Dielectric actuation of uids on a microchip...

Fagpakkeprojekt Report

Dielectric actuation of fluids on amicrochip II

Casper Skovby, s021689Peder Skafte-Pedersen, s021678Simon Eskild Jarlgaard, s021982

Supervisors:

Henrik Bruus

&

Anders Kristensen

MIC – Department of Micro and Nanotechnology

Technical University of Denmark

April 16th 2004

ii

Abstract

This report, made in connection with a fagpakke project, treats of the design, fabricationand test of a microfluidic system integrated in a silicon/glass based microchip.

The primary purpose is to develop a microchip which exploits the parallel capacitor’sability to suck in dielectrica. This principle of dielectric actuation will be utilized to controlthe flow of two immiscible fluids with different dielectric constants.

The goal is that the design, fabrication and test will result in a chip, which is able toproduce bubbles of one liquid in a stream of another liquid by means of turning on andoff an embedded capacitor.

A microfluidic system was designed and fabricated where problems during fabricationprocess caused the chips to be produced without electrodes. Hence the measurementsconcentrated on whether it was possible to obtain the right pressure conditions for acapacitor to act as a valve near an equilibrium.

The test of the chip revealed that this was not possible with the used immiscibleliquids. But experiments with miscible liquids and ethanol and air respectively provideda sensitive system indicating that it might be feasable to produce bubbles by dielectricactuation with a suitable liquid combination.

iii

iv ABSTRACT

Contents

List of figures viii

List of tables ix

List of symbols xi

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Theory 3

2.1 Fluid mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Flow rate and resistance . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.2 Capillary effects – surface tension and Young-Laplace pressure . . . 5

2.2 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Parallel-plate capacitor . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Energy stored in a capacitor . . . . . . . . . . . . . . . . . . . . . . 7

2.2.3 Force and pressure on a dielectricum . . . . . . . . . . . . . . . . . . 8

3 Design 11

3.1 Physical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Physical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Properties of the capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.2 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Fluidic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.1 Overall models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.2 Pressure calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.5 Dimensioning the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5.1 Comments on the channel design process . . . . . . . . . . . . . . . 25

3.5.2 Further investigations . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 Applying the capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6.1 Implementation on the silicon/glass structure . . . . . . . . . . . . . 27

v

vi CONTENTS

4 Production of the microchips 29

4.1 Applying the insulation layer . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Back side contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Fabrication of the channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4 Etching fluidic in- and outlets . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5 Applying glass lid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.6 Summary of the processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Test and measurements of the chip 37

5.1 The setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2.1 First experiment - silicone oil . . . . . . . . . . . . . . . . . . . . . . 405.2.2 Macroscopic experiments . . . . . . . . . . . . . . . . . . . . . . . . 415.2.3 Flow rate measurements . . . . . . . . . . . . . . . . . . . . . . . . . 435.2.4 Alternative fluid combinations . . . . . . . . . . . . . . . . . . . . . 45

5.3 Uncertainty calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.3.1 flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Summary and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Conclusion 55

A Deriving the Navier-Stokes equation 59

B Deriving velocity profile for parallel plates 63

C Flow in a rectangular channel 65

D Processes in the clean room 69

E Exposure masks 75

F Viscosity and density of the grape seed oil 77

G Water flow rates using the water channels 81

H Water flow rates using the oil channel 83

I MatLab-program: Geometriberegning 85

J MatLab-program: Geometriberegning2 89

K Maple simulations 91

L Maple simulations 2 95

Bibliography 109

List of Figures

2.1 Velocity profile for laminar flow . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Radius of surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Contact angle and relation to height . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Capacitor with dielectrica . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Pressure principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Construction of capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Capacitormodel for voltage distribution . . . . . . . . . . . . . . . . . . . . 14

3.4 Capacitor pressure at different heights . . . . . . . . . . . . . . . . . . . . . 163.5 Capacitor pressure at different dielectric constants . . . . . . . . . . . . . . 173.6 Maximum voltage at different dielectric constants . . . . . . . . . . . . . . . 173.7 Two principle models of the fluidic system. . . . . . . . . . . . . . . . . . . 19

3.8 Presumed flow structure in the two models. . . . . . . . . . . . . . . . . . . 193.9 Model with common water inlet. . . . . . . . . . . . . . . . . . . . . . . . . 203.10 Final model with common water inlet and reduced number of right angles. . 203.11 Diagram of the channel system. . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.12 Alternative diagram of the channel system. . . . . . . . . . . . . . . . . . . 213.13 The two final designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.14 Two possible oil pressure drops. . . . . . . . . . . . . . . . . . . . . . . . . . 243.15 Two possible oil pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.16 Design of the capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.17 Cross section of chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.18 Final design implemented in L-edit . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 Overview of the chip position on the wafer. . . . . . . . . . . . . . . . . . . 29

4.2 AZ-resist spun onto the wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Chip after exposure and development. . . . . . . . . . . . . . . . . . . . . . 314.4 SiO2 removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.5 Ti and Al covering the backside of the chip. . . . . . . . . . . . . . . . . . . 31

4.6 Wafer with back side electrodes . . . . . . . . . . . . . . . . . . . . . . . . . 324.7 Chip with SU-8 structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.8 Wafer with spoiled SU-8 structure. . . . . . . . . . . . . . . . . . . . . . . . 334.9 Cross section of chip ready for ASE etch . . . . . . . . . . . . . . . . . . . . 334.10 Structure of ASE etch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vii

viii LIST OF FIGURES

4.11 AZ-resist used as glue was put in certain areas . . . . . . . . . . . . . . . . 344.12 Ring on wafer from ASE etch . . . . . . . . . . . . . . . . . . . . . . . . . . 354.13 Structure of fabricated chips . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.1 Pictures of the package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Basic structure of the setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Pictures of the setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.4 Silicone oil with Rhodamine B. . . . . . . . . . . . . . . . . . . . . . . . . . 405.5 Silicone oil and water formations . . . . . . . . . . . . . . . . . . . . . . . . 415.6 Miscibility tests with silicone oil . . . . . . . . . . . . . . . . . . . . . . . . 425.7 Contact angle between two fluids . . . . . . . . . . . . . . . . . . . . . . . . 425.8 A drop of silicone oil on an open wafer . . . . . . . . . . . . . . . . . . . . . 435.9 Plots of flow rate measurement . . . . . . . . . . . . . . . . . . . . . . . . . 445.10 Miscibility test of grape seed oil . . . . . . . . . . . . . . . . . . . . . . . . . 455.11 Formations with water and grape seed oil . . . . . . . . . . . . . . . . . . . 465.12 Formation with ethanol and grape seed oil . . . . . . . . . . . . . . . . . . . 475.13 Ethanol displacing grape seed oil . . . . . . . . . . . . . . . . . . . . . . . . 475.14 Attempting to establish equilibrium using ethanol and grape seed oil . . . . 485.15 Deposits in a chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.16 Ethanol and water mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.17 Ethanol and air flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.18 Ethanol and air equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.19 Bubble of air in ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

A.1 Velocity field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A.2 Forces on a fluid element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A.3 Friction on fluid element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

List of Tables

3.1 Selected physical properties of the GE Silicone SF96®-series silicone oils. . 153.2 Electrical properties of the two types of insulating materials. . . . . . . . . 153.3 Maximum voltages and capacitor pressures . . . . . . . . . . . . . . . . . . 183.4 Channel dimensions of the two designs. . . . . . . . . . . . . . . . . . . . . 23

5.1 Ratio between inlet pressures at equilibrium . . . . . . . . . . . . . . . . . . 405.2 Estimates of the uncertainty of the parameters used to calculate the flow

rate in the chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

F.1 Estimates of the uncertainty of the parameters used to calculate viscosityof the grape seed oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

F.2 Experimental data for the viscosity measurements . . . . . . . . . . . . . . 79F.3 Constants used for the viscosity measurements . . . . . . . . . . . . . . . . 79F.4 Density data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

G.1 Data for the flow rate measurements in the water and common channel . . 81G.2 Dimensions of the chip used for the flow rate measurements in the water

and common channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82G.3 Resistances and constants used for the flow rate measurements in the water

and common channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

H.1 Data for the flow rate measurements in the oil and common channel . . . . 83H.2 Dimensions of the chip used for the flow rate measurements in the oil and

common channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84H.3 Resistances and constants used for the flow rate measurements in the oil

and common channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

ix

x LIST OF TABLES

List of symbols

Symbol Description Unit

ρ Mass density kg m−3

v Velocity vector m s−1

a Acceleration vector m s−2

v Velocity m s−1

f Body force density N m−3

g Gravity N kg−1

P Pressure N m−2

Q Volume flow rate m3 s−1

R Fluidic resistance Pa s m−3

µ Dynamic viscosity kg m−1 s−1

σ Surface tension N m−1

T Temperature KC Capacitance A2 s4 m−2 kgE Electric field strength V m−1

V Voltage Vq Electric charge A s

xi

xii LIST OF SYMBOLS

Chapter 1

Introduction

The following sections will briefly give an introduction to the motivation for carrying outthe project as well as how this is planned to be approached.

1.1 Motivation

The motivation for the project is to be found in the development of micro analysis systems- the so called lab-on-a-chip systems. These chip based micro structures are in the futurehoped to be a cheap, fast and reliable alternative to ordinary laboratories for scanning andanalysing biological samples in order to determine if a patient for instance suffers fromcancer, HIV etc.

One of the problems with lab-on-a-chip systems is that they still suffers from beingconnected to a massive amount of external equipment in order to control in- and outletof fluids, electrical interconnections, information retrieval and other devices. An elementoften used in the analysing process is dye lasers which operates by excitating a laser dyein a cavity by an external source.

These cavities, which have to have a mirroring function, can be constructed in severalways. One of the possibilities is to encapsulate the dye dissolution in liquid bubbles. Ifthese bubbles have a refraction index higher than the surrounding fluid, the fluidic interfacecan in this manner act as a mirror transforming the bubbles to small tunable laser cavities.

In short terms this project is therefore, by developing a chip which can produce liquidbubbles, the first step in the process of integrating tunable lasers on lab-on-a-chip systemsby means of adjustable laser cavities.

1.2 Implementation

The production of bubbles can theoretically be obtained by embedding a parallel-platecapacitor in the top and bottom of a channel in the chip. In this manner it will bepossible, by making a suitable design of the fluidic system, to use the fluid with highestdielectric constant as a valve by sucking it into a channel with the capacitor establishing a

1

2 CHAPTER 1. INTRODUCTION

pressure equilibrium. Hereby it is possible to stop the flow of the fluid with low dielectricconstant.

Beginning with the theory for fluid mechanics and electrostatics, this will be appliedto the actual problem in order to make a design of a capacitor as well as a microfluidicsystem, which theoretically can fulfil the purpose of a valve function. After having madethe design, clean room processes will be used to fabricate the given chips. Finally a testsetup will be designed and fabricated in order to characterize and test the functionality ofthe chips and compare it to the theoretical calculations.

Chapter 2

Theory

In the following chapter the two main topics of the theory concerning the project, namelythe theory of flow geometry and electrostatics, will shortly be treated.

In both cases the subject of interest to this project is the magnitude of force andpressure obtained either by external pressure of the liquid or by electrostatic forces.

2.1 Fluid mechanics

The first part of the theory to be treated is the fluid mechanics covering the concepts offlow rate, hydraulic resistance and pressure drops.

2.1.1 Flow rate and resistance

When dealing with fluids one often has to take the Navier-Stokes equation into consid-eration. This equation is essential when calculating velocity distributions, flow rates andhydraulic resistances in fluidic systems.

These three quantities depend in particular of the geometry of the system which will beshown in the following sections, where only non-compressible Newtonian fluids in laminarflow are considered. That is fluids with velocity independent viscosity.

The Navier-Stokes equation which is derived in App. A is given by

ρ

[

∂v

∂t+ (v · ∇) · v

]

= −∇P + µ∇2v. (2.1)

This equation has the strength of enabling one to deduce both velocity profile andfluidic resistance for a given geometry.

For this project, the channels are rectangular with a width much larger than thecorresponding height. A suitable approximation to this structure is the situation, wheretwo infinitely wide parallel plates are positioned in a cartesian coordinate system as shownin Fig. 2.1.

If the situation is considered stationary - that is the velocity is independent of thetime - and the pressure drop ∆P is resistricted to the x-direction, Eq. (2.1) can be used

3

4 CHAPTER 2. THEORY

Figure 2.1: The velocity profile for a laminar flow parallel to the x-axis bounded by two infinetelywide parallel plates. The profile is from Eq. (2.2) seen to be parabolic.

to show that the velocity profile in the particular geometry is given by

v(z) =∆P

2µL(a2 − z2). (2.2)

The derivation is given in App. B.The next step is to determine the corresponding flow rate which is defined as the

volume per time passing perpendicular through a given surface. As velocity is defined asdistance per time, it is clear that multiplying the area gives the infinitesimal flow rate, sothe total flow rate is given by

Q =

∫

A

v · ndA =

∫

A

v⊥dA. (2.3)

As in electric circuits, fluidic systems have a resistance Rhyd which is defined by thefluidic analogy to Ohm’s law,

Rhyd =∆P

Q. (2.4)

For the parallel plate geometry where the plates, though theoretically being infinitelywide, has been given a width w the flow rate and fluidic resistance is given by

Q =

∫

A

∆P

2µL(a2 − z2)dA =

2wa3∆P

3µL, (2.5a)

Rhyd =∆P

Q=

3µL

2wa3=

12µL

wh3, (2.5b)

where a in Eq. (2.5b) has been substituted by h2 where h is the total height which is

the common notation. It should be noticed that the resistance is only affected by thesymmetry of the system and the viscosity of the liquid. This means when knowing the

2.1. FLUID MECHANICS 5

geometry, viscocity and pressure drop of a certain system, it is possible to calculate thecorresponding flow rate and the pressure at any given point in the system, as the rules forserial and parallel connections known from electrical circuits also apply to fluidic systems.

This property will be used later on in the following chapters, where it can be seen thatthe resistance used for calculations is not entirely identical to Eq. (2.5b), but given by

Rhyd =12µL

(w − 0.63h)h3, (2.6)

as this is a better but more complicated expression for the resistance of a rectangularchannel encounting for the effect of the sides. A derivation is given in App. C1.

2.1.2 Capillary effects – surface tension and Young-Laplace pressure

Another aspect of the fluidic part of the theory is the presence of surface tension in theinterface between different fluids. As shown in the following, this gives rise to a pressuredrop across the interface, causing the fluid to move if the channels are small enough. Thiseffect is known as capillary effect.

In a fluid interface a given surface tension σ is present. This is defined as the energyper area in the surface and caused by the fact that the molecules in the surface are notbonded as tight as the bulk molecules. Therefore the surface tension for a given interfaceis a material specific constant.

The pressure drop caused by the surface tension can be derived using energy equilib-rium between surface tension and pressure work. Having a fluid surface with the radii R1

and R2 as shown for the one radius in Fig. 2.2 the pressure drop across the surface is givenby the Young-Laplace equation,

∆PYL = σ

(

1

R1+

1

R2

)

. (2.7)

Given a channel where the width is much greater than the height, the smallest radius willdominate and thereby making it possible to neglect the other radius. In this case, theYoung-Laplace pressure will be given by

Figure 2.2: A surface with radius R1 between two fluids in a cross section of a tube. The pressuredrop ∆PYL across the surface caused by the surface tension of the curved surface is shown.

1This derivation is made by supervisor Henrik Bruus and is only included for interest of the reader.

6 CHAPTER 2. THEORY

(a) Contact angle of liquid drop on solid (b) Contact angle in tube

Figure 2.3: Illustration of the contact angle of a drop on a solid surrounded by a gas. In (b) therelation between contact angle θ, height h of the tube and radius R of the surface is shown usingsimple geometry in a cross section of the tube.

∆PYL = σR−1. (2.8)

The disadvantage of Eq. (2.8) is that the radius is varying with the dimension of thechannel in a way that it is not easy to measure. The introduction of contact angle θ is away to overcome this problem.

The contact angle is defined as the angle a given fluid makes with for instance a gasand solid surface as shown in Fig. 2.3.

The contact angle can be calculated from an energy consideration, as the surface willalways attempt to have a shape with the lowest possible energy. Using energy balance,the contact angle can be shown to depend on the surface tensions between solid and gas,liquid and solid and liquid and gas given in the following expression known as Young’sequation,

cos θ =σsg − σls

σgl

. (2.9)

Considering Fig. 2.3 it can be seen that the radius of the surface can be expressed as

R cos θ =h

2. (2.10)

Combining this relation with Eq. (2.8), the Young-Laplace pressure is given by

∆PYL =2σ cos θ

h. (2.11)

Since the contact angle and surface tension is specific for a given surface combination,∆PYL can be calculated for a given channel, if θ and σ is known for the specific materialcombination.

2.2 Electrostatics

Having treated the fluid mechanics in Sec. 2.1.1 a short introduction to electrostatics isrequired, beginning with the parallel-plate capacitor.

2.2. ELECTROSTATICS 7

2.2.1 Parallel-plate capacitor

A parallel-plate capacitor consists of two parallel conducting plates of area A separatedby a distance h.

Provided that the area A of the plates is reasonably large compared to h2, it can beshown that the charge on the plates when exerted to a voltage drop V is given by

q = εA

hV, (2.12)

where ε is the permittivity of the dielectricum between the plates. The quantity ε Ah

isalso known as the capacitance C.

2.2.2 Energy stored in a capacitor

To find the energy stored in a capacitor, one has calculate how much work is done in orderto move a charge dq from one plate to the other.The work is

dW = V (q)dq. (2.13)

By integration this yields,

W =

∫ q

0dEc =

∫ q

0V (q′)dq′ =

∫ q

0

h

Aεq′ dq′

=1

2

h

Aεq2 =

1

2

εA

hV 2 =

1

2CV 2 =

q2

2C. (2.14)

ε can also be written in terms of ε0 and εr, ε = εrε0. This means that if the gapbetween the plates is filled with dielectricum, with εr > 1, the total energy in the systemwill be lower compared to a capacitor with an empty gap.

Now, considering the situation in Fig. 2.4, the system will, in order to achieve thelowest possible energy configuration, pull the dielectricum further into the gap.

This effect is essential to the project, since it allows one to suck in a dielectricum.

Figure 2.4: A parallel-plate capacitor of length L with a dielectricum of dielectric constant ε withthe front positioned at x.

8 CHAPTER 2. THEORY

2.2.3 Force and pressure on a dielectricum

Considering the same situation as before, shown in Fig. 2.4, one is interested in findingthe force and pressure acting on the dielectricum. The electrostatic potential energy

F · dx = −dWtot, (2.15)

gives a relation between the force F and the energy stored in the system dW . As thedielectricum moves further into the gap the energy will fall, hence the negative sign.

Rearranging Eq. (2.15), and replacing dWtot with Eq. (2.14), gives an expression forF ,

F = −d

dx

(

q2

2C

)

. (2.16)

Since q does not depend on x, Eq. (2.16) can be written as

F = −q2

2

d

dx

(

1

C

)

. (2.17)

Now differentiating Eq. (2.17) yields

F =q2

2

C ′(x)

C(x)2. (2.18)

In order to express C ′(x) in already known terms, one has to know an expression for thecapacitance of the system, C(x)system. The situation in fig. Fig. 2.4 can be considered asan parallel connection between two parallel-plate capacitors; one with length x filled withdielectricum, and one with length L − x with an empty gap.Knowing the capacitance from Eq. (2.12) leads to,

C(x) =εwx

h+ ε0

w(L − x)

h

=wL

h

(

ε − ε0

Lx + ε0

)

. (2.19)

Differentiating Eq. (2.19) and using the definition of the capacitance it follows that

C ′(x) =w

h(ε − ε0)

=C

L

(

1 −ε0

ε

)

. (2.20)

Substituting C(x) and C ′(x) with Eq. (2.19) and Eq. (2.20) respectively into Eq. (2.18)yields

F =q2

2C

1 − ε0

ε

L. (2.21)

Writing Eq. (2.21) in terms of the voltage drop V amounts to,

F =1

2(V )2 C

1 − ε0

ε

L. (2.22)

2.2. ELECTROSTATICS 9

Substituting with Eq. (2.20) one finally obtains,

F =1

2(V )2 C ′(x). (2.23)

Now knowing the force, the pressure is easily found as the force divided by the crosssectional area.

10 CHAPTER 2. THEORY

Chapter 3

Design

As written in Chap. 1, the general purpose of the project is to design a microfluidic sys-tem, which uses a parallel-plate capacitor in combination with a fluid with high dielectricconstant as a valve.

3.1 Physical considerations

The challenge connected to this function is that the pressure Pcap generated by the capac-itor is very low.

In order to deal with this problem, one has to consider which physical situation iswanted and which parameters that can be altered in the process of obtaining this particularsituation.

Generally states of equilibrium are preferable, since in this situation even the actionof very small forces can cause considerable changes in the system. In the given situationthe equilibrium must be established by exploiting the pressure applied by the capacitorand the pressure connected to the flow of the two liquids through the channel system.

Practically an equilibrium is obtained when the pressure of the capacitor Pcap and thepressure in the intersection Px equals the inlet pressure Po in the channel with the fluidthat has to be stopped minus the Young-Laplace pressure ∆PYL, meaning Pcap + Px =Po − ∆PYL, as seen in Fig. 3.1.

In other words, when the capacitor is turned on, the liquid with the high dielectricconstant will be sucked into the gap of the capacitor and the equilibrium will arise. Thismeans, that the liquid with low dielectric constant will be hindered from flowing. On theother hand both of the liquids will flow, when the capacitor is turned off.

3.2 Physical parameters

It is clear, that in order to achieve an optimum system the pressure applied by the capacitorshould be as large as possible at a given channel dimension, whereas the pressure dropin the channel must be kept at a minimum. As shown in Chap. 2, there are certainparameters which will affect the two pressures.

11

12 CHAPTER 3. DESIGN

Figure 3.1: Sketch of a channel with a fluid interface positioned at the edge of the channel coveredby a capacitor plate. The conditions for equilibrium of the curved surface demand a pressure dropof ∆PYL in the channel to balance out the capillary pressure.

Concerning the pressure drop in the channel these parameter are the flow rate Q,height h, width w, length L and the viscosity µ, as it can be seen from Eqs. (2.4) and (2.6).Some of these parameters also interact on the force generated by the capacitor, as thisdepends on h, w, the voltage V , and the dielectric constants of the fluids filling the gap;cf Eqs. (2.20) and (2.23). By dividing the capacitor force by the cross sectional area toobtain the corresponding pressure the width of the channel is seen to vanish.

Before designing the channels for the fluidic system, one has to know the magnitudeof the pressure generated. Therefore the properties of the capacitor has to be determinedfirst.

In connection to this some of the parameters of the chip were given as a guideline forthe design process. The first parameter is the channel height that has to be in the orderof 10 − 25 µm, whereas the width must be at least 1 mm. Secondly one must be able tovisually survey the channels, meaning that the capacitor electrode and insulator on top ofthe channels must be transparent. Furthermore the chip must be able to work with water.

3.3 Properties of the capacitor

To make a thorough investigation of the influence of the individual parameters, a precisemodel of the actual capacitor is required. As the capacitor is meant to contain two liquids,it is clear that the two electrodes must be sealed by an insulating material to avoid shortcircuitry. The situation can be sketched as shown in Fig. 3.2(a). This configuration canbe compared to a circuit of simple parallel-plate capacitors connected in series as well asin parallel. If the two insulating shields are considered to be dissimilar the equivalentdiagram corresponding to the physical situation can be drawn as in Fig. 3.2(b)

Using the common rules for parallel and series connection of capacitors, the resultingcapacitance can be found

C(x) = (L − x)

(

d1

εi1w+

h

εl1w+

d2

εi2w

)−1

+ x

(

d1

εi1w+

h

εl2w+

d2

εi2w

)−1

. (3.1)

As the force acting on the dielectricum is given by Eq. (2.23), a differentiation of Eq. (3.1)

3.3. PROPERTIES OF THE CAPACITOR 13

(a) Construction of capacitor (b) Equivalent diagram for the capacitor

Figure 3.2: The build up of the capacitor containing two fluids with dielectric constants εl1 andεl2 and height h. The electrodes are sealed from the fluids by insulating material with dielectricconstants εi1 , εi2 and height d1, d2. In (b) the equivalent diagram for the capacitor consisting ofseries and parallel connected capacitors is shown.

is required. This yields the following,

C ′(x) = w

(

−

(

d1

εi1

+h

εl1

+d2

εi2

)−1

+

(

d1

εi1

+h

εl2

+d2

εi2

)−1)

. (3.2)

The corresponding pressure can now be calculated by combining Eqs. (2.23) and (3.2) anddividing by the cross sectional area given by A = hw,

Pcap =1

2h

(

−

(

d1

εi1

+h

εl1

+d2

εi2

)−1

+

(

d1

εi1

+h

εl2

+d2

εi2

)−1)

V 2. (3.3)

It can be seen, that the pressure Pcap only depends on the height of the different layersand their respective dielectric constants. At first it seems, that the pressure can be raisedby simply adjusting the heights of the layers, but this gives rise to another problem.

This problem has to do with the breakdown voltage Ebreak of the given material. Thebreakdown voltage is a parameter, which determines the maximum electric field allowedin a material without causing for instance an insulator to become conducting resulting ina short circuit. To deal with this, it is essential to know the voltage distribution in thesystem. Supposing the insulating layers are of the same height and material, a single sideof the capacitor can for use of calculations be rearranged in a manner as shown in Fig. 3.3.From Eq. (2.12) it can be seen, that

V1 =Q

C1, V2 =

Q

C2. (3.4)

As the total voltage V is the controllable parameter, the proportion of interest is therelation between the total voltage drop and V1 and V2 respectively, where V is the sum ofV1 and V2. Using the capacitance for the parallel-plate capacitor it can be shown, that V1

and V2 as functions of the heights, dielectric constants and the total voltage drop can beexpressed as

V1 =V

1 + εih2εld

, V2 =V

1 + 2εldεih

. (3.5)


Figure 3.3: The voltage distribution of the total voltage drop V in one single side of the capacitorcontaining fluid of height h with dielectric εl constant and rearranged insulators of total height 2dwith dielectric constant εi. The capacitances C1 and C2 for each part are shown.

Introducing the breakdown voltages, E1,break, E2,break, this means that the maximumvoltage applied to each layer in the capacitor can be expressed as the following,

V1,max = E1,break2d, V2,max = E2,breakh. (3.6)

Combining Eqs. (3.5) and (3.6) yields the following expression for the total maximumvoltage allowed,

Vmax = E1,break2d

(

1 +εih

2εld

)

or Vmax = E2,breakh

(

1 +2εld

εih

)

. (3.7)

As seen in Eq. (3.7) there are two different expressions for the maximum allowed voltageover the capacitor. This is due to the voltage distribution and different values for thebreakdown voltage of the individual layers. Changing the parameters by altering theheights or material properties leads to a change of the maximum voltage, meaning thateither the insulating material or the fluid determines the maximum voltage.

As the number of parameters has a size, where it is not possible to fully predict thebehavior of the system, numerical simulations are necessary to determine the optimumcombination of the parameters. For this purpose, Matlab has been used to produce thesimulations using the programs listed in Apps. I and J. These programs were designedespecially for this chip making it possible through graphical representation to get anoverview of the properties of the electrical part of the chip. In that manner, the heightsof the channels and insulating layers have been chosen.

3.3.1 Materials

Before the numerical analysis can be carried out considerations about the materials usedhave to be done.

First of all the fluid which have to be displaced by the other has to be found. In relationto the capacitor, this fluid both must have a very low dielectric constant and a high breakdown voltage. Furthermore it also has to be insoluble in water as well as having a lowviscosity for obtaining the highest possible flow rate at a given pressure drop. Althoughnot having crucial importance for the chip, it is preferable if the fluid is harmless when


handling it. At least it has to be so harmless that it does not spoil the chip nor the testsetup.

As water is polar a nonpolar fluid has the advantage of being immiscible with water.A nonpolar harmless fluid is oil, which in general also has a low dielectric constant. Afterthorough searching on the internet it was found that silicone oils are well suited for thepurpose, as they fulfill the mentioned demands. More specifically, the SF96®-series fromGE Silicones has been chosen having the properties as given in Table 3.1, see Ref. [4].

Parameter Value

Dielectric constant εl2 2.72ε0 F/mBreakdown voltage Ebreak 3.5 × 107 V/mViscosity µ 3 × 10−3 − 1000 × 10−3 Pa sDensity ρ 0.95 kg/m3

Table 3.1: Selected physical properties of the GE Silicone SF96®-series silicone oils.

The next material to be chosen is the insulating material separating the fluids from theelectrodes. The fabrication process dictates that the insulating material on top of thechannels has to be either made of the polymer PMMA or a layer of an oxide. Theadvantage of the polymer is the transparency, whereas the height of the oxide is restrictedto 100 nm in order to be transparent.

The electrical properties of the to types of insulating materials, PMMA and SiO2, aregiven in Table 3.21.

Parameter \ Material PMMA SiO2

Breakdown voltage Ebreak 1.0 × 105V/m 1.0 × 107V/mDielectric constant εi 2.0ε0 4.0ε0

Table 3.2: Electrical properties of the two types of insulating materials.

3.3.2 Numerical analysis

Having derived all the relevant expressions and implemented them in MatLab the simu-lations can be made using the data given in the two previous tables. In the followinganalysis a safety factor of 0.75 has been multiplied to the breakdown voltage in order totake uncertainties related to the practical situations into account.

First it is investigated how the pressure Pcap depends on the channel height h at differ-ent thicknesses of the insulating layers at the maximum voltage for the given configuration.As seen at Fig. 3.4, the pressure increases with the thickness d of the insulating layer but

1These values for dielectric constant and break down voltage were given by supervisor Anders Kris-tensen.


1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

x 10−5

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

h [m]

Pcap

[Pa

]

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

x 10−5

50

55

60

65

70

75

80

85

90

h [m]Pc

ap [

Pa]

Figure 3.4: The pressure Pcap from the capacitor at different thickness of insulating layer as afunction of the channel height. Both situations contain water and SF96 silicone oil and correspondto the maximum achievable pressure at Vmax. The left plot shows a PMMA configuration with tendifferent thicknesses from 1 µm to 25 µm whereas the right shows SiO2 varying from 50 nm to 200nm. The highest pressure corresponds to the thickest layer.

decreases with channel height. Furthermore it is clear that the pressure achieved by usingPMMA is far from adequate to be used. This low pressure is due to the low breakdownvoltage of the polymer.

On this background, it can be concluded that the most suitable material for sealingoff the electrodes is a layer of oxide.

Having determined the optimum insulating material an investigation of the maximumvoltage with different fluids is carried out.

As it can be seen from Fig. 3.5, the ability of the fluid to displace the oil varies withthe dielectric constant. At first sight one should from Eq. (3.3) think that the pressureincreases with the dielectric constant εl2 of the displacing fluid, but this is only valid forconstant voltage drop. It is from Fig. 3.5 clear that the actual maximum pressure doesnot increase with the dielectric constant but has a peak at a fairly low value. This has todo with the fact that the voltage distribution changes with the liquid and therefore themaximum applied voltage before breakdown decreases with increasing dielectric constant.

The actual maximum voltage as a function of the dielectric constant is shown in Fig. 3.6from where it is clear that a displacing fluid with dielectric constant close to the oil is notpreferrable due to very high voltages.

The choice of water as displacing fluid with dielectric constant of εl1 = 80.1ε0, see Ref.[3] p. 6-154, may be seem, just by looking at the pressure, not to be a very good choice.But as the project from the beginning has aimed for using water, as this for instance isoften used as solvent in chemical reactions, the designs will nevertheless be based on this.Furthermore water has the advantage of being harmless and easy to handle. Another veryimportant property of water is the very low dynamic viscosity of µ = 1.002× 10−3 Pa s at20◦C, see Ref. [3] chap 6, making the fluidic resistance low and thereby having relativelyhigh flow rates at low pressures.


0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

400

Dielectric constant

Pcap

[Pa

]

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

400

Dielectric constant

Pca

p [P

a]Figure 3.5: The pressure Pcap from the capacitor at maximum voltage as a function of thedielectric constant εl1 of the displacing fluid when having SF96 silicone oil as the other fluid. Bothplots are based on a 100 nm SiO2 layer in the top and the bottom as insulator. Left and right plotcorrespond to a channel height h of 10 µm and 25 µm respectively.

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

Dielectric constant

Vm

ax [

V]

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

Dielectric constant

Vm

ax [V

]

Figure 3.6: The maximum voltage Vmax as a function of the dielectric constant εl1 of the displacingfluid. Both plots are based on a 100nm SiO2 layer in the top and the bottom as insulator. Theleft and right plot correspond to a channel height h of 10µm and 25µm respectively.

As an alternative to water, ethanol with dielectric constant of εl1 = 25.3 and dynamicviscosity of µ = 1.074 × 10−3 Pa s at 25◦C, see Ref. [3] p. 6-187, can be used, althoughthe high vaporization of ethanol can give rise to problems with the test setup, which willbe treated in details in the later sections. Furthermore it is not known if the oil is solublein ethanol.

The values for the maximum capacitor pressure and corresponding voltage is given inTable 3.3 for channel heights of 10 µm and 25 µm.

Considering the pressures it can be seen that the decrease of pressure with the channelheight is not critical compared to the flow rate gained by increasing h as Rhyd decreaseswith h3, cf. Eq. (2.6). This means that the pressure required to give a certain flow rate can


Parameter \ Fluid Ethanol Water

Pcap @ 10 µm 156.1 Pa 66.42 PaVmax @ 10 µm 13.36 V 5.25 V

Pcap @ 25 µm 146.8 Pa 55.48 PaVmax @ 25 µm 31.14 V 10.88 V

Table 3.3: Maximum voltages and corresponding capacitor pressures at two channel heights forwater and ethanol respectively displacing SF96®silicone oil.

be reduced considerably by raising the channel height with only a small loss of capacitorpressure, why the 25 µm channel is preferable. At this height the capacitor is able toestablish a reasonable pressure at a low voltage.

All-together it can be summarized that the analysis of the capacitor has resulted inthe choice of 100nm SiO2 for insulation layer, a low viscosity silicone oil from GE SiliconesSF96®-series as the fluid with low dielectric constant, and finally the channel height hasbeen chosen to 25 µm.

3.4 Fluidic system

Having analysed the capacitor and found the maximum achievable pressure at a givenchannel height, the next task is to design a fluidic circuit which in coorporation with thecapacitor is able to cut off the oil stream.

3.4.1 Overall models

Generally it is necessary to be able to control the pressures of the two fluids. This meanscontrolling the pressures at the inlets as well as in the interface, where they meet in orderto adjust the ratio between the flow rates of the two liquids. Furthermore the channelsystem must be able to lead the fluids out of the chip through a common channel.

An easy way to solve this problem is to use a system where the channels cross eachother designed in such a manner, that it is possible to control the pressure in the cross.Two general systems with these qualities are shown in Fig. 3.7 constructed as a simpleT-cross with two inlets and an intersection with three inlets respectively.

It is clear that in both models raising the inlet pressure of the water will, at a sufficientlyhigh value, prevent the oil from flowing into the system leaving only water to be in thechannels. In a similar way it is possible by correct adjustment of the inlet pressures toestablish an equilibrium where the oil is not flowing but staying statically in the channelor flowing with a constant flow rate into the common channel.

Comparing the two alternative systems the T-cross at first seems to be the most simplesystem, as this model only contains two inlets and three channels. In this way only twopressures have to be adjusted relatively in order to obtain the wanted pressure in the cross.But on the other hand when both fluids flow, the structure of the flow in the common

3.4. FLUIDIC SYSTEM 19

Figure 3.7: Two principal models for the design of the fluidic system. In the T-cross oil and waterare led into the cross from each channel. In the other solution, the water is fed from two channelsand thereby surrounding the oil in the common channel. The hatched area represent the capacitor.

channel is presumably not symmetric but instead having the oil flowing along one side asshown in Fig. 3.8. This assumption of asymmetry is based on the fact that the height ofthe channel is extremely small compared to the width intuitively making it unlikely thatthe fluids will flow on top of each other.

The lack of symmetry may have consequences for the way, the water will be able tocut off the oil flow, as this has to be done by the water coming from the top and therebycutting it off from just one direction. It is uncertain how effective this method is comparedto the other model.

In the system with the ordinary cross, the oil flow will be cut off from both sidessimultaneously by the water if the flow in the water channels is symmetric. In that waythe water will presumable act as a pair of scissors cutting off the oil stream at the end ofthe oil channel. Thereby it separates the oil in the oil channel from the oil in the crossand common channel which now flows as a bubble surrounded by the water. Furthermorethis model has the advantage of being symmetric making the oil flowing in the middle ofthe common channel as long as this channel is straight. On the other hand this designsuffers from having three inlets making it hard to obtain equal pressures and flow rates inthe water channels. To solve this problem, the design can be altered to contain only two

Figure 3.8: The presumed flow structure of the two fluids in the two models. The T-cross ispresumed not to be symmetric, whereas the ordinary cross most likely will enclose the oil in themiddle of the common channel.


Figure 3.9: Principle for the fluidic system with two water channels sharing the same inlet forobtaining equal flow rates and inlet pressure. The capacitor given by the hatched area is placed atthe intersection.

Figure 3.10: Principle for the fluidic system with reduced number of right angles in order toreduce the risk of having nonuniform flow in the corners.

inlets by giving the water channels a common inlet as shown in Fig. 3.9.

These considerations led to the decision to proceed with the cross design.

Having chosen the overall solution in Fig. 3.9 it is now necessary to optimize the designand functionality of the chip.

It is desirable to make the flow as uniform as possible, in order to achieve the moststable system, which will ease the control of the flows. This stable situation might bedifficult to obtain in the model shown in Fig. 3.9 because of the right angles. To avoidthese right angles the model was reshaped to mainly consist of arcs of circles as shown inFig. 3.10.

3.4.2 Pressure calculations

As the overall principle of the chip has been chosen, calculations concerning flow ratesand pressure drops are the next steps to be carried out. First of all one must make clear,which parameters determine these quantities.

Using the theory for fluidic systems described in Chap. 2, these parameters are fromEq. (2.6) seen to be the channel dimensions, the viscosity and the in- and outlet pressure.Using the fluidic analogy to Ohm’s law, Eq. (2.4), it is now possible to handle the channelsystem as an electrical circuit given by the diagram in Fig. 3.11. It can be seen from this

3.4. FLUIDIC SYSTEM 21

Figure 3.11: The fluidic system handled as an electrical circuit with indication of the resistancesand flow rates. The pressure P = 0 is a convinient way of excluding the reference pressure P0,that otherwise should be added to both inlet pressures.

figure that neither the Young-Laplace pressure ∆PYL nor the capacitor pressure Pcap ispresent in the diagram. The reason for this is that ∆PYL can always be balanced out byadjusting the inlet pressures and thereby having no influence on the overall properties ofthe system why it can be included in Po. Furthermore ∆PYL is an unknown factor, asneither contact angle nor surface tension between the fluids is known.

In the following part indexes will be used to distinguish the different flow rates andresistances, where index o refers to oil, w to water, c to the common channel and finallyQtot to the total flow rate.

Examining Fig. 3.11 it can be seen that, by using the rules for parallel connectedresistors, the replacement resistance Rw,rep for the water channels is given by

Rw,rep =1

2Rw. (3.8)

As the total flow rate through the water channels is 2Qw, Fig. 3.11 can be replaced by thesimpler diagram shown in Fig. 3.12.

As the external inlet pressures Pw and Po as well as the resistances Ro, Rw and Rc,

Figure 3.12: An alternative and simpler representation of the fluidic system when handled as anelectrical circuit.


which are controlled by the channel dimensions, are known there are three unknown factorsleft. These factors are the flow rates Qw and Qo and finally the pressure Px in the cross.In this simple representation it is now possible to exploit the fluidic analogy to Ohm’s lawto find the unknown factors. This is done through the following three equations referringto each part of the system

Px − 0 =Rc(2Qw + Qo) (3.9a)

Pw − Px=RwQw (3.9b)

Po − Px =RoQo. (3.9c)

By use of simple algebra these three equations give the expressions for Px and the twoflow rates,

Px =Rc(2PwRo + PoRw)

RwRo + Rc(2Ro + Rw)(3.10)

Qw =Pw(Ro + Rc) − PoRc

RwRo + Rc(2Ro + Rw)(3.11)

Qo =Po(Rw + 2Rc) − 2PwRc

RwRo + Rc(2Ro + Rw). (3.12)

Although these equations seem to determine the system, there is still one factor that isnot fully known. This is the resistance Rc of the common channel, as it is not knownexactly how the fluids are distributed in this channel. Still the maximum and minimumvalues corresponding to the situations where the channel is filled completely with oil andwater respectively can be determined.

3.5 Dimensioning the system

As mentioned in Sec. 3.3.2 the height was chosen to 25 µm and a total flow in the proximityof 60 µL

hr was also wanted. The length of the water channels should furthermore be thesame to obtain symmetry. Moreover the minimum width of the channels had to be 1 mmand as it appears in Fig. 3.10 the water channels had to be longer than the oil channel.The last requirement was that the inlets and outlet were separated enough to make itpossible to connect the chip to the outer macroscopic system. Unfortunately this was notenough information to determine a unique design and therefore some of the remainingparameters were assigned chosen values suitable for obtaining the required flow rates.

Some of the parameters which were assigned values were the dimensions of the commonchannel, this was given the length Lc =5 mm and the width wc=1.5 mm. The next chosenparameters were the dimension of the oil channel, which was chosen to Lo =3 mm andwo =1 mm for the SF96-5®silicon oil with viscosity 4.6×10−3 Pa s, see Ref. [4]. Thelast parameter was the width of the water channels, which was set to the same value asthe common channel, namely 1.5 mm. Setting the flow rate of the oil to a given fractionof the flow rate of the water at the same inlet pressure, allowed the length Lw of thewater channels to be calculated. This resulted in a length Lw = 10.35 mm when wanting

3.5. DIMENSIONING THE SYSTEM 23

(a) Channel design 1 (b) Channel design 2

Figure 3.13: The two designs sent to production showing the exact dimensions in µm. The wateris led into the chip at the inlet hole at the left side of the system whereas the oil is fed through theinlet in the small channel surrounded by the water channels. The water and oil leaves the chip atthe big quadratic outlet at the right side of the chip.

Qo = 0.2 Qtot, the calculations can be found in App. K. The length of the water channelswas approximated with the centerline.

Similar considerations for the SF96-100®oil with viscosity µ = 100 × 10−3 Pa s, seeRef. [4], and choosing Q0 = 0.05 Qw led to Lw = 12.5 mm. The two designs are shown inFig. 3.13 with the dimensions given in Table 3.4. The intersection is included as a part ofthe water channels.

Dimension \ Design Chip 1 Chip 2

h [µm] 25.00 25.00ww [mm] 1.50 1.50wo [mm] 1.00 1.50wc [mm] 1.50 1.50Lw [mm] 10.35 12.50Lo [mm] 3.00 2.50Lc [mm] 5.00 5.00

Table 3.4: Channel dimensions of the two designs.

Having chosen the parameters simulations based on the expressions derived in Sec. 3.4.2were made to investigate if the chip met the requirements mentioned earlier in this sectionand in Sec. 3.4.1. These simulations, where the resistance in the common channel was


varied between the two extrema at different inlet pressures, showed that at reasonablepressures, it was possible to let the oil flow as well as pressing it back, meaning thatequilibrium was obtainable. Examples of flows and presure drops in the oil channel canbe seen in Fig. 3.15 and 3.14 where both positive and negative oil flows are represented.The simulations used for the graphs can be found in App. L. Although having 25 µm asprefered height, it has been investigated, that h = 10 µm will also work on the cost of alower oil flow rate and higher inlet pressures when demanding the same total flow rate.

–80

–70

–60

–50

–40

–30

–20

Po-Px [Pa]

4e+12 6e+12 8e+12 1e+13

Resistance in common channel [Pa s m^–3]

140

150

160

170

Po-Px [Pa]

4e+12 6e+12 8e+12 1e+13


Figure 3.14: Examples of two possible pressure drops in the oil channel as a function of theresistance in the common channel varying between the minimum and maximum value correspondingto the situation where the common channel is filled with water or SF96-5®silicone oil respectively.The pressures applied are Pw=250 Pa and Po=100 Pa in the left graph and Pw=100 Pa, Po=250Pa in the right graph.

–25

–20

–15

–10

Qo [muL/hr]

4e+12 6e+12 8e+12 1e+13


48

50

52

54

56

58

60

Qo [muL/hr]

4e+12 6e+12 8e+12 1e+13


Figure 3.15: Examples of two possible flows in the oil channel as a function of the resistancein the common channel varying between the minimum and maximum value corresponding to thesituation where the common channel is filled with water or SF96-5®oil respectively. The pressuresapplied are Pw=250 Pa and Po=100 Pa in the left graph and Pw=100 Pa, Po=250 Pa in the rightgraph.

3.5. DIMENSIONING THE SYSTEM 25

3.5.1 Comments on the channel design process

In retrospect the chosen way of dimensioning the chip might not have been the optimalway. Since the problem was approached from a dynamic point of view the equilibriumpossibilities were investigated after dimensioning the chip. Even though the simulationsshow that the chip should work properly, it is possible that an optimized design couldhave been achieved through an equilibrium approach. This was unfortunately done afterthe fabrication had begun, and it was therefore not possible to alter the design.

In the following section the calculations originating from a equilibrium point of viewwill be carried out for evaluating the utilized design.

3.5.2 Further investigations

Using the representation in Fig. 3.12 and still having included the Young-Laplace pressurein Po, the condition for equilibrium with the capacitor turned off is

Po = Px. (3.13)

Substituting this into Eq. (3.10) yields an expression for the relation between the two inletpressures Pw and Po,

Pw =Rw + 2Rc

2RcPo. (3.14)

This means that for any Pw smaller than the pressure given by Eq. (3.14), the oil flow willbe positive and vice versa. As expected, the resistance of the oil channel does not figurein the expression since the flow in this channel equals zero.

Choosing the same width for the water channel and common channel as done in thechosen design, Eq. (3.14) reduces by inserting the expression for hydraulic resistance givenby Eq. (2.6) to

Pw =µwLw + 2µcLc

2µcLcPo. (3.15)

As Qo is zero, there is only water in the common channel resulting in µc = µw. Insertingthis into Eq. (3.15) gives the final expression for Pw,

Pw =Lw + 2Lc

2LcPo. (3.16)

Substituting the expression for Pw given in Eq. (3.14) into Eq. (3.11) yields an expressionfor the flow rate of the water in equilibrium as a function of Po and Rc,

Qw =Po

2Rc. (3.17)

Including the pressure Pcap exerted by the capacitor, the equilibrium condition willnow be

Px = Po − Pcap. (3.18)


Performing calculations analogous to the previous, Pw and the flow rates of oil and waterwhen the capacitor afterwards is turned off will be

Pw =Rw + 2Rc

2RcPo −

RwRo + 2RoRc + RcRw

2RcRoPcap (3.19)

Qw =RoPo − Pcap(Ro + Rc)

2RcRo(3.20)

Qo =Pcap

Ro. (3.21)

Analysing Eqs. (3.14) and (3.19) it can be seen that for obtaining an equilibriumwithout capacitor the larger Rc the closer the two inlet pressures will be to the samevalue. Furthermore, as Qo only depends on Pcap and Ro when including the capacitor, itseems, that a higher Rc will result in a greater fraction of the total flow to be oil. Thisfraction given as the oil flow rate divided with the total flow rate is given by

Qo

Qtot=

PcapRc

Ro(Po − Pcap). (3.22)

This shows, that a smaller h will result in a decrease of the oil fraction when demandingthe same total flow rate, as Pcap does not increase with the same factor as Ro.

In the light of this it can now be seen that improving the design could include adecrement of the resistance of Ro although making the oil channel much shorter couldlead to problems when establishing the equilibrium. Furthermore Rc could be increasedthough giving higher inlet pressures.

3.6 Applying the capacitor

The last step in the design process is the shape and positioning of the capacitor. Havingshown in Sec. 3.3 that the area of the capacitor plates has no influence on the pressure, theshape of the electrodes can be chosen arbitrary from a pressure point of view. Howeveravoiding sharp edges is preferred since these increase the risk of electric breakthrough inthe form of sparks. But in order to exert a pressure the capacitor should be placed so itcovers both fluids as it only works on the interface between these.

From a bubble generating point of view the capacitor should not be able to slow downthe bubbles nor force them back into the oil channel. Slowing down the bubbles couldhappen when a bubble is caught in the capacitor gap by the water trying to occupy the gapand thereby exerting a pressure on the bubble. The other phenomenon, namely forcing theoil back could occur if the front of the oil stream is still positioned between the capacitorplates when voltage is applied.

A design fulfilling these requirements is shown in Fig. 3.16. It can be seen that theelectrode is not extended to cover the entire oil channel. This is due to the fact that if thepressure from the capacitor is much higher than the pressure drop in the oil channel, thegiven design will only pull the water into the back edge of the electrode making the oilprogress to the cross sooner when removing the voltage than if the water had been pulledall the way into the oil channel.

3.6. APPLYING THE CAPACITOR 27

Figure 3.16: The shape and placement of the capacitor in the cross making it possible to use thewater from the top and lower channel to produce bubbles of the oil loaded from the small channelin the middle.

3.6.1 Implementation on the silicon/glass structure

As the design of the channels as well as the choice of materials have been done it is nowtime to implement the design on the chip before fabrication. In order to do this, one musthave a sketch of how the chip is build. A cross sectional view of the structure is shown inFig. 3.172. From here it can be seen how the channel system is embedded in the polymersSU-8 and PMMA and surrounded by the oxide layers placed on glass lid and silicon base,where the silicon base and top conductor acts as electrodes.

In order to visually survey the flow in the channel systems from above, all the inter-connections must be made from the bottom. Apart from holes for fluids, an extra accesshole for accessing the top electrode via a bonding pad must be applied to the design. Thefinal design with electrodes, through holes, bonding pad and channel system is shown inFig. 3.18. This figure is based on the design of the photo masks made in the microchipdesign program L-edit. The use of these masks will be explained in the next chapter.

Figure 3.17: Schematic cross sectional view of the chip with channel system embedded in SU-8 andPMMA. Furthermore the top and bottom electrodes lying between glass and oxide and underneaththe silicon wafer can be seen. The holes shown represent the through holes for one in- and outletand access hole for top electrode.

2This figure is based on figures from supervisor Anders Kristensen


(a) Chip 1 (b) Chip 2

Figure 3.18: The final design of the two chips with fluidic channels (red), top and bottom elec-trodes (green and grey), in- and outlets and acces hole (purple) and bonding pad (blue) for upperelectrode. The water is loaded in the left inlet hole and the oil in the middle. Both fluids leave thechip at the outlet to the right.

Chapter 4

Production of the microchips

The next step in the process is the fabrication of the microchips based on the chosendesigns. As the microfluidic system consists of channels with a height in micron scale,a clean room is necessary for carrying out the production. This is done through a widenumber of various processes which will be described chronologically in the next sections.For recipes and specific data refer to App. D.

Generally several chips are made at the same time from a 350 µm thick wafer with adiameter of 100 mm from which the individual chips will be sawn out as the last step.

The first part of the production to be handled is the bottom wafers made of single sidepolished silicon. The fabrication begun with a total amount of twenty wafers in order tomake a reservation for loss of wafers during the process. The production was made in

Figure 4.1: The layout of a single wafer showing the positioning of the chips with channels, inlets,electrodes and contacts. The figure is based on the photo mask design.

29

30 CHAPTER 4. PRODUCTION OF THE MICROCHIPS

cooporation with another group1 doing a similar project, but producing the chips withoutelectrodes, using ten of the wafers. In this way each group was supposed to fabricate tenwafers; five with their own design and five with the other group’s design.

4.1 Applying the insulation layer

As mentioned in Sec. 3.3 the two electrodes must be separated by an insulating materialto avoid short circuitry. On the bottom wafers this is SiO2.

Therefore a layer of 100 nm SiO2 was grown on both sides of the silicon wafers bythermal dry oxidation in a furnace since dry oxidation provides a more dense structureand thereby a higher breakdown voltage compared to wet oxidation which on the otherhand is faster, see Ref. [1, p. 53].

4.2 Back side contacts

The purpose of the next steps was to apply electrodes to the backside of the wafers, whichwas done through several processes beginning with photolithography. This is a processexploiting a light-sensitive photoresist to make a specific pattern on the wafer by exposingthis with light through a mask containing the pattern. There are two kinds of photoresist,a positive and a negative. The positive resist will be washed away if it has been exposedwith light whereas the negative remains. For that reason the mask should contain patternsdepending on the type of the resist. Before applying the photoresist, the wafers was driedin an HMDS oven, which displaces possible water on the wafers to achieve the optimumphotoresist adhesion.

Afterwards a layer of photo resist was spun onto the backside of the wafers where thethickness of the layer was determined by rotational velocity of the spinner. In connectionto the spinning the wafers were individually pre-baked in the spinner to harden the resist.In Fig. 4.2 the cross section of the chip is sketched2.

Figure 4.2: AZ-resist spun onto the back side of the wafer for use with lithographic process. Thefigure shows the cross section of the wafer with silicon, SiO2 and photoresist.

1Morten Bo Lindholm Mikkelsen, s021709 and Arne Nedergaard Hansen, s021852.2This and the following cross sectional figures are made by supervisor Anders Kristensen.

4.2. BACK SIDE CONTACTS 31

The light sensitive photo resist was after exposure developed in NaOH. In this case apositive resist called AZ-photoresist was used, therefore the mask contained a patternthat covered the areas where the electrodes should not be applied. This mask patterncan be seen in App. E. As the fabrication required multiple masks, these contained tinymarks used for alignment of the different masks. Fig. 4.3 shows the cross section of thechip after development.

Figure 4.3: Cross section of the chip after exposure and development leaving holes in the pho-toresist allowing access to the SiO2 in the wanted areas.

Afterwards the SiO2-layer was removed all the places which were not covered with resistusing an isotropic wet etching in HF-acid, see Fig. 4.4. The other side of the wafers wascovered with a film to prevent the oxide to be etched on this side.

Figure 4.4: Cross sectional view of the silicon wafer showing how the SiO2 has been etched fromthe back side in the wanted places not covered by photo resist.

Having made contact to the silicon, the wafers were to be coated with layers of metalconsisting of 10 nm Ti and 200 nm Al, see Fig. 4.5. This was done by vaporizing themetal onto the backside of the wafers. The Ti was used as an adhesion layer for the Al.

(a) (b)

Figure 4.5: The chip with oxide, photoresist and bottom covered by Ti/Al before lifting off theresist, see Fig. 4.5(a). Fig. 4.5(b) shows the chip after having removed the surplus resist and metaljust leaving the back side electrodes and SiO2 on the back of the wafer.


Figure 4.6: Wafer with bottom electrodes of Ti/Al for eighteen chips on the unpolished back side.

By means of acetone and ultra sound the AZ-resist and the metal layer on top of this wasremoved leaving the electrodes on the wafer as seen in Fig. 4.5 and 4.6. Finally the waferswere annealed in a furnace for bonding the metal layers together.

4.3 Fabrication of the channels

In order to make the channels in which the liquids should flow, a layer of the light sensitivephotoresist SU-8 with a thickness of 20 µm was spun onto the front side of the wafers.Before this process the wafers were dried in an oven to improve adhesion. The first timethe HMDS oven was used, but it turned out that this did not work as the SU-8 contractedupon the wafers after the spinning process. This contraction made the wafers useless andfor that reason the SU-8 was removed by development making the wafers ready for anothertry.

The second time the wafers were placed in an oven overnight to make sure that theywere completely dry before executing the SU-8 process again. This time the result wasexcellent. Following the spinning the SU-8 was prebaked and exposed through a mask,hard baked in a special sequence to avoid internal stress and finally developed in a specialdeveloper PGMEA and isopropanol. During the exposure it was found that the alignmentmarks on the back side of the wafers were blurred due to the non polished back side. Thiscaused the alignment with the channel mask not to be very precise. Although this was nota major problem since the channel structures were fairly large, it can not be recommendedto use non polished wafers for finer structures.

Fig. 4.7 shows a cross section of a chip as it was supposed to look after development.

Unfortunately all the SU-8 fell off in the development process resulting in useless wafersas shown in Fig. 4.8. Although not knowing the reason, the failed process could be due tothe fact that the SU-8 had been spun on twice.

4.4. ETCHING FLUIDIC IN- AND OUTLETS 33

Figure 4.7: Chip with bottom electrode, oxide and channels placed on top after exposure anddevelopment of SU-8.

Figure 4.8: An example of a wafer with useless SU-8 channel structure after completed but faileddevelopment process showing how most of the SU-8 has fallen off leaving the dark SiO2 uncovered.The reason for the failed process is not fully known but resulted anyhow in the destruction of allthe wafers.

Because all the wafers were now ruined and due to a tight clean room schedule it wasnecessary to proceed with some wafers from the other group1, although these were withoutelectrodes.

4.4 Etching fluidic in- and outlets

The next step in the fabrication was the making of through holes for fluidic in- and outletsthrough the silicon wafer.

After the SU-8 development the front side of the wafers was covered with AZ-resistand exposed through the through hole mask, baked and developed, leaving a result asshown in Fig. 4.9.

Figure 4.9: Cross sectional view of the chip with oxide, SU-8 channels and photoresist ready foretching the through holes from the top by means of Advanced Silicon Etch.


(a) (b)

Figure 4.10: Fig. 4.10(a) shows a structure made by Advanced Silicon Etch with SF6 plasma.The alternating use of anisotropic plasma etch and teflon coating gives the characteristic bulgystructure. A cross sectional view of a chip after the etch of throughholes is shown in Fig. 4.10(b).

Furthermore a thin layer of resist was applied on the backside and the oxide on top of thenot yet finished through holes was removed by means of buffered HF acid. These stepswere carried out by the other group1.

The making of the through holes was done using of a process called Advanced SiliconEtch. That is an etching method using ionized SF6 for etching and thin teflon layers forpacifying the walls and bottom by turns. This gives an anisotropic etching as it etchesmore downwards than to the sides. The result of an ASE etch is in principle shownin Fig. 4.10(a), where the finished holes are covered with a coating of teflon electricalinsulator between the fluid and silicon. This way of making through holes in conjunctionwith channel systems in SU-8 has never been used before and therefore the result was notknown with certainty. Fig. 4.10(b) shows the cross section of a chip.

During the etching process the wafer was cooled down by He from underneath. Inorder to avoid penetration to the cooling system a carrier wafer was glued to the back sideof the wafers using AZ-resist. To ease removal, the AZ-resist was only applied in certainareas as shown in Fig. 4.11.

Only putting the AZ-resist in certain areas turned out to be a bad idea. As it can beseen in Fig. 4.12 a ring where the bonding is not satisfying can be observed. This ring

Figure 4.11: The distribution of AZ-resist when used as glue on the carrier wafers. An unevendistribution gives an uneven coling making it possible for thermoplasts to contract differently onthe wafer. The left figure shows the used distribution whereas the right shows an alternativemethod, which could avoid uneven cooling.

4.5. APPLYING GLASS LID 35

Figure 4.12: The bonded and sawn out wafer showing the ring where the bonding is not satisfyingdue to thermal contraction of the SU-8 in the ASE etch used with inconvenient gluing to the carrierwafers.

is presumed to originate from the cooling during the etching process. As the AZ-resistwas not uniformly distributed between the two wafers the cooling might have been unevenduring the process. This influences the height of the SU-8 since this polymer contractswhen heated. To avoid this problem, one could use the alternative resist distribution asshown in Fig. 4.11.

4.5 Applying glass lid

After having removed the carrier wafers, the bottom part of the chips was finished. Allthat was left in having made the final wafers now was assembling the 500 µm glass lids andthe bottom wafers. Originally the lids should also contain conductors and an insulatingoxide as shown in Fig. 3.17. But since the silicon wafers with the conductors were lost thelids were made without electrodes and oxide.

The lids were prepared by the other group1 by washing, cleaning and finally spinningon and baking PMMA to one of the sides. In this way the PMMA was used as a gluebetween the lid and the SU-8 structure.

At last the lids was bonded onto the wafers by means of the Thyra bonding machineoutside the clean room. This machine simply bonds the lid to the wafer by applying highpressure during heating.

Originally the assembling of the lid and wafer should have included an inking processresulting in having no PMMA on top of the channels but only on the SU-8 and therebyraising the channel height with the height of the PMMA layer, see Fig. 3.17. But althoughbeing prepared, this method was not used, as the first attempt with ordinary bondingfailed. On this background it was decided not to use the more risky inking method, as theamount of wafers had been rapidly decreasing during the clean room processes.

Finally the chips were sawn out by a laboratory technician making them ready for test.


4.6 Summary of the processes

In short terms the fabrication has made use of common as well as untested clean roomprocesses, where some were more successful than others.

The first problem encountered was the low quality of the alignment marks on thenon polished back side, why this cannot be recommended for use with finer structures.Secondly the SU-8 processes contained two problems; one related to the insufficient prepa-ration in HMDS oven, and the other not fully known but resulting in lost wafers duringdevelopment. Finally the cooling in the ASE etch resulted in an uneven structure result-ing in a ring without proper bonding on the wafer. Therefore the assemblage with carrierwafers should be altered.

The structure of the final chip without electrodes and with a channel height of only10 µm differs thereby from the originally wanted design in Fig. 3.17 now having a crosssectional view as seen in Fig. 4.13.

Figure 4.13: Cross sectional view of the fabricated chip with a channel height of 10 µm SU-8 andtop lid of PMMA and glass, sides of SU-8 and bottom of silicon covered with SiO2.

Chapter 5

Test and measurements of the chip

After having used the theory to design chips and later on fabricated them in the clean room,it is now time to test if the behaviour of the chip agrees with the theoretical predictions.

5.1 The setup

As mentioned in Sec. 3.4.1 it is essential to be able to control the pressure of the two fluidsat the inlets within a few pascals. A possible and easy way of obtaining these pressures isby means of the gravity g, that is having two reservoirs in appropriate heights connectedto the inlets by tubes. Thereby the mass of the fluids will exert pressures at the twoinlets. If the exact heights h and the densities ρ of the fluids are known the pressure canbe calculated by

P = ρgh. (5.1)

To make sure that the pressures do not change dramatically during an experiment it is im-portant that the cross section of the reservoirs is so big that the height of the fluid columnsdoes not vary much. For this reason syringes with a diameter of 18.9 mm correspondingto a pressure drop of approximately 2.1 Pa for each 60 µL water were used.

(a) Package without chip (b) Package with chip

Figure 5.1: The package to contain the chip and allow for fluidic and electrical interconnectionwith the outer world. The package is produced in polycarbonates and contains a hole in the toplid for visual inspection through microscope.

37

38 CHAPTER 5. TEST AND MEASUREMENTS OF THE CHIP

Figure 5.2: Basic structure of the setup with reservoirs for applying inlet pressures, Vernier gaugefor measuring the heights of the surfaces and microscope for visual surveillance.

Figure 5.3: The setup for applying pressure by means of gravity on the reservoirs which can beadjusted in height with high precision. The microscope and chip package can be discerned to theright.

To connect the tubes to the inlets of the chip it is necessary to have a device intowhich both the chip and the tubes will fit. Furthermore this device has to direct the flowof the fluids from the tube to the inlets without leakage resulting in pressure drop andshort circuitry of the electrical interconnections. Moreover the device should be able tofix the chip horizontally at a given height and also be transparent for visual surveillance.The last required feature should be the possibility of applying voltage to the electrodes ofthe chip.

These requirements taken into consideration the device shown in Fig. 5.1 was designedand fabricated1.

1The fabrication of the packaging system was carried out by the MIC workshop staff.

5.2. EXPERIMENTS 39

Before beginning the experiments another device enabling precise height adjustment ofthe fluid columns had to be constructed. This device should enable both coarse adjustmentand finetuning when the area about equilibrium is reached. These simple requirementsled to the device sketched in Fig. 5.2 and pictured in Fig. 5.3. For measuring the heightof the fluid columns, a table mounted Vernier gauge was used.

Furthermore, a microscope with digital mounted camera was used for visual surveil-lance.

The last equipment required was a timer, a ruler and a thermometer used in connectionto flow rate measurements.

5.2 Experiments

Not having capacitors embedded in the chips, neither measurements of the pressure Pcap

nor the break down voltage of the chip were possible to perform. This however still leftplenty of measurements to be performed in the process of characterizing and testing thechip. These measurements can be divided into three main categories.

1. Qualitative measurements.

- Observe if the flow in the common channel is divided into layers having the oilin the center.

2. Quantitative measurements.

- Obtain equilibrium and compare to the theoretical values.

- Investigate if it is possible to make bubbles from the equilibrium within thepressure limit restricted by the theoretical capacitor pressure by adjusting waterpressure.

- Measure the flow rate and compare to the theory.

- Examine if it is possible to obtain equilibrium different places in the oil channel.

3. Macroscopic measurements

- Measure contact angle and surface tension between the fluids in order to cal-culate the Young-Laplace pressure.

- Test the miscibility of different liquids.

Although having channel heights of only 10 µm instead of 25 µm, the relation betweenthe inlet pressures in equilibrium given by Eq. (3.16) is still the same. Inserting the actualvalues for the two designs given in Table 3.4 the pressure relations are found to be as givenin Table 5.1.


Chip 1 Chip 2

Pw=2.03 Po Pw=2.25 Po

Table 5.1: The ratio between water inlet pressure Pw and oil inlet pressure Po required fortheoretically obtaining an equilibrium where the oil and water interface stays staticly at the endof the oil channel when the Young-Laplace pressure PYL is not included.

5.2.1 First experiment - silicone oil

The oil bought for the experiment was a clear SF96-3 silicone oil having the physicalproperties as given in Table 3.1 with a viscosity µ = 3 × 10−3 − 4 × 10−3 Pa s.

In order to be able to distinguish the fluids from each other, one of the fluids had to becolored, as the silicone oil is clear. The best combination would be to have the oil coloredas when both the oil and the other fluid were flowing in the common channel just a smallamount of oil were supposed to be present. Furthermore the oil is supposed to be the lasercavity, why the laser dye must be in the bubbles.

Therefore it was attempted to color the oil with the red dye Rhodamine B. The resultof the failed attempt is shown in Fig. 5.4. For that reason deionized water with Rhodaminewas used instead.

In the first experiment silicone oil and colored water was loaded to see if the two fluidswere flowing as supposed in the common channel. Unfortunately the silicone oil tendednot to flow at all in the chip and it was only possible to move it by applying high externalpressure with the syringe piston. When removing the piston the oil settled in the channelsin at first sight unphysical formations. Examples of this is shown in Fig. 5.5.

Even though the oil did not flow in the chip under normal pressures in the order of afew thousand pascals it was possible to make bubbles when the pistons were used. Thebubbles, however, did not minimize the surface area as expected, nor flowing with the

Figure 5.4: The result of attempting to color the SF96-3 silicone oil with Rhodamine B. It is seenthat the Rhodamine is not soluble in the oil but instead lies as crystals in the oil giving the darkopaque substance in the bottom of the reservoir.

5.2. EXPERIMENTS 41

Figure 5.5: The silicone oil (black) and dyed water (green) in the chip positioned at apparentlyunphysical static situations. The formations have been made using external pressure from thesyringe pistons, which were afterwards removed in order to return to normal inlet pressures. Thegreen color is due to refraction of the microscope spot light.

water under normal pressure conditions. To verify this, an oil bubble was placed in thecenter of the cross. After one night, all the water from the reservoir had flowed throughthe chip but the bubble was still stuck in the same position. Nevertheless it was withsufficiently high pressures applied with the pistons possible to make a laminated structurewith the oil centered in the channel as presumed in Sec. 3.4.1.

As this fluid combination did not work, the water was replaced with ethanol. Thisdid not result in a better but only a different situation, where the the oil still tendednot to flow. Furthermore the interface between the fluids was not distinct when externalpressures were applied.

5.2.2 Macroscopic experiments

As the behaviour of the fluids in the chip was not as one apparently should think, macro-scopic experiments were carried out in order to investigate the fundamental propertiesof the fluids. First of all the solubility of the fluids was investigated by simply mixingsilicone oil with water and ethanol based rhodamine dissolutions respectively. The resultin pictured Fig. 5.6 shows that the oil is immiscible with water as expected whereas itis soluble in ethanol. This fact explains, that the interface between the silicone oil andethanol was not well-defined.

Afterwards a measurement of the contact angle between the water and oil was at-tempted. First a drop of water was placed on a wafer with the same surface as the chipand on top of this an oil drop was placed as in Fig. 5.7. The equipment for angle mea-


(a) SF96-3 and ethanol (b) SF96-3 and water (c) SF96-3 and water

Figure 5.6: Macroscopic miscibility experiments showing that the clear silicone oil is soluble inthe red dyed ethanol but not in the red dyed water. Fig. 5.6(a) shows the ethanol and silicone oilafter being shaked. Fig. 5.6(b) and 5.6(c) shows the water and silicone oil before and after havingbeen shaked. It can be seen that the oil lies in droplets in the water. A few minutes later, thesituation was again as in Fig. 5.6(b).

surement was not able to find the interface between the fluids why the angle could not bedetermined. As seen in Fig. 5.8 the oil is flattened out on the surface, meaning that froman energy point of view it is beneficial for the oil to be in close contact with the surface.

As this has its effect for both the SiO2 and PMMA, having only 10 µm channels theoil tended to stick to the top and bottom and thereby behaving as a glue.

On this background it can be concluded that this particular silicone oil is not a goodchoice if a flow is wanted. On the other hand it is well suited as a movable barrier cuttingoff or redirecting a water flow at low pressures.

Figure 5.7: Two drops positioned at a solid surface with the contact angle θ shown at theircommon interface.

5.2. EXPERIMENTS 43

Figure 5.8: A wafer containing both a drop of Rhodamine dyed water and silicone oil. It is clearlyseen that the oil droplet, which is the colored pattern in the bottom of the photo, has flattenedout on the wafer, meaning that it tends to stick to the surface.

5.2.3 Flow rate measurements

Before attempting to obtain equilibrium with other fluid combinations, flow rate measure-ments were carried out in order to see if the hydraulic resistance and thereby the pressuredistribution inside the chip corresponded to theory.

The measurements were done using only one inlet at a time by blocking the other inletby means of clamps on the outer silicone tubes. In this way it was possible to make twomeasurements; one on the oil and common channel and another on the common channelsand water channels. Having two different designs and using both water and ethanol itwas the intension to carry out eight different measurements. Unfortunately there was onlytime to perform characterization of the design shown in Fig. 3.13(a) using water as fluid.

Practically the measurements were carried out by applying a certain inlet pressureand loading the chip. By mounting a ruler on the external outlet tube, it was possible todetermine the flow rate by measuring the length of the fluid in a given time and afterwardsmultiplying with the cross sectional area of the tube. During the measurements, the roomtemperature was surveyed as the viscosity of water changes with temperature, see Ref.[3], p. 6-186. By varying the inlet pressure a series of data set was obtained.

Strictly speaking, the resistance of the external tubes should be included in the resis-tance calculations, but having an inner radius of a = 0.40 mm the resistance of a L = 0.50m tube given by

Rtube =8µL

a4π(5.2)

is less than 1 ‰ of the resistance in the chip calculated from Eq. (2.6) and can thereforebe neglected. The indirect flow rate measurement is calculated from the inlet pressureP using the fluidic analogy to Ohms law, Eq. (2.4) where the chip resistance is found byseries connection of the common and water or oil channel respectively.

The result of the measurements are shown in Fig. 5.9 and the data given in Apps. Gand H.

As it can be seen on the plots, there is a linear relation between the flow rate and pres-sure in both cases. Furthermore, the direct and indirect measured values corresponded wellalthough not being limited completely by the error bars made from the uncertainty calcu-lations in Sec. 5.3 meaning that the pressure distribution in the chips are approximately


(a) Direct and indirect measured flow rate through water and common channel

(b) Direct and indirect measured flow rate through oil and common chan-nel

Figure 5.9: Result of the flow rate measurements showing the flow rate as a function of the appliedpressure to the water and oil inlet respectively when using water. The inlet not used has beensealed off in order to avoid flow from this source.

5.2. EXPERIMENTS 45

as calculated theoretically.

The deviations might originate from the assumptions of using the centerline as a mea-sure of the length and using the fluidic analogy to Ohm’s law for calculations on this linemeaning that the resistance in the water channels is smaller than estimated.

The deviation of the resistance in the oil channel can be due to the fact that the flow isnot originating at the end of the oil channel as the inlet hole is positioned with the center0.5 mm from the end of the channel. Having a shorter channel alters the slope of theindirect measured graph making it more parallel to the direct measurement, cf. Eqs. (2.4)and (2.6). That the indirect flow rate is lower than the direct measured can be due toimpurities and irregularities in the channel.

5.2.4 Alternative fluid combinations

Having verified that the resistance and the pressure distribution of the chip correspondedwell with the theory one would expect that an equilibrium was obtainable using alternativefluid combinations.

Since oil is not soluble in water it was obvious that another oil should be tried. Thistime a more common and viscous grape seed oil was used together with water. In orderto find the theoretical equilibrium values the density of the oil had to be known. Theobtained data and measurement details can be found in App. F, where the viscosity isalso estimated. The average density was found to be ρoil = 910 kg/m3.

As with the silicone oil this oil was also tested for miscibility with water and ethanolgiving results shown in Fig. 5.10. From here it is clear that the grape seed oil was notsoluble in neither of the two fluids although the Rhodamine from the ethanol dissolutiontended to color the oil slightly. Furthermore the curvatured water-oil interface indicatedhigh tensions between the two fluids.

A contact angle measurement on the previously used wafers was also attempted, butalthough this oil did not flattened out but kept the bubble shape with a contact angle lessthan 90◦ in the air interface as illustrated in Fig. 5.7, the equipment was still not able to

(a) (b)

Figure 5.10: Miscibility of grape seed oil (clear) with water (red) and ethanol (red) respectively.(a) shows water and oil and (b) shows ethanol and oil. It is seen that the oil is immiscible withboth fluids and heavier than ethanol but lighter than water. Furthermore the curvature of theoil-water interface indicates a smaller contact angle in the oil than that of the ethanol-oil interface.


identify the interface. For this reason the Young-Laplace pressure was still not known.

Anyway it should still be possible to find the Young-Laplace pressure as the constantdeviation between measured and theoretical pressures at equilibrium calculated withoutencounting the Young-Laplace pressure as given in Table 5.1.

Water and grape seed oil

The first combination tried was grape seed oil and water. Loading chip 2, see Fig. 3.18(b),so that both oil and water were present in the common channel at the same time, it wastried to raise the pressure of the water in order to cut off the oil stream and force it backinto the oil channel. Attempting to do this, it was observed that the behaviour of thesystem was similar to the water and silicone oil combination as it was not possible withthe pressure only originating from the fluid columns to obtain an oil flow when gettingin contact with the water. Instead the oil tended to get stuck in the channels and wasonly moveable when applying high pressures with the syringe pistons. When removing thepistons, the oil again settled. It should be noticed, that this experiment was not carriedout over a longer period as with the silicone oil, meaning that it might be possible thatthe oil is able to flow very slow although not having observed this.

When trying to make an interface in the oil channel using the pistons for applyingpressure, the water did not cut through the oil nor forced it back. Instead it was observedthat the water crept into the oil channel along the sides surrounding the oil and eventuallyentered the oil inlet.

Although not knowing the exact reason the behaviour could be analysed from an energypoint of view. When loading the oil without letting it enter the common channel the oilis interested in being in contact with the solid surface area if having a contact angle lessthan 90◦. In this case the oil loses the smallest surface contact area when detaching fromthe walls instead of being pressed back into the inlet as the walls with 10 µm in heighthave very small areas compared to the top and bottom.

Another situation is when the oil is loaded so it enters the common channel and

(a) High pressure applied with pistons to bothwater and oil.

(b) Situation without high pressures. The flu-ids have been forced in by use of pistons.

Figure 5.11: The result of loading a chip with Rhodamine dyed water (green) and grape seed oil(dark). It is clear that this combination is not suitable for the chip, as the water when put underhigh pressure tends to creap along the channel sides surrounding the oil as in (b). Moreover it isvery difficult to obtain a flow of the oil at all under normal pressure.

5.2. EXPERIMENTS 47

Figure 5.12: Rhodamine dyed ethanol (green) and grape seed oil (dark) when applied high pres-sures with the syringe pistons. The formation is under these conditions very stable.

applying pressure to the water with the piston. When cutting through the oil an incrementof energy will arise as the oil and water interface area is increased. If this increment islarger than the energy required for creaping in between the oil and side walls and if thepressure drop in the oil channel is not too large this will tend to happen.

Fig. 5.11 shows examples of the formations with water and grape seed oil, one showing asituation with high pressure applied with pistons and one with normal pressure conditions.

Beyond indications of surface tensions making it impossible to establish an equilibriuminterface this fluid combination had a tendency to deposit material in the channel systemand thereby contaminating the chip making it hard to cleanse them for reuse. Thisdeposition supported the assumption that the oil was eager to maintain contact withthe channel surfaces.

On this background it must be concluded that the grape seed oil and water combinationis not at all suitable for this purpose.

Ethanol and grape seed oil

As seen in the miscibility test, the interface between grape seed oil and water was verycurved indicating strong surface tension. To investigate, if this had the supposed influenceon the behaviour of the flows, the water was replaced with ethanol. In this case it waspossible to make the oil flow in the common channel in a divided structure as shown inFig. 5.12 when applying high pressure with the pistons.

Figure 5.13: Rhodamine dyed ethanol (green) creaping into sides of oil channel and filling thisas it is not possible to cut through the oil. This means that an oil/ethanol interface across the oilchannel cannot be established.


(a) (b)

Figure 5.14: Attempts of trying to load ethanol (green) and grape seed oil (dark) in a mannerwhere the oil does not enter the common channel before being stopped by ethanol. As seen in thefigures it is not possible to produce an interface as the ethanol creaps along the sides into the oilchannel. Furthermore it is seen that the oil is a bit greenish indicating, that a thin ethanol filmmight surround it or that the Rhodamine can diffuse from ethanol to oil.

But trying without pistons it turned out that it was impossible for the ethanol to cutthrough the oil flow when first this had entered the common channel. Instead the ethanolcrept into the oil channel along the sides and in this way entered the oil inlet as shown inFig. 5.13. Changing the chip to another design did not alter the situation.

Attempting to avoid this phenomenon the loading process was altered, so the oil didnot reach the common channel before getting in contact with the ethanol. In this wayit should have been possible to make an interface across the oil channel. Unfortunatelyexactly the same situation occurred as the ethanol again entered the channel along thesides as shown in Fig. 5.14 and thereby made it impossible to establish an equilibrium.

In short terms the behaviour of the ethanol and grape seed oil was in general analogueto the water and oil combination. Only this time the oil although being slow flowedwithout applying high pressures. It has not been possible to find a reasonable explanationfor this difference from the water and oil experiment why the behaviour is still a mystery.

It was also observed that if having had the ethanol in the oil inlet, the oil tended tobe colored a little when reloaded indicating that it could be encapsulated by a thin filmof ethanol as shown in Fig. 5.14(a). Anyhow this did not seem to alter the behaviour ofthe system as the ethanol still crept into the oil channel along the sides.

Ethanol and water

Having made several unsuccessful attempts to establish equilibrium with two differentoils with various loading sequences at different chips, the fluid combination was altered towater and ethanol. Well knowing that the interface would not be distinct as the two liquidsare indeed miscible this was nevertheless carried out to try as many fluid combinations aspossible.

Using water with Rhodamine in the water channels and ethanol in the oil channel itwas investigated if it was possible to produce a stationary interface in the oil channel.First a simple flow was established to determine if an interface could be observed in spiteof the diffusion. As shown in Fig. 5.16 this was possible although the interface was not

5.2. EXPERIMENTS 49

Figure 5.15: Example of a chip with several deposits originating from water and ethanol interfacescorresponding to various inlet pressure combinations. The ethanol is loaded from the oil channelin the center.

well-defined. In connection to the experiment it was observed that the edge of the outlethole seemed to contain a ridge probably originating from the ASE etching which couldinfluence on the resistance of the common channel.

Furthermore deposits occurred in the interface meaning that when altering the inletpressures, the new flow was partially bounded by these. An example of several of thesedeposits is shown in Fig. 5.15 where each deposit was created by a water and ethanolinterface placed at the given position over a period. These deposits could however beflushed away by applying high inlet pressures using the pistons.

(a) Pw=2044 Pa, Pe=1773 Pa (b) Pw=2044 Pa, Pe=1339 Pa (c) Pw=2044 Pa, Pe=1339 Pa

Figure 5.16: Water with Rhodamine (green) and ethanol (dark) at various pressures. It is seenhow the decrement of ethanol pressure Pe from Fig. 5.16(a) to 5.16(a) as expected reduces the flowof the ethanol. In Fig. 5.16(c) the pressures are the same as in the previous figure, but here thepressures have been raised temporarily in order to flush the channel system before returning tonormal pressure. This shows that deposits in the previous interface disturbs the flow.


The height of these deposits is not known, but it is certain that although allowing thefluids to pass them, their appearance had influence on the flow and pressure conditions inthe system. This was observed in the process of establishing an equilibrium since graduallyaltering the pressures in order to create an interface in the oil channel caused deposits tooccur. When having obtained a situation where the diffusion interface oscillated slightlyback and forth in the oil channel in resemblance to an equilibrium, it was not possible to re-establish this with the same inlet pressures after cleansing the channels from the deposits.After numerous attempts with the same result, it was concluded that the deposits had acrucial influence on the pressure conditions making comparising with theory impossible.

It was furthermore observed that with high pressures applied with the pistons the flowwas very stable returning to the same situation after making small fluctuations in the inletpressures. This implies that the not so well-defined interface at low pressures was mostlikely caused by diffusion and not due to turbulence. In general the system was with thisfluid combination very sensitive to changes in the inlet pressures. This indicates that evensmall changes in the pressure can lead to considerable changes in the system, making itreasonable to believe that a capacitor could be used to control low viscosity fluids.

Ethanol and air

After several unsuccessful liquid combinations it was in a final attempt to establish anequilibrium decided to test with ethanol and air using the air in the oil channel.

As the setup was not designed for use with air, it was not possible to determine theinlet pressure as this was established using pistons and a clamp. Hereby the experimentwas no longer quantitative but qualitative in the sense of not knowing the ratio betweenthe pressures at equilibrium. Still it was possible to measure the change in Pw necessaryto change the position of the interface when having found an equilibrium.

When carrying out the experiment, the chip was loaded with air under pressure higherthan the atmosphere and afterwards with ethanol. In this way it was avoided to haveethanol in the oil channel giving a symmetric flow as shown in Fig. 5.17. From thisthe ridge at the edge of the outlet hole can be observed as with the water and ethanolexperiments again changing the pressures and flow rates.

Figure 5.17: Flow with Rhodamine dyed ethanol (green) and air (dark) indicating a ridge at theedge of the outlet hole disturbing the flow. The inlet pressure to the air is of a magnitude wherethe ethanol is not capable of stopping the this but leaving an air flow centered in the commonchannel.

5.2. EXPERIMENTS 51

Figure 5.18: Equilibrium with air (dark) and ethanol (green) positioned different places in the oilchannel due to alterations of the ethanol inlet pressure.

Naturally the external air pressure decreased as the air flowed through the chip result-ing in a situation where the air pressure was no longer high enough to maintain a flow. Itwas observed that as the air flow was cut off by the ethanol, the situation became unstableand the air began to dispatch bubbles into the common channel with an interval gettinglarger still. When a bubble left the chip the interface in the oil channel was forced towardsthe inlet as the resistance of the common channel increased when containing no air. Thiscaused the air pressure to rise in the oil channel. However the situation was not stablesince the pressure in the air rose again forcing the interface towards the intersection. Inthis manner the interface oscillated back and forth in the oil channel eventually not dis-patching any more bubbles. Hereby it was possible to establish an equilibrium and place itat a given position in the oil channel by adjusting Pe. But as the system was very sensitiveand the air pressure not constant due to possible leakage in the setup, the equilibrium wasnot fully static but still oscillating slightly. Fig. 5.18 shows the equilibrium positioneddifferent places in the oil channel.

Although not being sure about the reason for the pressure increase of the air, anreasonable explanation could be evaporation of ethanol into the air. In this manner thetotal pressure of the gas will rise due to the partial pressure of the ethanol. As the ethanolevaporates, the pressure of the gas will eventually rise above the intersection pressurecausing a bubble to be dispatched. For this process to repeat itself as observed the vapourpressure must be high enough so that just a fraction of this is sufficient to force theinterface towards the intersection and thereby producing bubbles. If the entire vapourpressure was required to produce bubbles the phenomenon would only happen once sincenothing could cause the pressure of the gas to rise once again. Fortunately this vapourpressure was is of the order 104 Pa at 29.2◦C, see [3] p. 6-74.

Having found the equilibrium it was investigated how small changes in the ethanolinlet pressure were necessary to produce bubbles. It was found that the with a change ofthe ethanol column of 15 mm corresponding to an inlet pressure of 116 Pa it was possibleto produce bubbles as seen in Fig. 5.19. Using the expression for the inlet pressure inrelation to the cross pressure given in Eq. (3.19), it was found that with ethanol and air2,this corresponded to an approximated change in cross pressure Px of only 1.7 Pa which isfar from the limit restricted by the capacitor. It should be emphasized that Eq. (3.19) inthe calculations have been used under assumption of only having ethanol in the common

2The used viscosity of air is µ = 18.6 × 10−6 Pa s, see [3], chap 6


Figure 5.19: A bubble of air (dark) in rhodamine dyed ethanol (green) generated by changing theethanol inlet pressure with approximately 120 Pa corresponding to a change in Px of 1.7 Pa. Thisindicates that it should be possible to produce air bubbles with the use of a capacitor.

channel, reducing the value of Px to an approximation.

This result indicates thereby that it should indeed be possible to control an air andethanol configuration with a capacitor although being hard to maintain a stable situationwith the used test setup.

5.3 Uncertainty calculations

5.3.1 flow rate

In order to estimate the uncertainty connected to the flow rate it is necessary to findthe uncertainty linked to each parameter used to calculate this. To be able to do so theuncertainty of the measurements performed have to be estimated. These can be seen inTable 5.2, where H is the height of the reservoir, t is the time, r is the radius of the tube,l is the distance the fluid has flowed, L is the length of the other channels, Lo is the lengthof the oil channel, w and h are the width and height of the channels respectively andfinally the dynamic viscosity µ.

u(H) u(t) u(r) u(l) u(L) u(Lo) u(w) u(h) u(µ)

1 mm 0.05 s 0.001 mm 0.25 mm 1 µm 0.5 mm 1 µm 0.15 µm 5 ×10−5 Pa s

Table 5.2: Estimates of the uncertainty u(x) of the parameters x used to calculate the flow ratein the chip

First the uncertainty of the measured flow rates will be calculated. Since this is given asQmeasured = l A

t, with A = πr2, one has to find the uncertainty of A. This is a function of

the form

Y = cXp1

1 · Xp2

2 · · ·XpN

N , (5.3)

5.3. UNCERTAINTY CALCULATIONS 53

where c, pi (i = 1, 2, . . . , N) are constants, and Xi (i = 1, 2, . . . , N) are the parameters.The relative uncertainty can therefore be calculated using, see Ref. [2] p.10,

u(y)

y=

√

(

p1u(x1)

x1

)2

+

(

p2u(x2)

x2

)2

+ · · · +

(

pNu(xN )

xN

)2

. (5.4)

This yields

u(A) = A2u(r)

r= 2πru(r). (5.5)

It is now possible to calculate u(Q) using Eq. (5.4),

u(Q) = Q

√

(

u(l)

l

)2

+

(

u(t)

t

)2

+

(

u(A)

A

)2

= Q

√

(

u(l)

l

)2

+

(

u(t)

t

)2

+

(

2u(r)

r

)2

. (5.6)

When calculating the uncertainty of P = ρgH, which is of the form

Y = p0 + p1X1 + p2X2 + . . . pNXN , (5.7)

since ρ and g are presumed to have u(ρ) = 0 and u(g) = 0 respectively, the expression,see Ref. [2] p. 9,

u(y) =√

(p1u(x1))2 + (p2u(x2))2 + · · · + (pNu(xN ))2 (5.8)

is used. This leads to the following

u(P ) = ρgu(H). (5.9)

The uncertainty values for Qmeasured and P can be seen in Table G.1. The uncertainty ofthe height has been estimated using SEM microscopy on a cut through chip. Unfortunatelythe pictures could not be included due to technical problems.

It is now time to find the uncertainty of the flow rate calculated by the fluidic analogyto Ohm’s law, where Rhyd = 12µL

(w−0.63h)h3 . Since Q is of the form Eq. (5.3) u(Q) can found

if u(P ) and u(Rhyd) are known. Already knowing u(P ) from Eq. (5.9) only u(Rhyd) is leftto be calculated. Since none of the parameters in Rhyd are correlated, this can be doneusing the law of error propagation, see Ref. [2] p. 9, in the general form

u(y) =

√

(

∂Y

∂X1u(x1)

)2

+

(

∂Y

∂X2u(x2)

)2

+ · · · +

(

∂Y

∂XNu(xN )

)2

. (5.10)

Using the common rules for series and parallel connection of resistances the resistance inthe water and common channel Rhyd,c+w becomes

Rhyd,c+w =6µ(Lw + 2Lc)

(w − 0.63h)h3. (5.11)


This leads to the following uncertainty for Rhyd,c+w

u(Rhyd,c+w) =

(

(

∂Rhyd,c+w

∂µu(µ)

)2

+

(

∂Rhyd,c+w

∂Lwu(Lw)

)2

+

(

∂Rhyd,c+w

∂Lcu(Lc)

)2

+

(

∂Rhyd,c+w

∂wu(w)

)2

+

(

∂Rhyd,c+w

∂hu(w)

)2) 1

2

(5.12)

The uncertainties can be seen graphically in Fig. 5.9(a) and the numeric values are listedin Table G.1.

Similar calculation can be carried out when using the oil and the common channel, seeFig. 5.9(a) for the graphically uncertainties and Table H.1 for the numeric values.

5.4 Summary and evaluation

In retrospect none of the tests with two liquids fulfilled the goal of establishing equilibriumnor producing bubbles. Instead several other phenomena were observed.

When using oils it was generally a problem that they tended to stick to the channelsurfaces thereby making it virtually impossible to establish an interface across the oilchannel. In the case with silicone oil and water this phenomena was so pronounced thatthe oil behaved as a glue. This could however be exploited as a moveable barrier in lowpressure pressure systems if the position of the oil can be controlled.

Using miscible fluids as ethanol and water it was possible to establish an situationsimilar to equilibrium which unfortunately was not reproduceable due to deposits in thesystem.

Having found that it was possible to establish equilibrium and produce bubbles withair and ethanol indicates in conjunction with the ethanol and water experiment, that itmight be possible to exploit dielectric actuation to produce a liquid-in-liquid bubble gen-erator if finding a suitable liquid combination.

Evaluating the testing process it is clear that the transition from quantitative to quali-tative measurements has resulted in less direct data. However repeating the flow rate mea-surements to achieve a better statistical foundation for characterization of the resistanceand thereby pressure distribution would be preferable. Likewise thorough investigationsof the contact angle and surface tensions of the fluids by macroscopic experiments wouldhave been a desirable tool for deeper analysis of the observed behaviour. If the project hadto be repeated it could thereby be recommended to include such macroscopic experimentsearlier in the process.

But as the test period was relatively short due to the long fabrication process anddeveloped in a direction not predictable, the time did not allow for this. Hereby theproject, although having revealed many basic observations of the fluidic behaviour, stillprovides material for further investigations.

Chapter 6

Conclusion

During the project the theory was exploited to design a chip with channels and a capacitortheoretically making it possible to use the chip as a valve controlling the flow of two fluids.

To simplify the design the channel system was based on a design where the two fluidsintersected in a cross allowing one to control the flow rate of one of the fluids by adjustingthe pressure of the other.

A capacitor was placed in the intersection in such a manner, that turning it on wouldtheoretically cause one of the fluids to be sucked into the capacitor and thereby stoppingthe other.

After the design process, the fabrication was commenced. During this several problemswere encountered having impact on the properties of the chip. The far most importantalteration was the loss of electrodes meaning that the concept of dielectric actuation wasno longer present.

Having designed and fabricated a suitable test setup the measurements of the flow andpressure in the chips without capacitors were started using a silicone oil and water. In theattempt of establishing the pressure equilibrium it was found that fluids did not behave aswanted as certain material properties played a more important part than expected. Thismade the required equilibrium unattainable in spite of attempts with other immiscibleliquid combinations.

Trying with the miscible liquids ethanol and water it was however found possibleto establish a situation similar to equilibrium but with diffusion blurring the interface.Furthermore ethanol and air was used resulting in production of air bubbles within therequired pressure limit.

Moreover it was observed during the experiment with ethanol and water and the ex-periment with ethanol and air that the system was very sensitive to a change in the inletpressures.

In general it can on this background be concluded that it was not possible to fulfil thegoal of producing liquid bubbles. But the two last experiments indicate that this mightbe achieved by dielectric actuation if finding the correct liquid combination.

55

56 CHAPTER 6. CONCLUSION

Aknowledgements

During the project period several persons have been of great help.

First of all we wish to thank supervisors Anders Kristensen and Henrik Bruus for offer-ing the opportunity to carry out the project and for supervision, inspiration and supportwith theoretical as well as practical aspects of the project.

Furthermore we would like to thank laboratory technician Helle Vendelbo Jensen forvital assistance and instruction with several clean room processes and process specialistJonas Michael Jensen for help with ASE and SEM as well as Theodor Nielsen for bondingthe wafers.

Concerning the test setup we wish to thank Detlef Snakenborg for thorough assistanceand advice with the design of the package for the chip as well as MIC workshop staff PoulErik Hyldbo and Stig Ahrent Petersen for help with production of the setup.

Finally we would like to thank students Morten Bo Lindholm Mikkelsen and ArneNedergaard Hansen for great collaboration during the process.

Casper Skovby, s021689

Peder Skafte − Pedersen, s021678

Simon Eskild Jarlgaard, s021982

MIC – Department of Micro and NanotechnologyTechnical University of Denmark

April 16th 2004

57

58 CHAPTER 6. CONCLUSION

Appendix A

Deriving the Navier-Stokesequation

In order to carry out the calculations, the concept of fluid elements is introduced.Applying Newtons Second Law to a fluid element with volume V we obtain the fol-

lowing relation,m

Va =

F

V. (A.1)

As the first factor represent the density of the fluid, Eq. (A.1) can be expressed in termsof the density and the specific force acting on the particle,

ρdv

dt= f . (A.2)

For further calculations the velocity field vfield is introduced as sketched in figure Fig. A.1.The field is a function in four variables, namely the three cartesian coordinates (x, y, z)and the time, t.

Figure A.1: The velocity field of four variables along the x-axis.

In the field, the coordinates are independent of the time, but when following a specificparticle this is no longer the case. This gives rise to the following relations,

59

60 APPENDIX A. DERIVING THE NAVIER-STOKES EQUATION

vfield(x, y, z, t) =vparticle(x(t), y(t), z(t), t) (A.3a)

d

dtvfield(x, y, z, t) =

d

dtvparticle(x(t), y(t), z(t), t). (A.3b)

When applying the chain rule to Eq. (A.3b), the following is obtained

dvfield

dt=vx

∂v

∂x+ vy

∂v

∂y+ vz

∂v

∂z+

∂v

∂t

=∂v

∂t+ (v · ∇)v. (A.4)

As the time derivative of the velocity equals the acceleration, using Newtons Second Lawin the form of Eq. (A.2) leads to the following expression containing both velocity andforce vectors,

ρ

[

∂v

∂t+ (v · ∇)v

]

= f . (A.5)

This is the first part of the Navier-Stokes equation. But unfortunately the specific force f

is still an unknown factor which has to be expressed in terms of known physical quantities.To do this, Fig. A.2 of a fluid element is used.

Figure A.2: Forces on a fluid element given from the pressure P in 0 and ∆x as given in Eqs. (A.6a)and (A.6b)

The force as a function of x, can be expressed in terms of the pressure P on the surfaceA = ∆y∆z, as

F (0) =P (0) ∆y∆z, (A.6a)

F (∆x) =P (∆x) ∆y∆z, (A.6b)

which together with the general relation,

F (x) = P (x) A, (A.7)

61

yields the following expression for the x-component of the force vector

Fx = F (0) − F (∆x). (A.8)

As it is the volume specific force f that is the unknown factor, it is clear that this can beexpressed by the following equation using Eqs. (A.7) and (A.8)

fx =F (0) − F (∆x)

∆x∆y∆z

=P (0) − P (∆x)

∆x. (A.9)

It can be seen that the righthand side of Eq. (A.9) is the difference quotient of the pressure,P , with respect to x, why one by letting x approach 0 yields

fx = −∂P

∂x. (A.10)

In the three-dimensional case, the specific force can thereby be expressed as the negativepressure gradient:

f = −∇P (A.11)

This means, that knowing the pressure gradient and density, the velocity profile af of aspecific flow can be approximated by use of Eqs. (A.5) and (A.11) and suitable boundaryconditions.

But for obtaining precise models of velocity profiles and flow rates, the friction due tothe dynamic viscosity µ must be taken into consideration.

In general the friction force F f is proportional to area, viscosity and velocity, and (cb.Fig. A.3) the force at z = 0 and z = ∆z in the x-direction can be expressed as

Fx,f (0) = − µ∂vx

∂z

∣

∣

∣

0∆x∆y, (A.12a)

Fx,f (∆z) =µ∂vx

∂z

∣

∣

∣

∆z∆x∆y. (A.12b)

The total force due to friction is given by addition of the forces at the top and bottom atthe volume element, which yields

Fx,f =µ ·

(

∂vx

∂z

∣

∣

∣

∆z−

∂vx

∂z

∣

∣

∣

0

)

· ∆x∆y, (A.13a)

fx,f =µ

∆z

(

∂vx

∂z

∣

∣

∣

∆z−

∂vx

∂z

∣

∣

∣

0

)

. (A.13b)

Eq. (A.13b) can like Eq. (A.9) be rewritten to a differential quotient, so the specific forcedue to viscous friction can be expressed in three dimensions as

ff = µ∇2v. (A.14)

62 APPENDIX A. DERIVING THE NAVIER-STOKES EQUATION

Figure A.3: Friction on fluid element in dynamic flow giving rise to the friction forces given inEqs. (A.13a) and (A.13b)

By combining Eqs. (A.5), (A.11) and (A.14), the Navier-Stokes equation is then givenby

ρ

[

∂v

∂t+ (v · ∇) · v

]

= −∇P + µ∇2v. (A.15)

Appendix B

Deriving velocity profile forparallel plates

Considering the situation given in Fig. 2.1 stationary and having restricted the pressuredrop ∆P to the x-direction, the no-slip boundary condition at the plates gives

v(z = ±a) = 0. (B.1)

This implies that the velocity vector only has a component in the x-direction as well asthis component is only depending on z due to the boundary conditions,

v =

vx(z)00

. (B.2)

It is clear that the derivative of v in respect to time is zero. As the velocity is alsoindependent of x and has no y- or z-component, it can be seen, that the two terms on theleft side of Eq. (2.1) are given by

ρ∂vx

∂t= 0, ρ(v · ∇)v = ρ(vx

∂

dx)

vx(z)00

= 0. (B.3)

Concerning the righthand side of the Navier-Stokes equation, the Laplacian of v can beexpressed using the second derivative in respect to z. The pressure gradient due to linearityis seen only to be dependent of the pressure drop and the length L so the righthand sideis given by

∆PL

00

+ µ

∂2vx(z)∂z2

00

. (B.4)

The one-dimensional Navier-Stokes equation suitable for the present geometry canthereby from Eqs. (2.1), (B.3) and (B.4) be expressed as

63

64 APPENDIX B. DERIVING VELOCITY PROFILE FOR PARALLEL PLATES

∂2vx(z)

∂z2= −

∆P

µL. (B.5)

As Eq. (B.5) is an ordinary differential equation of second order with a constant right-hand side, it is clear that vx(z) is a polynomial given by

vx(z) = −∆P

2µLz2 + C1z + C2 (B.6)

To determine the two constants C1 and C2, the boundary conditions Eq. (B.1) can beused to show that

v(z) =∆P

2µL(a2 − z2). (B.7)

Appendix C

Flow in a rectangular channel

Solve

0 = −∇P + η∇2ux(y, z) (C.1)

∇2ux =∇P

η(C.2)

Use a Fourier series expansion after z (so that ux(y, 0) = ux(y, h) = 0).

ux(y, z) =

∞∑

n=1

fn(y) sin(

nπz

h

)

⇒ ∇2ux(y, z) =

∞∑

n=1

[

f ′′n(y) −

n2π2

h2fn(y)

]

sin(

nπz

h

)

(C.3)

∇P

η=

∇P

η

4

π

∞∑

n,odd

sin(

nπz

h

)

(C.4)

Solution only possible if

fn(y) = 0, n even (C.5)

f ′′n(y) −

n2π2

h2fn(y) =

∇P

η

4

π

1

n, n odd (C.6)

General homogeneous solution: f ′′n − k2

nfn = 0 ⇒ fn(y) = A cosh(kny) + B sinh(kny)

Particular inhomogenous solution: fn = const. ⇒ fn(y) = ∇Pη

4h2

π31n3

From this we find,

fn(y) =∇P

η

4h2

π3

1

n3

[

cosh(

nπ yh

)

cosh(

nπ w2h

) − 1

]

, so that fn

(w

2

)

= fn

(

−w

2

)

= 0 (C.7)

Thus

ux(y, z) =∇P

ηh2 4

h3

∞∑

n,odd

1

n3

[

cosh(

nπ yh

)

cosh(

nπ w2h

) − 1

]

sin(

nπz

h

)

(C.8)

65

66 APPENDIX C. FLOW IN A RECTANGULAR CHANNEL

This agree completely with F.M.White using, h → 2a, z → y − h2 , w → 2b, y → z,

But White has problems with Q.

Q = 2

∫ w

2

0dy

∫ h

0ux(y, z) (C.9)

2

∫ w

2

0dy cosh

(

nπy

h

)

= 2h

nπ

[

sinh(

nπz

h

)]w

2

0=

2h

nπsinh

(

nπw

2h

)

(C.10)

∫ h

0sin(

nπz

h

)

=h

nπ

[

− cos(

nπz

h

)]h

0=n odd 2h

nπ(C.11)

Thus we find

Q =∇P

ηh2 4

π3

∞∑

n odd

1

n3

[

2h

nπtanh

(

nπw

2h

)

− w

]

2h

nπ(C.12)

Q =∇P

ηh3w

8

π4

∞∑

n odd

[

2h

πw

1

n5tanh

(

nπw

2h

)

−1

n4

]

,∞∑

n odd

1

n4=

π4

96(C.13)

Q =−(∇P )

ηh3w

8

π4

(

π4

96−

∞∑

n odd

2h

πw

1

n5tanh

(

nπw

2h

)

)

(C.14)

Q =−(∇P )

12ηh3w

8

π4

(

1 −

∞∑

n odd

192h

π5w

1

n5tanh

(

nπw

2h

)

)

(C.15)

This is not identical to F.M.White’s result, this result is a factor 8 to small.

Some limits:assume w� then h

w≈ 0 and tanh

(

nπ w2n

)

≈ 1

Q0: Q(w � h) = (−∇P )12η

wh3 (the infinitely large parallel plate geometry)Next correction:

w > h ⇒ tanh(

nπw

2h

)

> tanh

(

nπ1

2

)

=

0, 917 , n = 1 , 0, 9960, 9998 , n = 3 , 1, 0001, 000 , n = 5 , 1, 0001 : 1 2 : 1

Q1 : Q(w > h) ≈(−∇P )

12ηwh3

(

1 −h

w

192

π5

∞∑

n odd

1

n5

)

=(−∇P )

12ηwh3

(

1 −192

π5

31

32ξ(5)

h

w

)

Q(w > h)

≈(−∇P )

12ηwh3

(

1 − 0, 630h

w

)

(C.16)

67

Numerical results(

∇Pη

104, sum taken to 51)

hw

1,0 0,5 0,3 0,1 0,05

Q 354,1 71,46 18,246 0,78081 0,100844Q1 308,3 71,35 18,248 0,78083 0,100885Q0 833,3 104,2 22,5 0,8333 0,104167

68 APPENDIX C. FLOW IN A RECTANGULAR CHANNEL

Appendix D

Processes in the clean room

This appendix contains recipes and data from the various clean room processes.

Thermal oxidation

Growth of 100nm SiO2 by dry oxidation.Use phophor drive oxidation furnace.Place wafers on glass carrier and insert in oven.Process 1 hr. 35 min. at 1050◦C.

HMDS

Adhesion promoter used prior to photoresist application. Displaces possible water on thewafers.30 minutes at 150 ◦C in vacumm, 10 wafers.Cool down for 10 minutes.

Photoresist application

Use track 1 and test on 4 dummy wafers alone. Afterwards 1 dummy and the wafers. 1,5µm AZ-resist spun on the unpolished back side.Program pr1 5.

Resist stripping

Immerse wafers in acetone bath 1 to remove main part of resist.Move to acetone bath 2 and immerse with ultrasound for 3 min.Clean in water with bubbles for 5 min.

Karl-Suss aligner, back side contacts

Exposure of the photoresist through mask.Press ”Select program” and select ”hard contact”.

69

70 APPENDIX D. PROCESSES IN THE CLEAN ROOM

Press ”Edit parameter” and select exposure time = 10 minutes and exposure = hard.(adjust with ”x” and select with ”y”).Press ”Change mask” and load the mask.Press ”Load”. Load the wafer with the flat against yourself.Press ”Enter”

Developer, NaOH

Development of AZ-resist. Remember face shield and gloves.Immerse the wafer in NaOH for 60 seconds. During the immersion move the wafer backand forth.Immerse the wafer in water with bubbles for 120 seconds.

Oxide etch in buffered HF

Blue film on the front side of the wafer.Immerse the wafer in buffered HF for 90 seconds.Immerse the wafer in water for 300 seconds.Remove the film from the wafer using a pair of tweezers.Immerse the wafer in water again to make sure all the HF has been rinsed off.Dry the wafer in the single spin drier.

Leybold

Use the instruction manual to apply 10 nm Ti as adhesion layer and 200 nm Al.The wafers are placed with the side down onto which the metal coating is wanted.

Metal and AZ-resist liftoff

Immerse the wafers in ultra sonic acetone one by one for 10 minutes.Immerse the wafer in water for 5 minutes.Make sure the wafers don’t dry out before immersed in water.

SU-8 application using the Karl Suss spinner

Before application dry the wafers in a 120 ◦C oven over night.Begin the spinning process by testing a dummy wafer using the rinsing program.Choose the thickness of the layer by adjusting the rpm’s.To apply 10 µm:

1000 rpm for 10 seconds

3000 rpm for 30 secondsTo apply 20 µm:

1000 rpm for 10 seconds

71

1500 rpm for 30 secondsBegin loading the wafer with the flat between the pins.Press ”Load Program”Apply a circle of SU-8 with a diameter of approximately 3 cm.Press ”Enter” on the panel.After use load ”chuck-clean with wafer” to clean the machine.Use the dummy (the program cleans with acetone).Repeat the program 5 times to make sure the machine is absolutely clean.Change the chuck.Remove and clean the metal cup.Replace plastic.Test with dummy.

Prebake SU-8 using the hotplate

Bake the wafers as the recipe below indicates:

65◦C 4 min.

65◦C to 90◦C for 7-8 min.

90◦C 3 min.

Karl-Suss aligner, channels

Exposure of the SU-8 through mask.Select the program ”proximity”.Select exposure time to 5 seconds and the exposure gap to 50 µm.Select multiple exposure.Select exposure time to 5 seconds and wait time to 5 seconds.Select 12 cycles if 20 µm is wanted and 8 cycles if 10 µm is wanted.Select ”constant intensity”.Find and take a picture, ”grab image”, of the alignmentmarks.Press ”load”. Load wafer.Align the back side.Press ”Enter”.

Hardbake SU-8 using the hotplate

Bake the wafers as the recipe below indicates:65 ◦ C for 5 minutes.

65 ◦C → 90 ◦C lasting 10 minutes.90 ◦C for 10 minutes.90 ◦C → 65 ◦C lasting 10 minutes, to avoid internal material tensions.65 ◦C for 5 minutes.


SU-8 development

Immerse the wafer in used PGMEA for 2 minutes. During the immersion move the waferback and forth.Immerse the wafer in clean PGMEA for 2 minutes. Again during the immersion move thewafer back and forth.Immerse the wafer in isopropanol for 2 minutes. During the immersion move the waferback and forth.Spray the wafer with isopropanol and blow dry afterwards.

Karl-Suss aligner, throughholes

No data, process done by other group.

Mounting the carrier wafer

Load the carrier wafer in the Karl Suss spinner.Select the ”ASE-resist” program.Apply a circle of AZ-resist with a diameter of approximately 3 cm and press ”Enter” onthe panel.Select ”ASE-acetone” and press ”Enter”. Select ”ASE-resist” again.Dose AZ-resist in a ring onto the wafer approximately 1 cm from the AZ-resist circle inthe middle while the spinner rotates.Press ”Enter”.Select ”ASE-EBR”.Pour acetone on the edge while the spinner rotates to remove the edge of the outer ring.Make a gap in the outer ring using acetone.Put on the carrier wafer to the wafer. The back side of the wafer against the AZ-resistlying on the carrier wafer.Clean the back side of the carrier wafer with acetone.Bake in 5 minutes at 90 ◦C.

ASE-etch

Press ”vent”.Check if the temperature is 20 ◦.Load the wafer with the carrier wafer underneath.Close the lid.Give the process a name.Press ”Pump and map”.Select the slot on which the wafer has been placed and press ”Load”.Select the program ”DeepEtch” with 400 cycles (1h:26m:40s).Press ”Process”.Check the cooling pressure. It should be below 15 mTorr.

73

When the process has ended press ”Unload”.Press ”vent”.Take out the wafer and load a new one.When the last wafer has been etched press ”Pump only”.

Remove carrier wafer

Immerse wafer with carrier wafer in acetone in the fumehood to dissolve resist.Disassemble wafer from carrier with tweezers.Shower the wafer with acetone.Dry in spin drier.

Preparing lids

No data, process done by other group.

Bonding glass lids

Use of the Thyra bonding machine outside clean room.Make a sandwich of foil, glass with PMMA up, wafer with SU-8 down, dummy wafer withPDMS, foil.Check that pneumatic system works.Place wafers between pins.Shut of ventilation. Close gate.Set temperature to 120◦C.Establish slowly vacuum to 9·10−2mBar.Apply pressure (2kN) for 10 min. at 120◦C.Cool down to normal temperature and remove vacuum.Cool pistons with nitrogen.Release pressure at 75◦C.Open gate and remove sandwich.

Cutting out chips

No data, process done by laboratory technician.


Appendix E

Exposure masks

This appendix contains sketches of the various masks used for the photolithography pro-cesses. The figures are based on the design made in L-Edit and are not in correct size.

(a) Overview of waferdesign with all fivemasks placed on wafer

(b) Mask for SU-8 channels

75

76 APPENDIX E. EXPOSURE MASKS

(c) Mask for bottom electrodes (d) Mask for through holes

(e) Mask for top electrodes (f) Mask for bonding pads

Appendix F

Viscosity and density of the grapeseed oil

Since the grape seed oil was bought in a commercial store neither the density ρ nor theviscosity µ was known, therefore these were estimated starting with the density. Thisvalue was found experimentally using a machine capable of producing a precise flow rate,delivering a volume onto a weight, thereby allowing the density to be found as

ρ =mden

Qden tden. (F.1)

The values can be seen in Table F.4.In order to measure the viscosity a reservoir was placed at a fixed height, making it

possible to calculate the pressure. Connected to the reservoir was a tube with knowndimensions. To allow the measurements to be comparable the tube had to filled with theoil at all times, ensuring the same resistance at any time. Now the measurements werecarried out, by recording the mass of the oil which had flowed through the tube at a givenamount of time. Using the fluidic Ohm’s law, see Eq. (2.4), with Rhyd = 8µL

πa4 yields

µ =πa4P

8LQ. (F.2)

Inserting Q = ρgh, Q = mρt

and ρ given by Eq. (F.1) leads to

µ =πga4mdenth

8LQ2dent2den

. (F.3)

Numerical values can be seen in Table F.2.

Uncertainty calculations for the viscosity

In order to find the uncertainty of the experimental found viscosity of the grape seed oilthe uncertainty of some parameters were estimated. These can be seen in Table F.1, where

77

78 APPENDIX F. VISCOSITY AND DENSITY OF THE GRAPE SEED OIL

H is the height of the reservoir, t is the mesurement duration, r and l is the radius andlength of the tube respectively, m is the mass of the fluid, Qden is the flow rate of the oiladjusted by the machine used in this experiment and tden is the time the machine waspumping oil.

u(H) u(t) u(r) u(l) u(m) u(Qden) u(tden) u(mden)

1 mm 0.05 s 0.001 mm 0.25 mm 5·10−4 gm 5·10−2 mLmin 0.005 s 2·10−4 gm.

Table F.1: Estimates of the uncertainty of the parameters used to calculate viscosity of the grapeseed oil

Using Eq. (5.10) yields

u(Q) =

(

(

∂µ

∂au(a)

)2

+

(

∂µ

∂mdenu(mden)

)2

+

(

∂µ

∂tu(u(t))

)2

+

(

∂µ

∂hu(h)

)2

+

(

∂µ

∂Lu(L)

)2

+

(

∂µ

∂Qdenu(Qden)

)2

+

(

∂µ

∂tdenu(tden)

)2) 1

2

. (F.4)

Inserting the values results in the uncertainties shown in Table F.2

79

H1 [m] H2 [m] H̄ [m] t[s] m[gm] ∆V [µL] Q[

µLhr

]

∆h [m] P [Pa] µ [Pa s] u(µ) [Pa s]

0.3135 0.3118 0.3127 344.8 3.109·10−4 341.5 3566 2.126 ·10−3 2.80·103 42.9·10−3 1.5·10−4

0.3118 0.3085 0.3107 320.8 2.849·10−4 313.0 3512 1.948 ·10−3 2.77·103 43.2·10−3 1.5·10−4

0.3246 0.3228 0.3237 325.8 3.026·10−4 332.4 3672 2.070 ·10−3 2.89·103 43.1·10−3 1.5·10−4

0.3228 0.3201 0.3215 310.8 2.882·10−4 316.6 3667 1.971 ·10−3 2.87·103 42.8·10−3 1.5·10−4

0.3201 0.3185 0.3193 336.2 3.093·10−4 339.7 3638 2.115 ·10−3 2.85·103 42.9·10−3 1.5·10−4

Table F.2: Experimental data for the viscosity measurements

Constants

Ltube 0.623 m

Lneedle 0.039 m

ρ 910.4 kgm3

Asyringe 1.6·10−4 m2

rmathrmtube 4·10−4 m

Table F.3: Constants usedfor the viscosity measure-ments

Q[

mLmin

]

t [s] m [gm]

5.00 60.03 4.5414

5.00 60.04 4.5678

Table F.4: Density data

80 APPENDIX F. VISCOSITY AND DENSITY OF THE GRAPE SEED OIL

Appendix G

Water flow rates using the waterchannels

Measured data Calculated data

Hwater [m] L [m] t[s] Q[

µLhr

]

P [Pa] QOhm

[

µLhr

]

u(Q)[

µLhr

]

u(P ) [Pa] u(QOhm)[

µLhr

]

0.302 0.050 574 157.6 2963 146.5 1.6 9.82 12.2

0.290 0.050 599 151.0 2843 140.6 1.5 9.82 11.7

0.279 0.050 638 141.8 2742 135.6 1.4 9.82 11.3

0.269 0.050 615 157.6 2637 130.4 1.5 9.82 10.9

0.259 0.050 694 147.1 2539 125.6 1.3 9.82 10.5

0.248 0.050 670 130.4 2435 120.5 1.4 9.82 10.0

0.229 0.050 718 135.0 2249 111.2 1.3 9.82 9.3

0.212 0.050 760 126.0 2086 103.2 1.2 9.82 8.6

0.193 0.052 873 119.0 1893 93.6 1.0 9.82 7.8

0.171 0.050 985 107.8 1678 83.0 0.9 9.82 6.9

0.148 0.050 994 91.9 1455 72.0 0.9 9.82 6.0

0.130 0.030 637 91.0 1276 63.1 1.4 9.82 5.3

0.109 0.030 884 85.2 1073 53.1 1.0 9.82 4.4

0.090 0.020 713 50.8 880 43.5 1.3 9.82 3.7

0.069 0.021 995 38.2 679 33.6 0.9 9.82 2.8

Table G.1: Data for the flow rate measurements

81

82 APPENDIX G. WATER FLOW RATES USING THE WATER CHANNELS

Dimension of the chip [m]

H 1.00 ·10−5

Lw 1.04·10−2

Lc 5.00·10−3

Lo 3.00·10−3

Lcross 1.50·10−3

ww 1.50·10−3

wc 1.50·10−3

wo 1.00·10−3

wcross 1.50·10−3

Table G.2: Dimensions ofthe chip

Resistances in the chip[

Pa sm3

]

12Rv 3.70 ·1013

Rc 3.58 ·1013

Ro 3.23 ·1013

Rcross 1.07 ·1013

Rtot, water 3.70 ·1013

Constants

µw 3.70 ·1013 Pa s

Atube 5.2·10−7 m2

Table G.3: Resistances andconstants used

Appendix H

Water flow rates using the oilchannel

Measured data Calculated data

Hwater [m] L [m] t[s] Q[

µLhr

]

P [Pa] QOhm

[

µLhr

]

u(Q)[

µLhr

]

u(P ) [Pa] u(QOhm)[

µLhr

]

0.311 0.041 514 144.3 3056 139.7 1.8 9.82 11.3

0.295 0.039 522 135.2 2895 132.4 1.8 9.82 10.7

0.280 0.030 444 122.3 2745 125.5 2.1 9.82 10.2

0.265 0.030 476 114.0 2601 118.9 1.9 9.82 9.6

0.250 0.030 496 109.4 2455 112.2 1.8 9.82 9.1

0.234 0.032 666 86.9 2294 104.9 1.4 9.82 8.5

0.220 0.030 659 77.8 2160 98.8 1.4 9.82 8.0

0.204 0.030 698 67.4 2005 91.7 1.3 9.82 7.4

0.188 0.030 806 119.0 1847 84.4 1.1 9.82 6.9

0.173 0.030 970 56.0 1500 77.7 0.9 9.82 6.3

0.153 0.020 773 46.8 1366 68.6 1.2 9.82 5.6

0.139 0.022 1140 34.9 1276 62.5 0.8 9.82 5.1

0.125 0.018 737 44.2 1224 55.9 1.2 9.82 4.6

0.104 0.020 977 37.0 1023 46.8 0.9 9.82 3.8

0.095 0.022 1299 30.6 931 42.6 0.7 9.82 3.5

Table H.1: Data for the flow rate measurements

83

84 APPENDIX H. WATER FLOW RATES USING THE OIL CHANNEL

Dimension of the chip [m]

H 1.00 ·10−5

Lw 1.04·10−2

Lc 5.00·10−3

Lo 3.00·10−3

Lcross 1.50·10−3

ww 1.50·10−3

wc 1.50·10−3

wo 1.00·10−3

wcross 1.50·10−3

Table H.2: Dimensions ofthe chip

Resistances in the chip[

Pa sm3

]

12Rv 3.70 ·1013

Rc 3.58 ·1013

Ro 3.23 ·1013

Rcross 1.07 ·1013

Rtot, water 3.70 ·1013

Constants

µw 3.70 ·1013 Pa s

Atube 5.2·10−7 m2

Table H.3: Resistances andconstants used

Appendix I

MatLab-program:Geometriberegning

1 function [] = geometriberegning(dlimit , hlimit , Vlimit ,dstandard ,hstandard ,antal)

2 %Funktionskald:

3 %

4 %[] = geometriberegning ([ dlimit ], [ hlimit ], [ Vlimit ],dstandard ,hstandard ,oploesning

)

56 %%% Konstanter %%%

7 %Standardkonfiguration

8 Emaxstandard =0.75*1 e7;

9 Emaxolie =0.75*3.5 e7;

10 %Permitiviteter

11 e0 = 8.85*10^( -12) ;

12 ep = 2* e0;

13 evand = 80.1* e0;

14 eolie = 2.72* e0;

15 %Viskositet

16 %eta = 10^( -3);

17 %Kanalbredde

18 b=1e -3;

1920 %Loebende variable

21 Ebreak = linspace (Emaxstandard , Emaxstandard , antal );

22 Ebreakolie = linspace (Emaxolie , Emaxolie , antal);

23 d1 = linspace (dlimit (1) , dlimit (2) , antal );

24 d2 = d1;

25 h = linspace (hlimit (1) , hlimit (2) , antal);

26 V=Vlimit (1):Vlimit (2) ;

27 Vfelt=linspace (Vlimit (1) ,Vlimit (2) ,antal);

28 evaeske = linspace (2, 80, antal );

2930 %Beregning af E-felt ud fra totalt spaendingsfald

31 %for k=1: V(length (V))

32 % for m=1: antal

33 % E(k,m)=V(k)/(2* d1(m));

34 % Eolie(k,m)=V(k)/(h(m));

35 % end

36 %end

3738 %Beregning af Spaending , kraft og tryk af 2 variable , h og d

39 for i=1: antal

85

86 APPENDIX I. MATLAB-PROGRAM: GEOMETRIBEREGNING

40 for j=1: antal

41 %Spaendingsprocent over polymer som funktion af h og d

42 Vpol(i,j)=100/(1+( ep*h(j))/(2* evand*d1(i)));

43 %Tilladelig maksspaending som funktion af h og d

44 Vmax(i,j)=Emaxstandard*2* d1(i)*100/ Vpol(i,j);

45 %Kraft af h og d

46 F(i,j)=0.5* b*(( d1(i)/ep+h(j)/evand +d2(i)/ep)^(-1) -(d1(i)/ep+h(j)/eolie +d2(i)/ep

)^(-1))*Vmax(i,j)^2;

47 %Tryk af h og d

48 p(i,j)=F(i,j)/(h(j)*b);

49 end

50 %Beregning af optimal hoejde

51 %maxpkt =find(F(i,:) ==max(F(i,:) ));

52 %Fafd(i)=F(i,maxpkt );

53 %hafd(i)=h(maxpkt );

54 end

5556 %Beregning af Spaending , kraft og tryk af 1 variabel , evaeske

57 for i=1: antal

58 %Spaendingsprocent over polymer som funktion af evaeske

59 Vpol2 (i)=100/(1+( ep* hstandard )/(2* e0*evaeske (i)*dstandard ));

60 %Tilladelig maksspaending som funktion af evaeske

61 Vmax2 (i)=Emaxstandard*2* dstandard *100/ Vpol2 (i);

62 %Kraft af evaeske

63 F2(i)=0.5*b*(( dstandard /ep+hstandard /(e0*evaeske (i))+dstandard /ep)^(-1) -(

dstandard /ep+hstandard /eolie +dstandard /ep)^(-1))*Vmax2(i)^2;

64 %Tryk af evaeske

65 p2(i)=F2(i)/( hstandard *b);

66 end

6768 %Rhyd = 12.* eta .*L./((b -0.63.* h).*h.^3);

6970 %%% Plotsektion %%%

7172 %Plot af E-felt over polymer for hele V

73 %figure ;

74 %hold on

75 %for i=1: length (V)

76 %plot(d1,E(i,:) )

77 %end

78 %plot(d1,Ebreak )

79 %title (’Felt over polymer som funktion af polymer for pkt.vis V’)

80 %xlabel (’Polymertykkelse’);ylabel (’Felt’);

81 %hold off

8283 %Plot af E-felt over olie for hele V

84 %figure ;

85 %hold on

86 %for i=1: length (V)

87 %plot(h,Eolie(i,:) )

88 %end

89 %plot(h,Ebreakolie )

90 %title (’Felt over olie som funktion af hoejde for pkt .vis V’)

91 %xlabel (’Hoejde ’);ylabel (’Felt’);

92 %hold off

9394 %3D-plot af Kraft

95 %figure ;

96 %mesh(h,d1 ,F);

97 %title (’Kraft som funktion af polymerlag og kanalhoejde ’);

98 %xlabel (’Hoejde ’);ylabel (’Polymertykkelse’);zlabel (’Kraft ’);

99

87

100 %3D-plot af tryk

101 %figure ;

102 %mesh(h,d1 ,p);

103 %title (’Tryk som funktion af polymerlag og kanalhoejde ’);

104 %xlabel (’Hoejde ’);ylabel (’Polymertykkelse ’);zlabel (’Tryk ’);

105106 %Optimal kanalh ?jde

107 %figure ;

108 %plot(d1,hafd)

109 %title (’Optimal kanalhoejde som funktion af polymerlag ’);

110 %xlabel (’Polymerlag ’);ylabel (’Optimal kanalhoejde ’);

111112 %Kraft som funktion af h ved Vmax

113 %figure ;

114 %hold on

115 %for i=1:10

116 %plot(h,F(( length (d1)*0.1*i) ,:))

117 %end

118 %hold off

119 %title (’Kraft som funktion af hoejde for 10 forsk . polymertykkelse v. Vmax’)

120 %xlabel (’Hoejde ’);ylabel (’Kraft ’);

121122 %Tryk som funktion af h ved Vmax

123 figure ;

124 hold on

125 for i=1:10

126 plot(h,p(( length (d1)*0.1*i) ,:),’LineWidth ’ ,0.5* i)

127 end

128 hold off

129 %title (’Tryk som funktion af hoejde for 10 forsk . polymertykkelser v. Vmax’)

130 xlabel (’h [m]’);ylabel (’Pcap [Pa]’);

131 grid on

132133 %Tryk som funktion af evaeske ved standardkonfiguration

134 figure ;

135 plot(evaeske ,p2)

136 title(’Tryk som funktion af epsvaeske ved standardkonfiguration og Vmax’)

137 xlabel (’Relativ vaeskepermitivitet ’);ylabel (’Tryk’);

138139 %3D-plot af Vmax som funktion af h og d

140 %figure

141 %mesh(h,d1 ,Vmax)

142 %title (’Maksimal spaending som funktion af hoejde og tykkelse ’)

143 %xlabel (’Hoejde ’);ylabel (’Polymertykkelse ’);zlabel (’Vmax ’);

144145 %3D-plot af spaendingsfordeling ved vand

146 %figure ;

147 %mesh(h,d1 ,Vpol)

148 %title (’Spaendingsfordeling over polymer som funktion af hoejde og tykkelse ’)

149 %xlabel (’Hoejde ’);ylabel (’Polymertykkelse ’);zlabel (’Spaendingsprocent ’);

150151 %Plot af spaendingsfordeling som funktion af vaesketype

152 %figure ;

153 %plot(evaeske ,Vpolafvaeske)

154 %title (’Spaendingsprocent i polymer som funktion af vaesketype , h=10, d=5’)

155 %xlabel (’Relativ vaeskepermitivitet ’);ylabel (’Spaendingsprocent ’);

156157 %Plot af maksspaending som funktion af h og d

158 %figure ;

159 %mesh(h,d1 ,Vmax)

160 %title (’Maksspaending som funktion af h og d ved vand ’)

161 %xlabel (’Hoejde ’);ylabel (’Polymertykkelse ’);zlabel (’Maksspaending’);

88 APPENDIX I. MATLAB-PROGRAM: GEOMETRIBEREGNING

162163 grid on;

Appendix J

MatLab-program:Geometriberegning2

1 function [Vmax ,pmax ] = geometriberegning2(Vstart ,dstandard ,hstandard ,evand ,eolie ,ep

,antal )

2 %Funktionskald:

3 %

4 %[Vmax ,p] = geometriberegning2(Vstart ,dstandard ,hstandard ,epsvand ,epsolie ,

epspolymer ,oploesning )

56 %%% Konstanter %%%

7 %Standardkonfiguration

8 Emaxstandard =0.75*1 e7;

9 Emaxstandardolie =0.75*3.5 e7;

10 %Permitiviteter

11 e0 = 8.85*10^( -12) ;

12 evand = evand*e0;

13 eolie = eolie *e0;

14 ep = ep*e0;

15 %Viskositet

16 %eta = 10^( -3);

17 %Bredde

18 b=1e -3;

19 %Loebende variable

20 Ebreak = linspace (Emaxstandard , Emaxstandard , antal );

21 Ebreakolie =linspace (Emaxstandardolie , Emaxstandardolie , antal);

22 evaeske =linspace (eolie/e0 , 100 , antal);

2324 %Beregning af spaendingsfordeling

25 Vpol =100/(1+( ep*hstandard )/(2* evand* dstandard ));

26 Volie =100/(1+(2* dstandard *eolie)/(ep*hstandard ));

2728 %Tilladelig maksspaending

29 Vmaxpol =Emaxstandard*2* dstandard *100/ Vpol;

30 Vmaxolie = Emaxstandardolie*hstandard *100/ Volie;

31 if Vmaxpol >Vmaxolie

32 Vmax=Vmaxolie ;

33 else

34 Vmax=Vmaxpol ;

35 end

3637 %Beregning af maxspaendinger som funktion af evaeske

38 for i=1: antal

89

90 APPENDIX J. MATLAB-PROGRAM: GEOMETRIBEREGNING2

39 %Spaendingsprocent over polymer som funktion af evaeske

40 Vpol2 (i)=100/(1+( ep* hstandard )/(2* e0*evaeske (i)*dstandard ));

41 %Tilladelig maksspaending som funktion af evaeske

42 Vmaxpol2 (i)=Emaxstandard*2* dstandard *100/ Vpol2 (i);

43 %Kraft af evaeske

44 F2(i)=0.5*b*(( dstandard /ep+hstandard /(e0*evaeske (i))+dstandard /ep)^(-1) -(

dstandard /ep+hstandard /eolie +dstandard /ep)^(-1))*Vmaxpol2 (i)^2;

45 %Tryk af evaeske

46 p2(i)=F2(i)/( hstandard *b);

47 end

4849 V=linspace (Vstart ,Vmax ,antal);

50 %Beregning af E-felt ud fra totalt spaendingsfald

51 Epol=V./(1+( ep.* hstandard )./(2.* evand .* dstandard ))/(2.* dstandard );

52 Eolie =V./(1+(2.* eolie .* dstandard )./( ep.* hstandard ))./( hstandard );

5354 %Kraft af h og d

55 for i=1: antal

56 F(i)=0.5*b*(( dstandard /ep+ hstandard /evand+dstandard /ep)^(-1) -(dstandard /ep+

hstandard /eolie+dstandard /ep)^(-1) )*V(i)^2;

57 %Tryk af h og d

58 p(i)=F(i)/( hstandard *b);

59 end

60 pmax=p(antal );

616263 %%% Plotsektion %%%

64 figure ;

65 hold on

66 %Plot af E-felt over polymer for hele V

67 plot(V,Epol ,’--k’)

68 plot(V,Ebreak ,’-.k’)

69 plot(V,Eolie ,’-r’)

70 plot(V,Ebreakolie ,’-.r’)

71 title(’Felt som funktion V ved standardkonfiguration ’)

72 legend (’E-polymer ’,’E-break ,poly ’,’E-olie ’,’E-break ,olie ’)

73 xlabel (’Spaendingsfald’);ylabel (’Felt’);

74 grid on

75 hold off

767778 %Plot af Tryk som funktion af spaendingsfald

79 figure ;

80 plot(V,p(:))

81 title(’Tryk som funktion af spaendingsfald ved standardkonfiguration ’)

82 xlabel (’Spaendingsfald’);ylabel (’Tryk’);

83 grid

8485 %Plot af Vmaxpol som funktion af evaeske

86 figure ;

87 plot(evaeske ,Vmaxpol2 (:) )

88 %title (’Maksimal spaending som funktion af vaesketype ’);

89 xlabel (’Dielectric constant ’);ylabel (’Vmax [V]’);

90 grid

9192 %Plot af tryk som funktion af evaske

93 figure ;

94 plot(evaeske ,p2(:) );

95 %title (’Tryk som funktion af vaesketype ’);

96 xlabel (’Dielectric constant ’);ylabel (’Pcap [Pa]’);

97 grid on

Appendix K

Maple simulations

91

92 APPENDIX K. MAPLE SIMULATIONS

93

94 APPENDIX K. MAPLE SIMULATIONS

Appendix L

Maple simulations 2

95

96 APPENDIX L. MAPLE SIMULATIONS 2

97


99


101


103


105


107


Bibliography

[1] Introduction to Microelectronic fabrication, Second edition,Richard C. Jaeger, Gerold W. Neudeck, Robert F. PierretPrentice Hall, Upper Saddle River, New Jersey 07458.

[2] M̊aletekniske begreber og behandling af m̊aledata, 2. udg. 1999.02.23, revision

2000.11.17, 1. udg. 1999.01.05,K.A.MørchInstitut for Fysik, DTU.

[3] CRC Handbook of Chemistry and Physics. 84th Edition, 2003-2004,David R. LideCRC Press Online version

[4] GE Silicones, Dimethyl Fluids, SF96®,http://www.gesilicones.com/gesilicones/am1/en/grade/

mastergrade series non color.jsp?masterGradeId=511Web site

109

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