ANALYSIS OF ELECTROKINETIC FLOW IN MICROFLUIDIC CHIPS

By

Sanket Aryal

Submitted in Partial Fulfillment of the Requirements

for the degree of

Master of Science in Engineering

in the

Mechanical Engineering Program

Youngstown State University

May 2012

ABSTRACT

.

MEMS

(Micro-electromechanical systems) and Chemical Engineering Modules

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

ABSTRACT ...................................................................................................................... iii

ACKNOWLEDGEMENTS ..............................................................................................v

LIST OF FIGURES ....................................................................................................... viii

LIST OF TABLES .............................................................................................................x

CHAPTER 1 INTRODUCTION ....................................................................................1

CHAPTER 2 MODELING AND VALIDATION OF ELECTROKINETIC FLOW IN MICROFLUIDIC CHIPS .............12

CHAPTER 3 ANALYSIS OF ELECTROOSMOTIC FLOW IN MICROFLUIDIC CHIPS ...............................................................39

CHAPTER 4 ANALYSIS OF ELECTROPHORETIC FLOW IN MICROFLUIDIC CHIPS ................................................................52

CHAPTER 5 CONCLUSIONS AND FUTURE WORKS ..........................................64

REFERENCES .................................................................................................................66

APPENDIX ..................................................................................................................70

LIST OF FIGURES

LIST OF TABLES

CHAPTER 1

INTRODUCTION

1.1 Lab on chip and its applications

1.2 Modes of flow motion in microfluidic chips

Table 1.1

Means Description Advantages Disadvantages

Panta et al,

2008, 2009, 2010

Electrokinetic

Fluid motion is induced

by electrostatic force.

Uniform velocity

No moving part

Low flow rate;

High electric field;

Depends on the characteristics

of the liquid-solid interface

1.3 Fundamentals of electrokinetic flow

1.3.1 Electroosmosis

Figure 1.1

http://www.bioscience.org/2009/v14/af/3500/figures.htm

p

Eupuutu

e

Edyd

dyvd

owx

y

dydvx dyd

Xow

eox Evv

XE

eov

XE oweo

1.3.2 Electrophoresis

eo

Ev

eo

oreo

Ev oweo

r o

1.4 Electric Double Layer (EDL)

Electrical Double Layer (EDL)

et al

Figure 1.2

et al

1.5 Modeling of electrokinetic flow

et al

et al

et al

1.6 Analysis of electrokinetic flow

1.7 T-Shaped microfluidic chip

et al

et al et al

1.8 Objectives of thesis

1.9 Organization of thesis

Chapter 1

Chapter 2

Chapter 3 Chapter 4

Chapter 3

Chapter 4

Chapter 5

CHAPTER 2

MODELING AND VALIDATION OF

ELECTROKINETIC FLOW IN MICROFLUIDIC CHIPS

2.1 Geometrical modeling

Figure 2.1

2.2 Mathematical modeling

a) Continuity equation

Vt

t

kz

jy

ix

V

V

b) Navier-Stokes equations

xgzu

yu

xu

xp

zuw

yuv

xuu

tu

ygzv

yv

xv

yp

zvw

yvv

xvu

tv

zgzw

yw

xw

zp

zww

ywv

xwu

tw

zu

yu

xu

xp

zuw

yuv

xuu

zv

yv

xv

yp

zvw

yvv

xvu

2.2.1 Problem setup in COMSOL Multiphysics

E1 E2

Figure 2.2

E1

E2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

a) Analyte parameters and physical constants

electro-osmotic flow electrophoretic flow

Table 2.1

)

b) Multi-Physics setup for electroosmotic flow:

Physics of fluid flow:

Governing equations:

Eeupuutu

Boundary conditions:

Table 2.2

oP

xE emdcEx

yE emdcEy

Vu r

emdcEx emdcEy

Physics of electrostatics:

Governing equations:

QJ

EJ

QV

V QJ E

Boundary conditions:

Table 2.3

c) Multi-Physics setup for electrophoresis

Physics of mass transport

Governing equations:

VFcuzcDtc

imiiii

i

i

iicz

VFcmzcDucN iiiiiii

Boundary conditions:

Table 2.4

oC

N

oC N

Physics of electrostatics

Governing equations:

QJ

EJ

QV

V Q

J E

Boundary conditions:

Table 2.5

2.3 Numerical modeling and validation

Table 2.6

Solver Types Usage

Multiphysics methodology.

2.3.1 Multiphysics methodology

Figure 2.7

Pre-processing

Solver

Post-processing

(a) Stationary segregated algorithm

L

L

(b) PARDISO direct solver

(c) Convergence criteria

2.3.2 Solver validation

et

al .

a) Solver validation for mixing

et al.,

Figure 2.8

Figure 2.9

0

500

1000

1500

2000

2500

0 2 4 6 8

b) Solver validation for pumping

et al.,

et al.,

et al.,

Figure 2.10

Figure 2.11

Aguilar et al. 2006)

c) Solver validation for concentration

et al.,

Figure 2.12

Figure 2.13

= =

d) Solver validation for electrokinetic flow

Figure 2.14 JM MacInnes, 2002

Figure 2.15

JM MacInnes, 2002

CHAPTER 3

ANALYSIS OF ELECTROOSMOTIC FLOW IN MICROFLUICIC CHIPS*

3.1 Introduction

et al.,

et al.,

et al.,

et al.,

et al.,

et al.,

et al.,

et al.,

http://www.comsol.com

3.2 Mathematical modeling

u

Eeupuutu

e E

Vu r

VFcuzcDtc

imiiii

u

V

ci Di

zi

u i F

Vu r

Figure 3.1

a b

c

3.3 Results and discussions

Figure 3.2

Appendix A.1

3.3.1 Effect of voltage difference in maximum velocity

Figure 3.3

Figure 3.4

3.3.2 Effect of potential difference in concentration distribution

et al

(a)

Figure 3.5

3.3.3 Transient analysis in concentration distribution in microfluidic chip

Figure 3.6

Appendix A.1

Figure 3.7

3.4 Summary

CHAPTER 4

ANALYSIS OF ELECTROPHORETIC FLOW IN MICROFLUIDIC CHIPS *

4.1 Introduction

et al.,

et al.,

et al.,

et al.,

et al.,

et al., et al., et al.,

et al.,

et al.,

et al.,

et al.,

4.2 Mathematical modeling

Table 4.1

Symbols Values Descriptions

Governing Equations

Physics of fluid flow

Eeupuutu

ErSlipu

Physics of chemical mass transport

VFcuzcDtc

imiiii

VFcmzcDucN iiiiiii

i

iii cz

Figure 4.1

eo Ev

eo

oreo

Ev oweo

r o

4.3 Results and discussion

et al,

4.3.1 Concentration profiles due to chemical mass transport modes

(diffusion, convection, and electrophoretic migration flows)

Figure 4.2

0

0.5

1

1.5

2

2.5

3

3.5

4

0.000 0.001 0.002 0.003 0.004 0.005

Figure 4.3

4.3.2 Effect of electrophoretic mobility on concentration distribution

Appendix A.2

4.3.3 Effect of zeta potential on concentration distribution at the outlet

Figure 4.4

0.1V 0.2V 0.3V 0.4V

Appendix A.2

4.3.4 Effect of potential difference on concentration distribution

Figure 4.5

Appendix A.2

4.4 Summary

CHAPTER 5

CONCLUSIONS AND FUTURE WORKS

REFERENCES

Electrophoresis

http://www.comsol.com

APPENDIX

A.1 SIMULATION CONTOURS FOR VELOCITY AND CONCENTRATION

CONCENTRATION CONTOURS FOR DIFFERENT MODES OF MASS TRANSPORT

Figure A.1.1

Figure A.1.2

Figure A.1.3

Figure A.1.4

Figure A.1.5

Figure A.1.6

VELOCITY CONTOURS

Figure A.1.7

Figure A.1.8

A.2 SIMULATION DATA SHEETS FOR CHEMICAL MASS TRANSPORT

76

Table A.2.1

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

Table A.2.2

92

Table A.2.3