EFFECTS OF SURFACE ROUGHNESS IN MICROCHANNEL FLOWS By AMIT S. KULKARNI A ...

94 Pages·2004·2.1 MB·English

EFFECTS OF SURFACE ROUGHNESS IN MICROCHANNEL FLOWS

By

AMIT S. KULKARNI

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2004
Copyright 2004

by

Amit S. Kulkarni
This document is dedicated to my parents for their ever-extending support and
contribution. .
ACKNOWLEDGMENTS
This thesis would not have been possible without help of certain people and hence I
would like to use this opportunity to thank them. I would like to thank my parents in the
first place for their constant support, encouragement and love all along my way. I would
like to express big thanks for Dr. J. N. Chung for allowing me to work on this project
under his tutelage and showing confidence in me and giving me insightful talks that went
as building blocks in my thesis as well as my master’s education. I would also like to
express my sincere gratitude towards Dr. William Lear, Dr. Darryl Butt and Dr. Wei
Shyy for their time and effort as my committee member. I would also like to thank Dr.
Siddarth Thakur for his assistance with regard to development of the code for the current
study. I would also like to thank my roommates for their support during my master’s
studies. Lastly I would also like to acknowledge the financial support from Motorola.

iv
TABLE OF CONTENTS

page

ACKNOWLEDGMENTS.................................................................................................iv
LIST OF TABLES............................................................................................................vii
LIST OF FIGURES.........................................................................................................viii
NOMENCLATURE.........................................................................................................xii
ABSTRACT.....................................................................................................................xiii
CHAPTER

1 INTRODUCTION........................................................................................................1
1.1 Introduction.............................................................................................................1
1.2 Liquid Flows in Microchannel................................................................................4
1.3 Unique Aspects of Liquids in Microchannels........................................................7
1.4 Commercial Aspects of Microfluidics....................................................................8
1.5 Scientific Aspects of Microfluidics......................................................................11
1.6 Milestones of Microfluidics..................................................................................11
1.6.1 Device Development..................................................................................11
1.6.1.1 Miniaturization approach.................................................................11
1.6.1.2 Exploration of new effects...............................................................12
1.6.1.3 Application developments................................................................12
1.6.2 Technology Development..........................................................................13

2 LITERATURE SURVEY...........................................................................................14
2.1 Introduction...........................................................................................................14
2.2 Wet Bulk Micromachining...................................................................................14
2.2.1 Wet Isotropic and Anisotropic Etching......................................................15
2.2.2 Surface Roughness and Notching...............................................................16

3 GOVERNING EQUATIONS AND OVERVIEW OF ALGORITHM......................22
3.1 Introduction...........................................................................................................22
3.2 Transformation to Body-Fitted Coordinates for 2D geometries...........................23
3.3 Discretized Form of Equations.............................................................................26
3.4 SIMPLE Method...................................................................................................29
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3.4.1 Staggered Grid:...........................................................................................34
3.4.2 Non-staggered Grids:..................................................................................34
3.5 Momentum Interpolation Technique....................................................................35
3.6 Validation of Computational Model.....................................................................36

4 FLOW CONFIGURATION AND TEST CASES.....................................................40
5 RESULTS AND DISCUSSIONS...............................................................................47
5.1 Introduction...........................................................................................................47
5.2 Pressure Drop........................................................................................................47
5.3 Flow Friction........................................................................................................59

6 CONCLUSION...........................................................................................................74
LIST OF REFERENCES...................................................................................................76
BIOGRAPHICAL SKETCH.............................................................................................80

vi
LIST OF TABLES
Table page

4.1 Geometric parameters of microchannels...............................................................45
5.1 Comparison of ∆P /∆P and ∆P /∆P for channels with 1µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................51
5.2 Comparison of ∆P /∆P and ∆P /∆P for channels with 2µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................52
5.3 Comparison of ∆P /∆P and ∆P /∆P for channels with 3µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................52
5.4 Comparison of ∆P /∆P and ∆P /∆P for channels with 4µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................53
5.5 Comparison of ∆P /∆P and ∆P /∆P for channels with 5µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................53
5.6 Comparison of ∆P /∆P and ∆P /∆P for channels with 6µm
sawtooth theo sawtooth theo
average surface roughness.....................................................................................54

vii
LIST OF FIGURES
Figure page

1.1 Scaling of things......................................................................................................2
1.2 Micro heat exchanger constructed from rectangular channels machined in
metal.........................................................................................................................5
1.3 Blood sample cartridge using microfluidic channels...............................................6
1.4 Knudsen number regimes........................................................................................7
1.5 Estimated sales of microfluidic components compared to other MEMS
devices....................................................................................................................10
2.1 A wet bulk micromachining process is used to craft a membrane with
pierzoresistive elements.........................................................................................15
2.2 Roughness caused in microchannels during anisotropic etching process..............16
2.3 Experimentally measured pressure gradient..........................................................19
2.4 A comparison of the measured data of pressure gradient vs. Reynolds
number with the predictions of conventional laminar flow theory........................20
2.5 A comparison of the experimental data of pressure gradient vs. Reynolds
number with the predictions of Roughness viscosity model.................................21
3.1 Collocated grid and notation for a 2-D grid on a physical plane...........................27
3.2 Collocated grid and notation for a 2-D grid on a Transformed
(Computational) plane...........................................................................................28
3.3 The SIMPLE algorithm..........................................................................................33
3.4 Streamlines for the driven cavity problem at Re = 100 on a grid of 100x100.......37
3.5 U-component of velocity contours for the driven cavity problem at Re = 100
on a grid of 100x100.............................................................................................38
3.6 V-component of velocity contours for the driven cavity problem at Re = 100
on a grid of 100x100..............................................................................................38
viii
3.7 U-component of velocity profile along the vertical centerline for the driven
cavity problem at Re = 100 on a grid of 100x100................................................39
5.1 Parallel plates configuration used in the current study..........................................41
4.1 Section of a channel with sawtooth surface roughness. Maximum height of
surface roughness is 1µm......................................................................................41
4.2 Selection of a channel with sawtooth surface roughness. Maximum height of
surface roughness is 2µm.......................................................................................42
4.3 Section of a channel with sawtooth surface roughness. Maximum height of
surface roughness is 4µm......................................................................................42
4.4. Section of a channel with random surface roughness. Average height of
surface roughness is 1µm.......................................................................................43
4.5. Section of a channel with random surface roughness. Average height of
surface roughness is 2µm.......................................................................................44
4.6. Profile of random surface roughness. Average height of surface roughness
is 6µm...................................................................................................................44
4.7. A comparison of pressure drop in Sawtooth 1 channel with 25000 grid
points and 50000 grid points..................................................................................45
4.8. A comparison of pressure drop in Sawtooth 2 channel with 25000 grid
points and 50000 grid points.................................................................................46
5.1. A comparison of pressure drop in channels with average surface roughness
of 1µm to that of theoretical pressure drop in a plain channel..............................48
5.2 A comparison of pressure drop in channels with average surface roughness
of 2µm to that of theoretical pressure drop in a plain channel.............................48
5.3 A comparison of pressure drop in channels with average surface roughness
of 3µm to that of theoretical pressure drop in a plain channel.............................49
5.4 A comparison of pressure drop in channels with average surface roughness
of 4µm to that of theoretical pressure drop in a plain channel.............................49
5.5 A comparison of pressure drop in channels with average surface roughness
of 5µm to that of theoretical pressure drop in a plain channel.............................50
5.6 A comparison of pressure drop in channels with average surface roughness
of 6µm to that of theoretical pressure drop in a plain channel..............................50
ix
5.7 A comparison of pressure drop in channels with sawtooth surface roughness
to that of theoretical pressure drop in a plain channel as the roughness is
increased................................................................................................................54
5.8 A comparison of pressure drop in channels with random surface roughness
to that of theoretical pressure drop in a plain channel as the roughness is
increased................................................................................................................55
5.9 Experimentally measured pressure gradient (a) SS and (b) FS microtubes,
and comparison with the classical theory..............................................................55
5.10 A comparison of the measured data of pressure gradient vs. Reynolds
number with the predictions of conventional laminar flow theory for
trapezoidal microchannels.....................................................................................56
5.11 A comparison of pressure drop in rough channels, reduced width channels and
smooth channel......................................................................................................58
5.12 A comparison of pressure drop in rough channels, reduced width channels
and smooth channel................................................................................................58
5.13 A comparison of pressure drop rough channels, reduced width channels and
smooth channel......................................................................................................59
5.14 A comparison of friction factor in channels with average surface roughness
of 1µm to that of theoretical friction factor in a plain channel..............................60
5.15 A comparison of friction factor in channels with average surface roughness
of 2µm to that of theoretical friction factor in a plain channel..............................61
5.16 A comparison of friction factor in channels with average surface roughness
of 3µm to that of theoretical friction factor in a plain channel..............................61
5.17 A comparison of friction factor in channels with average surface roughness
of 4µm to that of theoretical friction factor in a plain channel..............................62
5.18 A comparison of friction factor in channels with average surface roughness
of 5µm to that of theoretical friction factor in a plain channel..............................62
5.19 A comparison of friction factor in channels with average surface roughness
of 6µm to that of theoretical friction factor in a plain channel..............................63
5.20 A comparison of friction factor in channels with random surface roughness
to that of theoretical friction factor in a plain channel as the roughness is
increased................................................................................................................64
x