3. Equation Derivations 20

3.1 Governing Equations 20

3.2 Velocity Field 21

3.3 Pressure Analysis 24

3.4 Pressure Gradient and Constant Velocity Solution 28

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4. mixing analysis 29

4.1 Crossflow and mixing in obstructed and width-constricted 29

rotating radial microchannel

4.2 Two-fluid mixing in a microchannel 30

4.3 Single-phase fluid flow and mixing in microchannels 31

4.4 Gas–liquid two-phase flow in microchannel at elevated pressure 33

4.5 Liquid mixing in gas–liquid two-phase flow by meandering 34

microchannels

4.6 Mixing process of immiscible fluids in microchannels 35

4.7 Mixing of a split and recombine micromixer with tapered 37

curved microchannels

4.8 Pumping and mixing in a microchannel using AC 38

asymmetric electrode arrays

4.9 Parametric study on mixing of two fluids in a 39

three-dimensional serpentine microchannel

4.10 Mixing performance of a planar micromixer with 40

circular obstructions in a curved microchannel

4.11 Single phase electrokinetic flow in microchannels 42

4.12 Fluid mixing in microchannel with longitudinal vortex generators 43

4.13 Ideal micromixing performance in packed microchannels 44

5. CONCLUSION 45

REFRENCES 46

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List of Figures

Figure

no.

Name of figure Page no.

1 A top down view of the staggered herringbone pattern on the

floor of the channel

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2 The microchannels mask 10

3 Sample microchannel 5 after wet etching 11

4 Sample microchannel 3 fabricated by RIE 12

5 Sample microchannel 48 fabricated by DRIE 12

6 The developed microfluidic system 13

7 Microstructure design for micro fluidic system 14

8 Fabrication process flow of region from cross section AA’ to

outlet

15

9 Evaporating design on microfluidic system 15

10 Movement of saccharomycetes in microchannel by evaporating

force

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11 Microchannels fabricated by proposed method 17

12 Schematic for microchannel fabrication procedure 20

13 A diagram of the herringbone shape with respect to y

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1. Introduction

A microchannel is a channel that has a width and height in the order of micrometers (µm).

Conventional mixing methods for larger volumes of fluid are often not practical at such tiny

scales, so micromixing requires a separate area of research.

There are different methods of generating chaotic flows in channels, varying from placing

obstacles in the channel (Wang. et.al., 2002) to a very popular and effective solution called

the ”staggered herringbone” system (Stroock et.al., 2002).

The “staggered herringbone” system is where grooves in a herringbone shape are carved into

the floor of the channel (see figure 1). The herringbone pattern is periodic in the x-direction

and half way through each period the herringbone is flipped around, hence creating a

staggered pattern. In this system the efficiency of mixing is far greater than the mixing from

diffusion alone (Johnson et. al., 2002).

Figure 1: A top down view of the staggered herringbone pattern on the floor of the channel

(Stroock et.al., 2002)

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2. FABRICATION OF MICROCHANNELS

2.1 Fabrication of the microchannels by optical lithography

The first step in the fabrication process consists in the design of the desired mask. By means

of Raith 150 software we have designed the microchannels mask with following dimensions:

a) the reservoirs size 1000x1000μm; channels size 20x4800μm; distance between channels

20μm (fig. 2).

Fig. 2. The microchannels mask

We have fabricated the microchannel by standard procedure of the optical lithography. The

SiSiO2(SiO2 thickness 5μm.) wafer was cleaned primarily by acetone and isopropanol to

remove the contaminations. The wafer was then covered with primer and photorezist (AZ

5214E) by spin coating in order to form a thick layer. The spin coating was imposed at

4000rpm, 40sec. and has produced a layer between 1.2 - 1.3 μm thickness. The photorezist-

coated wafer was then baked 1min. at 120C to evaporate excess solvent. After baking, the

photorezist is exposed 3sec. to the designed microchannel mask at 14mW UV light (transfer

the pattern from the mask to photorezist). An another bake process (2min. at 112C) is

performed before flood exposure so thatthe photorezist becomes harder and the layer is more

durable for the wet chemical etching or RIE etching. As developer we have used AZ726 MIF,

and stoped the developing process by immersion the wafer in deionized water. The such

obtained microchannelsdepth is around 1.22μm .

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2.2. Wet chemical etching

For SiO2etching we have prepared the solution with ammonium fluoride NH4F (12g) in

water H2O (17ml.). When the salt was melt we put hydrofluoric acid 38% HF (3ml.). The

sample was immersed in this solution different time (5 min., 15min., 60 min. respectively)

and then the etching process is stoped by immersing the sample in deionized water. We can

see that the longer time is the wet etching process the microchannels profile is changing from

the rectangular shape in the sinusoidal one (fig. 3) due to the isotropic process imposed by

HF. For microfluidics application this cross-section not exactly rectangular cannot be

neglected because it adds extra impedance to the flow dueto the small dimensions used. This

drawback can be fixed by means of reactive ion etching (RIE).

Fig. 3. Sample microchannel 5 after wet etching a) 5min. immersion the microchannel depth

is around 1.3µm; b) 15min. immersion the microchannel depth is 2.1µm;

2.3. Reactive ion etching (RIE)

In contrast with the typically isotropic profiles of wet etching, the RIE can produce very

anisotropic etch features, dueto the mostly vertical delivery of reactive ions. Etch conditions

in RIE system (RIE IONVAC) depend strongly on the many process parameters, such as

pressure, gas flow and RF (radio frequency) power. We performed the RIE process by mixing

tetrafluoromethane CF4 (20sccm) and O2 (2sccm) at 200W, 20mtorr for 10min. In this way

the surface quality of the etched microchannels isvery good and will not affect the flow

behavior, as it still will be laminar flow. In figure 4 is shown the sample after optical

lithography process and the obtained profile after RIE process.

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Fig. 4. Sample microchannel 3 fabricated by RIE

For our applications neither this method is too convenient due to the channels’ depth not very

high (about 1.3 microm. before photorezist removal), therefore we tried a deep reactive ion

etching(DRIE) with STS Multiplex ICP AOE system. This machine consisting of multiplex

ICP AOE (Advanced Oxide Etch) can be setup to process wafers up to 200 mm, but currently

setup is 100mm wafers size. Against the above described RIE process, in DRIE we added a

gas flux of octafluorocyclobutane C4F8 (20sccm), set the pressure at 4mtorr and reduced the

etch time at 6min. A drawback of this method is that it should be used with a metal mask

layer. The metal layer (Cr 100nm) was evaporated before optical lithography process. By

means of this method the microchannels’ depth is around 4µm (fig.5). After lithographic

process we performed an evaporation of the 30nm Au layer and functionalization itwith 1,6

hexane dithiol in order to facilitate the covalent binding of the semiconductor nanocrystals to

the solid surface using self-assembled monolayers.

Fig. 5. Sample microchannel 48 fabricated by DRIE: a) profilometer; b) SEM image

2.4 Room Temperature Microchannel Fabrication for Microfluidic System

Silicon dioxide has hydrophilic property that was stable and it is thus preferable for

applications in which devices are used extensively, such as in high throughput screening.

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SiO2was also known for its superior optical properties, useful for optical detection and

analysis methods.

The microfluidic system was designed as shown in figure 6(a), including sample inlets,

particle separation region, and evaporation regions as shown on figure 6(b).

Figure 6: The developed microfluidic system: (a) Total system including separate region, and

(b) Evaporation region.

Microchannel with different area of evaporation region was designed, as shown on figure

7(a). Instead of heater design, external thermal source was used on the top to change

temperature at the outlet of microchannel for liquid flowing inside. Generally, the width of

comb was usually smaller than the width of main channel, to ensure that liquid will be

trapped on the end of microchannel.After processing, evaporating region of chips was fixed

on silicon bulk which was put on top of hot plate to keep on the same temperature, is shown

on figure 7(b).

As results, velocity of flow was proportion to area of evaporating region. It is linear relation

since operating on fixed width of main channel with different area of evaporating region. The

slope of velocity/evaporating-area ratio will decrease with width- increasing of main channel.

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Figure 7: Microstructure design for micro fluidic system (a) Total system including,

Evaporation region, and (b) Chip connected onto bulk silicon and hotplate.

Glass has material properties that are stable in time and it is thus preferable for applications in

which devices are used extensively, such as in high throughput screening. Glass is

hydrophilic, meaning it attracts and holds moisture. Most plastics, in comparison, are

hydrophobic and need treatment to become hydrophilic. If hydrophobic surfaces are needed,

we can modify the glass surface by applying a coating to the channels.

In this process, photoresist AZ9260 was used as sacrificial layer, which is easy to be

deposited and patterned. Another important issue for this developed process is to deposit

porous Silicon DI water Comb Hot plate Thermal couple silicon dioxide film by e-beam

evaporator, which degree of porosity could be controlled by adjusting deposition rate. By

using this porous property, organic solution can go through silicon dioxide thin film to

release structure and to form microchannel.

The process flow of microfluidic system was shown on figure 8 (Liu C. S. Y., Dai B.T 2005].

Glass wafer were cleaned in RCA-1 and piranha solutions at 950C. The clean wafers were

rinsed with deionized (DI) water and dried in pure N2. Then glass wafer was coated by

HMDS to improve the adhesion between PR and wafer. First, we patterned AZ9260

photoresist, which was coated with 3000 rpm and exposed under 200 mJ. Then, photoresist

was treated up to 1100for 60 seconds to be reflowed. Secondly, silicon dioxide/Ti (10000 Å

/1500 Å) was deposited by e-beam evaporator on top of PR and glass substrate. The

deposited structure was strong enough to make etching solution penetrate to release PR and to

form microchannel. The heaters was deposited and patterned at the entrance and exit by RIE

etching. The ercentage of oxygen in RIE etching process is very important. The high

percentages of oxygen will generate too much oxygen ions to damage PR and metal. If less

oxygen ions exist in chamber, organic residue will not be removed from surface of wafer.

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Then, microstructures were easily released by acetone or some organic solvent through

porous SiO2structures.

Figure 8:Fabrication process flow of region from cross section AA’ to outlet (a) Start from

Pyrex #7740, (b) Channel definition by AZ9260, (c) SiO2 / Ti deposition (d) Heater and

temperature sensor formation, (e) Entrance and exit formation, (f) Structure releasing.

Figure 9(a) and 9(b) are top view of microchannel with heater at the outlet of microfluidic

system. It shows that fabrication process was easy to integrate metal onto microchannel

structures. The most important is that microchannel structures were fabricated by porous

silicon dioxide. Moreover, the whole fabrication process was down under room temperature,

which is suitable for bio-medical application if bio-related layer was coated in the middle of

device fabrication.

Figure 9: (a) Evaporating design on microfluidic system, SEM pictures for (b) heater and

temperature sensor, and (c) entrance of microchannel

In figure 9(c), on the top of microchannel forms curvature at the sidewall of microchannelit,

that is clearly shown successful microchannel formation after releasing without damage.

From the results, the maximum height can bre reached up to 7μm and the width can be

created up to 60μm, if 1μm thin film of silicon dioxide was deposited as structure material.

After microchannel formation by developed fabrication process, microscale of particles,

accharomycetes, were used in microfluidic system to prove the liquid transportation by

evaporating force. By turning on the heater at exit of microchannel, the evaporation force

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would drive the liquid, as shown on figure 10. The particle movement is steady with time.

Each photo was taken every 0.28 seconds, and total moving length is about 0.18 µm. By

observing the movement of particles, velocity of saccharomycetes was estimated up to

500µm per second on controlling heater temperature at about 40℃.

Figure 10: Movement of saccharomycetes in microchannel by evaporating force

2.5 Cylindrical PDMS Microchannel Fabrication by Sacrificial Molding

using Caramel

Microfluidic channels fabricated by our sacrificial molding process are shown in

Fig.11. 3-D channel was made without extra layering process because our method can meke

3-D caramel template directly.We investigated relativity between conditions of caramel

patterning and cross-sectional area of fabricated channel (Fig.13). Cross-sectional

images taken on scanning electron microscope were also shown in the figure. This is

attributed to surface tension of caramel. After the deposition, a viscosity of the caramel

became lower by absorption of moisture or application of heat, thus surface tension made

its shape cylindrical. The cross-sectional shape depends on initial shape and deformation

time of depositted caramel. The reason why the cross-section tended to become circular as a

nozzle traveling speed higher is the initial shape was flat at lower nozzle traveling

speed (Masashi Ikeuchi ).

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Figure 11. Microchannels fabricated by proposed method. (a) fluorescent image of

channel network filled with rhodamine B solution, (b) reconstructed image of 3-D

interchange taken on conforcal microscopy (scale bar: 100μm).

2.6 One-stage fabrication of sub-micron hydrophilic microchannels on

PDMS

Polymeric materials such as poly(methylmethacrylate) (PMMA),polystyrene, polycarbonate

(PC), polyurethane, and poly(dimethylsiloxane) (PDMS) have been widely used as the

substrate materials for microchannels. Among them, PDMS has received more attention due

to its outstanding performances such as transparency, high permeability to gases, high

elasticity, easy processing and seals the channel readily, etc.( Makamba H. et.al.,2003).

Nevertheless, PDMS is extremely hydrophobic, which makes it very difficult for aqueous

solutions to flow inside the microchannels. In addition, the absorption function of PDMS

surface may generate fouling on the surface. The hydrophobicity has long been the bottleneck

to the application of PDMS as a microchannel material(D. Bodas et. al.,2008). Because of

this, different approaches,such as oxygen plasmas (Fritz J.L. et.al.,1995), ultraviolet light

(UV) (Lai J.Y. et.al.,1996), corona discharges and so on(8]have been employed to modify

PDMS to obtain a hydrophilic surface. In all these approaches, the microchannels were

produced firstly, then the microchannel surfaces modified indicating a time-consuming and

complicated process. What’s more, the hydrophilicity of the PDMS surface thus obtained will

not last long, say three weeks. In this communication, a relatively simple method, i.e., one-

stage fabrication of microchannels was reported, using vacuum ultraviolet light (VUV)

lithography in vacuum. As demonstrated below, the hydrophilicity on the PDMS surface can

be kept for a longer term after the treatment.

Sylgard 184, consisting of poly(dimethylsiloxane) and a reinforcing silica filler was prepared

by carefully mixing the precursors Sylgard 184 A/B at a ratio of 10:1 by mass. The PDMS

precursors were then spin-coated onto the cleaned glass coverslips at 5000 rps using the

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spincoater (Efimenko. et. al.,2002). The resultant PDMS thin films were then degassed under

vacuum and cured in an oven at 708C for 3 h to produce cross-linked PDMS. Then the

PDMS films under a closely contacted photomask, which consisted of a 3-mm thick quartz

glass plate, that is, 91% transparency at 172 nm, with a 0.1-mm thick chromium pattern, were

irradiated with the VUV light of 172 nm (Ushio Inc., UER20-172V, Intensity at the lamp

window = 10 mW/cm2 ) in a vacuum (500 Pa) for 15 min, the experimental setup is

described in the literature(Sugimura et.al.,2000).

In conclusion, sub-micron hydrophilic microchannels can be fabricated by vacuum ultraviolet

light (172 nm) lithography. XPS analysis showed that the chemical composition of the

microchannel surface was changed, and a silicon oxide glass-like crosslinking structure may

be formed, which can prevent the movement of hydrophilic groups from the surface to the

bulk and thereby gives rise to the longer hydrophilicity of the microchannel surface.

2.7 Microchannel Fabrication using photomask,SU-8,glass slide

Microchannel fabrication begins by creating a reusable master mold. The mold substrate is a

glass slide. The mold substrate is a glass slide. The slide is cleaned in a piranha solution

(H2SO4:H2O2) (Chan-Park. et. al.,2004). A rinse in deionized water follows. The clean glass

slide is dried using filtered-compressed nitrogen, and dehydrated at 120°C for thirty minutes.

Cleaning and dehydrating will prolong the life of the master mold (MicroChem].

Four mL of Epoxy-based SU-8 photoresist from MicroChem Corp (Newton, Massachusetts)

is spin-coated at 300 rpm with an acceleration of 83 rpm/s for 10 seconds and then to 3,000

rpm at 415 rpm/s for 30 seconds, per the manufacturer’s instructions (MicroChem]. The SU-8

coated glass is then set on a perfectly level surface for 20 minutes to allow the photoresist to

smooth out. This will allow for even heating of the SU-8 in the steps that follow. The mold is

ramp heated from 50°C to 95°C at 2°C/min for 23 minutes and then held at 95°C for six

minutes. Ramp heating is implemented for all heating processes to prevent thermal stresses

which may cause cracks in the mold and reduce its life.

A photomask is placed in contact with the SU-8 for the photolithography procedure. The

photomask was created by first modeling the channel geometry in CAD and then printing this

geometry on transparent medical film using a high resolution printer. The photomask must be

in direct contact with the SU-8. If there is any gap between the mask and the SU-8, a

widening of the pattern on the final mold will result due to diffraction of the UV light

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exposure which follows (Li P. (2007). The SU-8 is exposed for 45 seconds in an ELC-500

(Bethel, Ct.) UV light exposure chamber. This yields the necessary 240 mJ/cm2of exposure

energy for a 50 μm thick SU-8 film on a glass substrate (MicroChem].

Post exposure baking takes place immediately after UV light exposure in order to cross link

the exposed film. The SU-8 slide is ramp heated from 50°C to 95°C at 2°C/min for 23

minutes and then held at 95°C for six minutes. MicroChem SU-8 developer (Newton,

Massachusetts) is used to remove any unexposed SU-8 from the glass substrate. The mold is

developed for six minutes (MicroChem] while being agitated on a shaker at 150 rpm. After

an isopropyl alcohol rinse the mold is complete.

Dow Corning Slygard 184 silicone elastomer and curing agent (Philadelphia, Pa) is

thoroughly mixed 10:1 by weight (Chan-Park. et. al.,2004). The PDMS is poured on top of

the mold to the desired thickness. The PDMS is degassed in a vacuum for five minutes and

then the chamber isvented. The PDMS is then heated to 70°C for thirty minutes . After

curing, the PDMS is peeled off of the mold and an inlet and outlet is created using a biopsy

punch.

The PDMS negative relief and a clean glass slide are placed face up in a Diener Femto

plasma asher (Reading, Pa.). Vacuum conditions are created and held for five minutes.

Oxygen at 25 psi is introduced and the plasma asher is run for three minutes. This procedure

oxidizes the surface of both the PDMS and the glass, and surface-oxidized PDMS and glass

will form a bond (McDonald et.al.,2002). It is important that no mechanical stress is applied

to the PDMS or glass; otherwise the surface modification will diminish. After the two

surfaces are placed in contact with one another the channel is heated to 70°C for ten minutes

to allow for full bonding (McDonald et.al.,2002). The microchannel fabrication is now

complete.

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Fig 12. Schematic for microchannel fabrication procedure

3. Equation Derivations (Stroock et. al., 2002).

3.1 Governing Equations

The governing equations of the fluid motion are the Navier-Stokes equation and the

continuity equation

3.1

3.2

where u = (u, v, w), ρ is constant density and ν is the kinematic viscosity. For our problem the

flow is steady due to the low Reynolds number, so ∂u/∂t = 0. Also, for relatively low

Reynolds number, for flow in a microchannel with a large ratio of channel length to width,

the inertia effects can be neglected (Stroock et. al., 2002).

Therefore we neglect u · ∇ u. In addition, as ρ and ν are constants, we rescale p such that p =

p/ρν . The Navier-Stokes equation then reduces to the Stokes equation

3.3

There are also the following boundary conditions on the flow in the microchannel.

3.4a

Equations have been derived by Stroock et. al., 2002.

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3.4b

3.4c

where U (x, y) is the function of x and y which defines the flow on the base of the channel.

These equations satisfy the condition that there is no through flow on the walls of the channel

and the no-slip conditions on the floor and ceiling of the channel. However we have not

applied no-slip boundary conditions on the sides of the channel, because of the simplification

in the model. We impose a function at the base of the channel that is just shifted with respect

to a herringbone and not one which is 0 at the sides and hence at y = −ℓ/2 and ℓ/2 the velocity

u will not be 0. This simplification should not affect the result too much, as the channel has a

large ratio between width and height and the effects of not applying no-slip at the side walls

will change very little to the flow in most regions of the channel.

3.2 Velocity Field

Due to the low aspect ratio between h and ℓ, ‘Lubrication theory’ or ‘Thin Layer theory’ can

be applied to (2.3) to obtain equations for u, v and w and hence an approximate analytical

solution for velocity field can be found.

We begin by setting ε = h/ℓ. As ε is small, the changes in z are small compared to those in x

and y. Therefore using Lubrication theory we rescale z such that z → εz and hence ∂/∂z → ε

−1 ∂/∂z. For the same reason w → εw. Thus equation (3.3) becomes

3.5a

3.5b

3.5c

3.5d

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and (3.2) becomes

3.5e

Note that w → εw has cancelled the ε−1 given from ∂/∂z.

We define vertical averaging as

3.6

From this we find that . Also = 0 due to the boundary

conditions. Hence = 0 implies

3.7

This means that the vertically averaged velocity is incompressible.

We now assume that ∂/∂x and ∂/∂y are order 1. Therefore as ε2≪ 1, ε−2 is very large andhence

equations (3.5a),(3.5b) and (3.5c) reduce to

3.8a

3.8b

3.8c

In order to have a non-zero flow, equations (3.8a) and (3.8b) imply that the pressure must be

of order ε−2 at leading order, but must not depend on z in order to satisfy (3.8c). Therefore

3.9

where is of order unity.

Now equations for u, v and w are found. Equations (3.8a), (3.8b) and (3.9) imply:

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3.10a

3.10b

First we solve equation (3.10b). Using the boundary conditions, (3.4a) implies b0 = 0 and

(3.4b) implies

Therefore equation (3.10b) becomes

3.11

To satisfy the boundary condition at the side wall (3.4c), we require

3.12

Now we solve equation (3.10a). At z = 0, (3.4a) implies u(x, y, 0) = a0(x, y) = U (x, y). At z =

h, (3.4b) implies

SO

Which becomes

3.13

We now derive w using u and v by substituting (3.11) and (3.13) into (3.5e) to get

is now integrated w.r.t. z to obtain

3.14

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where the constant value has been set to 0 due to the boundary condition (3.4a). We now

have equations for u, v and w which only depend on x, y, z, P0 and U .

Figure 13: A diagram of the herringbone shape with respect to y.

3.3 Pressure Analysis

In order to use the u, v and w equations, we now need to find a solution for P0 . To solve for

P0 we use the vertically averaged equation (3.7) (i.e. ). The vertical average

of v and u can be easily found

3.15

Where

So 3.16

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Next we substitute (3.15) and (3.16) into the vertically averaged equation (3.7) to obtain the

Condition

3.17

This can now be solved for P0 and hence analytical solutions can be obtained for u, v and w.

However first we simplify w by substituting (3.17) into (3.14) to get

3.18

Which reduced to

Hence w does not explicitly depend on P0.

In order to solve (3.17) for P0 the specific form of U is needed. Figure 3.1 shows how the

herringbone depends on y within the channel. U is different for y ≤ a and y > a. To represent

the herringbone we define a function φ(y) such that

Therefore φ(y) is continuous in y. We now take a Fourier expansion of U in x, varying the

phase in y following the herringbone pattern,

3.19

where kn= 2πn/L. This equation is a sum of terms. Because equations (3.5a) to (3.5e) are

linear,we now look for a solution for each term, which can then be superimposed once they

have been found. U0is considered later. We now look at

26

3.20

where = 0 gives us the sin term where and = π/2 gives us the cos term

where depend on the step function at the base of the

channel. We may expand (3.20) as

3.21

We further divide this into two terms of the form

3.22

where for χ = 0 we get the ‘sin cos’ term and for χ = π/2 we get the ‘cos sin’ term in (2.21).

Again we will superimpose the solutions. We have thus reduced the problem of solving for

the boundary condition (3.19) to four boundary conditions of the form (3.22), with ( , χ) =

(0, 0), (0, π/2), (π/2, 0), (π/2, π/2).

Now we let

We now substitute P0 and U into equation (2.17) to get

Therefore

3.23

We noe define

So that

27

3.24

We look for a particular solution of the form

With the choice = Q, equation (2.24) becomes

Which implies

Therefore

3.25

Additionally, the complementary solution for is

So the solution for when y ≤ a and y > a are

3.26a

3.26b

There are 4 χ-dependent constants to find; AI , AII , BI and BII . These constants are

independent of . There are four conditions that we need to satisfy to find the constants

3.27a

3.27b

28

3.27c

3.27d

These conditions ensure that the pressure is continuous over the microchannel and that there

is no through flow at y = −ℓ/2 and ℓ/2.

.

3.4 Pressure Gradient and Constant Velocity Solution

In order for there to be an overall mean flow in the positive x-direction, there must be either a

pressure gradient or a nonzero mean velocity induced on the floor of the channel, in addition

to the herringbone induced velocities. On a global scale the herringbone velocities average

out because for every forward flow herringbone there is an equal and opposite backwards

flow herringbone due to the step function imposed. Having a constant velocity on the base of

the channel is equivalent to having a moving channel floor, which is only feasible for electro-

osmotically driven flow. This would be impossible with a grooved floor which would need to

be pressure driven.

The U0 term in the expansion for U is the constant velocity. The pressure gradient would only

be in the x-direction. Therefore we define the pressure for pressure driven flow as P0 = −rx

where r is positive. This will create a flow in the positive x-direction as the pressure gradient

(−r) is negative, so the pressure reduces as x increases and hence fluid will flow from high to

low pressure areas.

P0 = −rx and U = U0 which implies P0x = −r, P0y = 0, P0xx = 0 and Ux = 0. Therefore the

pressure equation (3.17) holds and the equations for v and w ((3.11) and (3.18) reduce to v =

0 and w = 0. However the equation for u (3.13) becomes

The velocity (u) generated by electro-osmosis is linear in z (Couette flow) whereas the

constant pressure gradient flow is quadratic in z (Poiseuille flow). For small z, this implies

that the velocity generated by the constant electro-osmosis is much greater than pressure-

driven flow. From a manufacturing stand-point the requirement for a high pressure to drive

the flow is undesirable and electro-osmosis is much easier and effective to use. As stated in

29

the introduction, this project will not look at pressure-driven flows. We set r = 0 and therefore

the global flow is created by U0 only. However, it is useful to know that the model can easily

be changed to model pressure driven flow by setting U0 = 0 and r to the non-zero value of the

pressure gradient. We label the flow in the x-direction due to U0 as ue:

4. mixing analysis

4.1 Crossflow and mixing in obstructed and width-constricted rotating

radial microchannel

The crossflow and mixing in rotating radial microchannels with various obstruction and/or

width-constriction geometries have been investigated to improve samples/reagents mixing

using a centrifugal microfluidic platform. It is found that a channel with repeated cycles, or

patterns, of obstruction followed by width-constriction (OWC) provides the best mixing

result. Crossflow in the microchannel is highly intensified even at moderate rotation speed

less than 100 rad/s, due to the OWC configuration with increased mixing from a combination

of (a) local centrifugal acceleration abthat arises from flow negotiating corners of the

obstructions in the channel, and (b) Coriolis accelerationacorinduced from throughflow in the

rotating microchannel, which is highly amplified in the two narrower sub-channels

partitioned by the center obstruction in the channel as well as the downstream channel with

width constriction. Moreover, mixing is further enhanced with flow splitting at the stagnation

point of an obstruction followed by flow recombination with jet–jet impingement mixing

downstream of the obstruction and upstream of the width constriction. Numerical and

experimental models have been developed and their results agree well with each other. As

much as 95% uniformity in mixing can be achieved for a short 30-mm long radial

microchannel with repeated OWC patterns at a moderate rotation speed of 73 rad/s withEk=

0.049 and Ro= 15.4. The performance of the rotating OWC channel far exceeds that of the

stationary OWC channel, the rotating unobstructed/obstructed microchannel, and the rotating

width-constricted microchannel.

The flow and mixing in rotating obstructed and or width-constricted radial microchannels

have been investigated by numerical simulation as well as complementary experiments. The

results have been bench-marked against several results: (a) rotating radial unobstructed

30

channel, (b) stationary radial obstructed/constricted channels, and (c) rotating channel with

width-constriction in the entire channel. Also, optimization on obstruction length and spacing

between adjacent obstructions has been made. The results can be summarized as follows,

(1) The crossflow in the cross-sectional planes of the rotating radial obstructed channel is

determined by interaction of theacor and localab.

(2) The flow rate in the channel is determined by the channel length, length of obstruction,

the width-constriction, and the rotation speed. Better mixing can be obtained from either

smaller obstruction length and/or larger spacing between adjacent obstructions. The

obstruction acts also as a barrier splitting/delaminating the flow into two narrow sub-streams,

one of which the two accelerations, Coriolis and local centrifugal accelerations, add up and

the other for which the two accelerations oppose creating complicated fluid folding and

mixing.

(3) Improvement can be best achieved in channel with OWC. This allows jet–jet

impingement and enhanced Coriolis effect from narrow channel with intense recirculation

rate and higher crossflow velocity as well as shorter distance for the crossflow to carryout

mixing. The latter could not have been achieved just by patterned obstructions, or width-

constriction.

(4) Higher rotation speed with smaller Ekincreases both acor and local ab (given increased

throughflow velocity) and reduces viscous friction effect, thus enhances mixing.

(5) With the special configuration of OWC, only moderate rotation speed is required to

obtain effective mixing in microchannel. .

The results of the investigation offer a new perspective for understanding the crossflow and

mixing in the rotating radial obstructed and/or width-constricted channel. This would be

useful for optimizing mixing in the microchannel, as well as lending itself to benefiting heat

and other transfer processes. (Leung , Ren .(2013)

4.2 Two-fluid mixing in a microchannel

A numerical study of the mixing of two fluids (pure water and a solution of glycerol in water)

in a microchannel was carried out.By varying the glycerol content of the glycerol/water

solution, the variation in mixing behavior with changes in the difference in the properties of

31

the two fluids (e.g., viscosity, density and diffusivity) was investigated. The mixing

phenomena were tested for three micromixers: a squarewave mixer, a three-dimensional

serpentine mixer and a staggered herringbone mixer. The governing equations of continuity,

momentum and solute mass fraction were solved numerically. To evaluate mixing

performance, a criterion index of mixing uniformity was proposed. In the systems considered,

the Reynolds number based on averaged properties wasRe=1 and 10. For low Reynolds

numberðRe¼1Þ, the mixing performance varied inversely with mass fraction of glycerol due

to the dominance of molecular diffusion. The mixing performance deteriorated due to a

significant reduction in the residence time of the fluid inside the mixers.

The mixing of two fluids was numerically modeled for two types of micromixer: a three-

dimensional serpentine mixer and a staggered herringbone mixer. In these calculations, the

mixing of pure water with a solution of glycerol in water was investigated for three different

mass fractions of glycerol (/¼0, 0.2 and 0.4). These fluids were chosen to test the mixing

behavior of fluids with different properties and a large concentration gradient. The

dependence of the mixing performance on/ atRe=1 and 10 was examined. AtRe=1, the

mixing performance of both mixers varied inversely with mass fraction of glycerol due to the

dominance of molecular diffusion. When the Reynolds number was increased to 10, the

opposite trend was observed for the serpentine mixer. This change in behavior was attributed

to the enhancement of flow advection at large/. However, no such change was observed on

increasing the Reynolds number in the herringbone mixer. In fact, not only was the expected

enhancement of chaotic advection absent on increasing the Rein the herringbone mixer, the

mixing performance actually deteriorated due to a significant reduction in the residence time

of the fluids inside the mixer. (Liu , et.al.,2004) )

4.3 Single-phase fluid flow and mixing in microchannels

In the last decade there has been an exponential increase in microfluidic applications due to

high surface-to-volume ratios and compactness of microscale devices, which makes them

attractive alternatives to conventional systems. The continuing growing trends of microfluidic

highlights the importance to understand the mechanism and fundamental differences involved

in fluid flow and mixing at microscale. In the present article, the experimental research

efforts in the area of microscale single-phase fluid flow and issues associated with

investigations at microscale flow have been summarized. The experimental data are being

analyzed in terms of friction factor, laminar-to-turbulent transition, and the effect of

32

roughness on fluid hydrodynamics for different cross-sectional geometries.The differences in

the uncharacteristic behavior of the transport mechanisms through microchannels due to

compressibility and rarefaction, relative roughness, property variations and viscous

dissipation effects are discussed. Finally, progress on recent development of micromixers has

been reported for different micromixer types and designs. The micromixers have been

quantified based on their operating ranges (in terms of characteristic dimensionless numbers

such as Reynolds numberRe, Peclet number Pe, and Strouhal number St) and mixing

characteristics.

Microscale devices are powerful tools for process development and have been successfully

applied for improvement of established chemical processes in industry. In recent years

microscale devices have been produced for a wide variety of unit operations in chemical

industry (such as mixers, reaction vessels, valves, pumps, extractors, heat exchangers, etc.).

From the patent and research article analysis carried out in the present review it can be seen

that most of the development is being carried out in the last decade and it is still in progress.

In last 2–3 years the focus is more in the field of applications rather than development of

microscale devices. For the applications in microreaction or mixing field, it is required to

develop understanding about the fluid flow behaviour and mixing effects in the microscale

devices. In the present review the experimental research efforts of fluid flow behavior and

mixing effects reported by various researchers have been analyzed and discussed.For the

friction factor and transition from laminar-to-turbulent analysis in microchannels, it was

observed that the good agreement with conventional theory has been reported by the authors

who have carried out the geometrical measurements before experiments and accounted for

losses (entrance and exit) during data collection and analysis. It is demonstrated that the

average roughness parameter is not adequate to characterize the surface roughness in

microchannels due to scale effects. Though in recent papers the discrepancies in

microchannels due to dimensional measurements and data collection and analysis have been

resolved with accurate measurements; more attention is required for the scale effects

(dho50mm), surface roughness and compressibility effects in microchannel. Therefore, much

work is required in this area to understand the complete fluid dynamics in microchannels.

Finally, different designs of micromixers and their operating conditions have been discussed.

The micromixers were categorized based on their principle of operation. Though, there are

numerous micromixer designs, still there is a room for new robust and professional designs. It

is found that micromixing research is focused mostly at the laboratory scale, and fewer

33

efforts are made on pilot-plant and industrial scale. As a future development it is required to

establish the micromixers as production apparatus in the chemical industry. Though the

performance of active micromixers is better than passive ones, benchmarking and application

based pilot-plant studies are still required. For future development of micromixers it is

required to characterize the mixing with real-case mixing solutions. (Kumar ,et.al.,2011)

4.4 Gas–liquid two-phase flow in microchannel at elevated pressure

The present study deals with pressure effects on the hydrodynamic characteristics of gas–

liquid two phases within a T-junction microchannel. The operating pressure is in the range of

0.1-5.0 MPa. Nitrogen and de-ionized water are selected as the test fluids. The gas Weber

numbers vary from 1.37x10-5to 3.46 at atmospheric pressure and from 1.70x10-3to 70.32 at

elevated pressure,respectively. The liquid Weber numbers are in the range of 3.1x10-3-4.9.

The operating pressure plays an important role in gas–liquid two phases flow. Seven typical

flow patterns such as bubbly flow, slug flow, unstable slug flow, parallel flow, slug-annular

flow, annular flow, and churn flow are observed. Based on the force analysis of the gas and

liquid phase in microchannel, the formation mechanisms of flow patterns are discussed at

great length, and the flow pattern maps are divided into five regions usingWeGSandWeLSas

coordinates. These results are beneficial for future investigation to understand gas–liquid

two-phase mass transfer and reaction characteristics in microchannel at elevated pressure.

Gas–liquid two-phase flow in T-junction rectangular microchannel with the hydraulic

diameter of 400mm at atmospheric and elevated pressure (1.0-5.0 MPa) has been

investigated. The superficial velocities range from 4.62x10-2to 23.15 m/s for gas and from

2.31x10-2 to 0.93 m/s for liquid. The gas Weber numbers vary from 1.37x10-5 to 3.46 at

atmospheric pressure and from 1.70x10-3 to 70.32 at elevated pressure, respectively. The

effect of operating pressure on the liquid Weber numbers can be ignored, which are in the

range of 3.1x10-3 -4.9.Seven typical flow patterns such as bubbly flow, slug flow, unstable

slug flow, parallel flow, slug-annular flow, annular flow and churn flow are also observed in

the T-junction rectangular microchannel at atmospheric and elevated pressure, respectively. It

is found that the same flow pattern shows different detail characteristics due to the operating

pressure, which may induce the different gas–liquid mass transfer and reaction performance.

The hydrodynamic characteristics of gas–liquid two phases are mainly affected by the

interfacial tension of gas–liquid two phases, the gas inertia force and the liquid inertia force.

Based on the force analysis of gas and liquid in microchannel, the formation mechanism and

34

process of observed flow patterns are discussed at great length. The flow pattern maps are

divided into five regions usingWeGSandWeLS as coordinates based on their formation

mechanisms. The transition lines shift to higher WeGS and lowerWeLSat elevated pressure

compared to the atmospheric pressure. The transition line, from zone I to II, shifts to higher

WeGSand lowerWeLSwhen the operating pressure increases from 1.0 MPa to 5.0 MPa.

Other transition lines from zone II to III, from zone III to IV, and from zone III to V almost

remain unchanged at elevated pressure. It is important to note that this study gives a

contribution to the influence of operating pressure on the gas–liquid system in T-junction

microchannel. This will serve as the basis for future gas–liquid two-phase mass transfer and

reaction characteristics in microchannel at elevated pressure. (Zhaoet et.al.,2013)

4.5 Liquid mixing in gas–liquid two-phase flow by meandering

microchannels

The influence of the channel radius on the mass transfer in rectangular meandering

microchannels (width200–400um and height of 150um) has been investigated for gas–liquid

flow. Laser induced velocimetry measurements have been compared with theoretical results.

The symmetrical velocity profile, known from the straight channel, was found to change to an

asymmetrical one for the meandering channel configuration. The changes in the secondary

velocity profile lead to an enhanced radial mass transfer inside the liquid slug, resulting in a

reduced mixing length. In the investigated experimental range (superficial gas velocity 0.08

m/s and superficial liquid velocity 0.01–0.07 m/s) the mixing time was reduced eightfold

solely due to changes in channel geometry. An experimental study on the liquid slug lengths,

the pressure drop and their relation to the mass transfer have also been performed.

Experimental results were validated by a simulation done in Comsol Multiphysics . To obtain

information for higher velocity rates, simulations were performed up to 0.64 m/s. These

velocity variations in the simulation indicate the occurrence of a different flow pattern for

high velocities, leading to further mass transfer intensification.

We investigated mixing in liquid slugs for gas–liquid Taylor flow in straight and meandering

microchannels. Velocity profiles were determined both, experimentally and numerically, to

explain the mixing results. Mixing length could be decreased by geometrical adaptions to

12% compared to the straight reactor design. Enhancement of the radial mass transfer in gas–

liquid microreactors was achieved by introducing regular bends. For a given channel width, a

smaller bend radius provides a more effective mass transfer over the channel center line.

35

Increasing the channel width solely leads to increasing mixing length. Since the liquid slug

volume increases as well, the mixed volume per mixing time decreases at increasing channel

widths. Hence an extrapolation to the miniscale (dh≈1 mm) will be a promising approach in

future projects. The decrease of mixing length by meandering channels is caused by an

asymmetrical velocity profile in the channel bend. Compared to the symmetrical recirculation

in straight channels, the inner vortex moves to the slug back and shifts across the center line

to the outer half. Depending on the velocity, the vortex at the outer half may be divided into

two vortexes or diminishes completely. This effect is only observed at sufficient high

velocities (>0.1 m/s) and corresponds to the Dean vortices observed for one phase flow in

curved channels. For low Dean numbers (low velocity, small channel width and large bend

radii, respectively) the asymmetrical velocity profile diminishes. Observations done at

different positions indicate a fast adaption of the flow profile on the geometry: As soon as the

slug enters the bend, the asymmetrical profile as it was proposed from numerical

considerations was observed and the symmetrical profile was obtained directly behind the

bend. Therefore fast and efficient mixing can be achieved by changing the flow direction

continuously. The total pressure drop per channel length increases by applying meandering

structures. However, the pressure drop per mixing length will decrease by applying

meandering structures. Beside Reactor A (straight channel), all reactors yield within the

measurement uncertainty in the same pressure drop per mixing length. Therefore no energy

dissipation occurs by applying meandering channels. In summary, meandering channels are a

useful tool to enhance mixing in gas–liquid flow in microchannels, whereas large Dean

numbers lead to a more efficient mixing (Fries , et. al.,2009)

4.6 Mixing process of immiscible fluids in microchannels

The paper is concerned with experimental investigations and numerical simulations of

immiscible flows in microchannels in the presence of interfacial surface tension. The aim of

the present study is to model the unsteady dynamics of the vortical structures and interface

shape in the Y-branching geometries with square cross-sections. The tested fluids are

Newtonian and weakly elastic polyacrylamide solutions in water (modelled as shear thinning

Carreau–Yasuda fluids). The experiments used specially designed configurations based on

optical and confocal microscopic devices; PIV measurements of the velocity distributions and

direct visualizations of the interface are obtained. The simulations performed with the VOF

solver implemented in the FLUENT code are validated by experiments for small and medium

Reynolds numbers (0.1 <Re< 200). The numerical solutions offer a detailed description of the

36

vortices formation in the vicinity of the interface, phenomena which directly influence the

mixing and diffusion processes within the micro-geometry here investigated.

The main goal of the present study was to investigate and model the formation of vortices in

the vicinity of the interface between two immiscible fluids, during the dislocation of one

liquid by another liquid in a micro-branching geometry. The work has focused on the 3D

numerical simulations of the unsteady flow patterns in a micro-bifurcation generated by the

travelling of a separation surface. The VOF subroutine from the commercial FLUENT code

(unsteady laminar and isochoric solvers) was first tested and validated against several

experiments, performed with Newtonian and weakly elastic viscous fluids, on two Y-channel

geometries with square cross-sections. In all cases accurate representations of the

experimental flow spectra and interface shape are obtained, which confirms that numerical

computations provide an accurate representation of the real flow patterns within the channel.

The presence of interfacial surface tension determines the shape of a clearly defined

separation surface between the contact phases. In its neighbourhood, transitory 3D-vortices

are formed, a phenomenon which determines the local mixing within each phase, even at

moderate and low Reynolds numbers. This unsteady complex hydrodynamics develops

rapidly in a microchannel, but it is well captured and described in our numerical simulations.

Even if the present studies are limited to only the flows of immiscible Newtonian and

generalized Newtonian liquids, the results offer a fair description of the unsteady patterns

developed in micro-bifurcations and their interdependence on the evolution of the interface

shape. The modelling of the 3D-vortical structures during the displacement of the primary

phase from the channel contains value information in developing novel lab-on-a-chip

applications, especially if a diffusion process between phases follows that dynamical process.

We believe that interfacial surface tension and normal stresses (together with no-slip

conditions at the walls) might be the major factor which influences the mixing process of

complex fluids in microchannels at low Reynolds numbers. This assertion is now being tested

experimentally with work in progress being focused on obtaining PIV measurements of the

micro-flows velocity distributions in the presence of the interface between a Newtonian oil

and polymer solutions with different concentrations of polyacrylamide in water. (Balan et.

al.,2010)

37

4.7 Mixing of a split and recombine micromixer with tapered curved

microchannels

We demonstrate a novel parallel laminar micromixer with two-dimensional staggered curved

channels with tapered structures. Dean vortex flows are produced in curved rectangular

channels by centrifugal forces. The split structures of the tapered channels result in the

uneven split of the main stream and the reduction of the diffusion distance of two fluids.

Furthermore, when one stream is injected into the other the impingement effects increase the

mixing strength. Cross-sectional concentration distributions and particle trajectories are

utilized to examine the flow characteristics inside the curved microchannel numerically. To

evaluate the mixing performance of the designed micromixer, four different designs of a

curved channel micromixer are introduced for the purpose of comparison. The mixing index

of the staggered curved-channel mixer with a tapered channel is 20% higher than those of the

other curvedchannel mixers: i.e., the staggered curved-channel mixer with sudden contracted

channels, the staggered curved-channel mixer with uniform channel width and the continuous

curved-channel mixer. However, a comparison of the pressure drop penalty for the mixing is

also reported. The pressure drop of the staggered curved-channel mixer with a tapered

channel is about 50% higher than those of the other two staggered curved-channel mixers.

The effects of various Reynolds numbers (Re) and channel configurations on mixing

performances are investigated in terms of the experimental mixing indices and the

computational interfacial patterns. It appears that the Dean vortex and split and recombine

(SAR) effects provide improved mixing when theReis increased above 5. At theReof 50, the

channel length necessary for mixing to be achieved is 5 times shorter compared to the case

where the Reequals 1. The comparison between the experimental data and numerical results

shows a very similar trend.

The centrifugal forces in curved flow channels cause fluids to produce Dean vortex flows.

The existence of the secondary flows, the split and recombine structures of the flow channels,

and the impingement effects result in increased mixing strength. On the basis of this

principle, a parallel laminar micromixer composed of several staggered three-quarter ring-

shaped channels and a semicircular channel is designed in our study. Three- dimensional

computational fluid dynamics simulations are performed to investigate the mass transfer and

fluidic behavior in a curved microchannel. The cross-sectional concentration distributions

and the particle trajectories are utilized to examine the mixing and flow characteristics inside

38

the staggered curved microchannel with tapered structures. The uneven split of two fluids

inside the staggered channels improves the mixing performance. The effects of various

Reynolds numbers and four different curved-channel configurations on mixing performances

are investigated in terms of the experimental mixing indices and the computational interfacial

patterns. The results indicate that for low Reynolds numbers (o5) the secondary flows are

negligible and only diffusion dominates the mixing performance. At Reynolds numbers

greater than 10, the interface configuration of two fluids is affected by the secondary flow

and the lamellar formation. The increased interface area of two fluids could promote

increased mixing. At the Re of 50, the mixing length at the third segment corresponding to

the downstream distance of 10.5 mm can be achieved in a distance 5 times shorter than when

the Re equals 1. The simulation results are in good agreement with the experimental

measurements. The simple two-dimensional microstructure is easily fabricated and can be

integrated with the pretreatment and/or detection microfluidic system. (Sheu et.al.,2012)

4.8 Pumping and mixing in a microchannel using AC asymmetric electrode

arrays

A numerical study of electroosmotic microchannel flow driven by arrays of AC (alternating

current) asymmetric electrodes was carried out. By installing asymmetric electrode arrays on

the top and bottom walls of the microchannel, pumping and mixing flow modes can be

generated. The ‘pumping mode’ (P) is generated when the sequences of asymmetric electrode

pairs (narrow to wide) on the top and bottom walls are in phase, whereas the ‘mixing mode’

(M) is generated by switching the sequence of electrode pairs of the top wall (e.g., wide to

narrow). By combining mixing and pumping modes, enhanced mixing performance can be

achieved without significantly reducing the flow rate. Among various combinations

ofPandMmodes, the alternatingPMmode showed the best mixing performance due to the

iterative convergent and divergent flow motions. The effects of Peclet number and channel

height on the mixing efficiency were analyzed in detail.

A detailed numerical analysis has been performed to elucidate the pumping and mixing

modes induced in a microchannel using AC asymmetric electrode arrays. The asymmetric

electrode arrays were installed on the top and bottom walls of the channel. The pumping

39

mode was obtained when the sequence of electrode pairs on the top wall was the same as that

on the bottom wall, whereas the mixing mode was generated by switching the sequence of the

electrode pairs on the top wall. Various combinations of pumping and mixing modes were

tested to optimize the channel performance in terms of the mixing efficiency and pumping

flow rate. The species equation was solved with the Stokes equation to obtain the

concentration and velocity field data. Most of the calculations were performed at Pe=104.

The results showed that for a given slip velocity, pumping was more effective in channels

with smaller heights. For the mixing mode, the shape of the circulation cell was gradually

distorted as the top wall position was shifted with respect to the bottom wall. By contrast,

such shifting of the relative positions of the top and bottom walls had little effect on the

pumping mode. The mixing efficiency (eo) at the outlet decreased as the Peclet number (Pe)

was increased. As the proportion of mixing modes within a sequence of mixing and pumping

modes was increased, the flow rate decreased linearly and the mixing efficiency (eo)

increased. Pumping was prohibited in systems with a very large proportion of mixing modes.

During each pumping mode, symmetric diverging and converging flow patterns were

observed; however, a zigzag motion was observed in theMM0 mode. Three mixing modes

were obtained: convective circulating motion; diffusive motion arising from forcing the main

flow through a narrow region; and diverging flow motion. The alternatingPMmode showed

good mixing performance throughout the entire calculation domain. As the channel height

decreased (H= 20, 10 and 5), almost 90% of the mixing efficiency was achieved at large

Pe(Pe= 200, 1000 and 7000). Systems with a smaller channel height and a smaller Pe

exhibited better mixing performance due to the strong diffusion across the channel height.

(Yoon et.al. 2008)

4.9 Parametric study on mixing of two fluids in a three-dimensional

serpentine microchannel

A flow analysis method using Navier–Stokes equations has been applied to a parametric

investigation of mixing two fluids in a three-dimensional serpentine microchannel, which has

not been reported so far. The serpentine microchannel with “L-shaped” repeating units is

found to be effective in mixing fluids at Reynolds numbers, 1, 10, 35 and 70. Mixing

performance and pressure drop characteristics with two geometrical parameters, i.e., the ratio

of channel height to channel width and the ratio of the length of a straight channel in an “L-

40

shaped” unit to the channel width, have been analyzed at four different Reynolds numbers. A

mixing index has been used to quantify and elucidate mixing behavior in the microchannel.

The vortical structure of the flow in the channel is also analyzed to identify the relationship

with mixing performance. The results reveal that mixing and pressure drop characteristics in

a serpentine channel are very sensitive to the geometric parameters, showing different

behavior at various Reynolds numbers.

A parametric study on the performance of a three-dimensional serpentine channel with “L-

shaped” repeating units has been performed using computational fluid dynamics. Mixing and

pressure drop characteristics have been investigated in terms of two geometric parameters

i.e., the ratio of channel height to channel width, h/w, and the ratio of the length of straight

channel in a “L-shaped” unit to channel width,d/w, as well as Reynolds number. The

presence of bends at the end of the straight section of the “L-shaped” unit strongly influences

the transverse flow structure in the channel, the vorticity contours on the planes perpendicular

to the flow direction, and variation of circulation and mixing index along this region. As the

Reynolds number increases from 1 to 70, both the levels of circulation and the mixing index

increase throughout most of the channel. The results reveal that mixing is significantly

dependent on both geometrical parameters. The mixing performance of the channel is

generally improved with a decrease in the value of d/w. The mixing index shows a minimum

value at h/w=1.0at higher Reynolds numbers, i.e., 35 and 70, as the lowest surface to volume

ratio of the channel is found under these conditions, while the effects ofh/wbecome negligible

at lower Reynolds numbers, i.e., 1 and 10. The pressure drop characteristic of the serpentine

channel is also sensitive to the two parameters. At lower Reynolds numbers, variation of the

two geometrical parameters has negligible effects on the pressure drop. However, the effects

of the two parameters on pressure drop become pronounced at higher Reynolds numbers. For

a given Reynolds number, the pressure drop increases as both parameters ,d/w and h/w, are

decreased (Ansari , Kim 2009)

4.10 Mixing performance of a planar micromixer with circular

obstructions in a curved microchannel

A numerical investigation of the mixing and fluid flow in a new design of passive

micromixer employing several cylindrical obstructions within a curved microchannel is

presented in this work. Mixing in the channels is analyzed using Navier–Stokes

equations and the diffusion equation between two working fluids (water and ethanol)

41

for Reynolds numbers from 0.1 to 60. The proposed micromixer shows far better

mixing performance than a T-micromixer with circular obstructions and a simple

curved micromixer. The effects of cross-sectional shape, height, and placement of the

obstructions on mixing performance and the pressure drop of the proposed micromixer

are evaluated.

A planar curved laminating passive micromixer that is capable of mixing at low

Reynolds numbers was proposed in this work. Detailed study of the effects of

geometry and placement of obstructions on mixing was carried out using Navier–

Stokes analysis. The study was performed using a Reynolds number range from 0.1 to

60. First, the effect of the cross-sectional shape of the obstructions on mixing was

investigated. Second, the mixing performances of the T-micromixer with obstructions

and a simple curved micromixer without obstructions were compared to that of the

proposed micromixer. Finally, the effects of the obstruction height and Reynolds

number on mixing performance were evaluated. Micromixers with circular and

hexagonal obstructions show almost the same mixing performances regardless of the

Reynolds number, while micromixer with diamond obstructions shows far less mixing

performance compared to the others except at Reynolds numbers greater than 50. The

curved channel with circular obstructions shows much higher mixing performance than

those of the T-micromixer with obstructions and a simple curved micromixer without

obstructions throughout the Reynolds number range considered. The proposed

micromixer with circular obstructions shows the best mixing index at the exit of the

micromixer, 88% among the tested micromixers, at Reynolds numbers of 0.1 and

greater than 15. The minimum mixing index, 72%, was seen at Re = 5. The pressure

drop increased with an increased number of obstructions. However, this increase in

pressure drop is not substantial, and can be an acceptable tradeoff for improved

mixing. The mixing generally increased as the height and number of the obstructions

increased. However, both of these effects disappeared as the Reynolds number

approached 60, where the formation of secondary flows due to channel curvature

dominated the other mechanisms due to obstructions. The proposed micromixer design

is planar, and hence requires only simple fabrication. (Alam A. et.al.,2013)

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4.11 Single phase electrokinetic flow in microchannels

This chapter reviews the basics of the electrical double layer (EDL) and focuses on single-

phase electrokinetic flow in microchannels. Electrokinetic-driven flow is an important pillar

of microfluidics; key applications on lab-on-a-chip devices require liquid pumping, mixing,

thermal cycling, and accurate sample dispensing and separating. A great majority of these

processes are carried out employing electrokinetic processes, which occur as a result of the

EDL. The two basic electrokinetic phenomena are electrophoresis and electroosmosis; this

chapter focus on the later. Electroosmosis is the liquid motion in a microchannel due to

interactions with the EDL under an applied electric field. Briefly, all charged surfaces will

have an EDL, and under the influence of the applied electric field, the counterions will move

toward the electrode with the opposite charge, pulling the liquid with them, resulting in

electroosmotic flow. One of the main advantages of electroosmotic flow is that it can

generate the required flow rate in very small microchannels, something that would be

difficult to achieve with pressure-driven flow. Additionally, plug-type velocity profiles are

obtained with electroosmotic flow, which decreases dispersion in microsystems.

Electroosmotic flow allows for liquid transport in complex microfluidic networks, since it

does not require any moving parts. This chapter presents a detailed analysis and numerical

simulations of electroosmotic pumping in a rectangular microchannel, a common

configuration in microfluidic devices. The main parameters affecting electroosmotic flow are

discussed, including the description of the EDL by the Poisson–Boltzmann equation along

with zeta potential, used as the boundary conditions on channel surfaces. The experimental

techniques for studying electroosmotic flow are also reviewed and their main characteristics

are highlighted. The nature of electroosmotic flow in heterogeneous surfaces is discussed,

describing how surface heterogeneity distorts electroosmotic flow. AC electroosmosis has

unique features and has been used in various applications, including the generation of bulk

fluid motion by employing specially designed electrodes. Electrokinetic mixing is an another

attractive use of electroosmotic flow, since, due to the small dimensions of microfluidic

channels, low Reynolds numbers are obtained and mixing is strongly dominated by diffusion.

Microfluidic mixing can be enhanced by electrokinetics by heterogeneous patches that distort

electroosmotic flow. Passive electrokinetic micromixers have been achieved by adding

regions of positive surface charge to microchannels with negatively charged surfaces, which

introduces an advective mixing component and increases circulation, thus significantly

enhancing mixing. An important challenge in lab-on-a-chip devices is the dispensing of

43

minute quantities of liquid to be used as samples in chemical and biomedical analysis.

Sample loading and dispensing is discussed, including mathematical model and simulation.

Finally, the effects of Joule heating, heat generation due to current passing through the buffer

solution, are analyzed in detail, explaining why higher average velocities are obtained due to

Joule heating. Practice problems are presented to reinforce the fundamentals of

electroosmotic flow ( Li, 2014).

4.12 Fluid mixing in a microchannel with longitudinal vortex generators

A heat transfer enhancement technique based on longitudinal vortex generators (LVGs) has

been well established for large-scale heat exchangers. Motivated by the success of the LVGs,

this paper is intended as an investigation of micromixers based on the T-shaped channel with

rectangular winglet pairs (RWPs) mounted on the bottom of the main channel. The RWPs

stay with an angle of attack to the main flow direction and generate longitudinal vortices to

enhance fluid mixing. The effects of geometrical parameters on the performance of

micromixers with micro-scale LVGs are investigated by numerical simulations and the

Taguchi method. The validity of numerical simulations is examined by comparing the

numerical and experimental results. The results obtained for a wide range of Reynolds

numbers show that the mixing efficiency of the micromixer with divergent RWPs is greater

than that of the micromixer without RWPs for convection-dominant cases as well as

diffusion-dominant cases. A static Taguchi analysis shows that the relative effectiveness of

the geometrical parameters can be ranked as: asymmetry index > angle of attack > winglet

height > winglet spacing. Based on the relative influence of the geometric parameters, we can

obtain an optimal parameter group on the parameter selected range.

Numerical simulations on fluid mixing in the T-shaped channel with micro-scale RWPs

mounted on the bottom of the channel are carried out. Besides, we fabricate the micromixer

by a lithography process and the fluid mixing in the micromixer is observed by using a

confocal spectral microscope imaging system. The numerical and experimental results are in

agreement qualitatively. The Taguchi method is applied to find out the better combination of

the geometrical parameters. The results show the following trends. (i) When the Reynolds

number is large enough, the RWPs generate longitudinal vortices which enhance fluid mixing

effectively. (ii) The results obtained for a wide range of Reynolds numbers show that the

44

mixing efficiency of the micromixer with divergent RWPs is greater than that of the

micromixer without RWs for convectiondominant cases as well as diffusion-dominant cases.

(Hsiao et.al., 2014)

4.13 Ideal micromixing performance in packed microchannels

In this work, the hydrodynamics and the micromixing characteristics in the packed and non-

packed microchannels were studied experimentally at low Reynolds numbers (8–300). The

mixing performances in microchannels were observed with high-speed CCD camera, and

were evaluated in terms of a segregation index by the Villermaux/Dushman method. The

fluid elements were drastically stretched, folded, and sheared with the effects of micro-

particles in packed microchannels, resulting in extremely shorter diffusion distance and larger

effective interfacial area, and much higher micromixing efficiency compared with those of

non-packed microchannels. Under enough packing length and appropriate packing position of

micro-particles, the ideal micromixing performance could be obtained in packed

microchannels. Furthermore, the micromixing time in packed microchannels was determined

based on the incorporation model, and its value was in the range of 0–0.1 ms.

The hydrodynamics and the micromixing characteristics in the packed and non-packed

microchannels were investigated by highspeed imaging techniques and Villermaux/Dushman

method, respectively. From the observation of the hydrodynamics, it is seen that the mixing

of miscible liquid–liquid two phases was dependent on the packing length of micro-particles

in the packed microchannel. As the same as the macromixing (or mesomixing), the

micromixing performance in the packed microchannel was improved obviously compared

with the non-packed microchannel. The reason is that the fluid elements were stretched,

folded, and sheared with the effects of micro-particles in packed microchanels, resulting in

much shorter diffusion distance and larger effective interfacial area. In particular, increasing

the packing length and decreasing the distance between T-junction and the threshold of the

packing section were both beneficial to the micromixing performance in packed

microchannels, and the ideal micromixing could be obtained under enough packing length

and appropriate packing position of micro-particles. The micromixing time in

microchannels was also evaluated based on the incorporation model, and its value was in the

range of 0–10-4s. The extremely low tm also provides a new approach for studying the ultra-

fast reaction kinetics. (Su et. al.,2011)

45

5.conclusion

Throughout this seminar the aim has been to model flow in a microchannel analytically. We

used electro-osmotically induced flow from a herringbone pattern on the floor of the channel.

We then continued to find some of the mixing properties of these flows. We have only

concentrated on simple configurations and have found some good results. We successfully

manipulated the governing equations of the flow and imposed the boundary conditions to get

an analytical solution for the velocity field.We have only modelled some simple

configurations of microchannels here. There are many studies that could follow from this

seminar.We have presented the lithographic techniques for the fabrication of the

microchannels, relying on the wet chemical etching and dry etching (optical lithography,

RIE, deep RIE).

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