(16.12) Capstone Report_2003 (Edit)

7/30/2019 (16.12) Capstone Report_2003 (Edit)

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CHAPTER 1

Introduction

1.1 Background of the Research

Recently, there has been a growing interest for development of micro-scale devices that

can manipulate and transport relatively small volumes of fluids. These devices have applications

in many areas of engineering, including propulsion and power generation of micro-satellites,

micro air vehicles, inkjet printer heads, and bio-analytical instruments (Meinhart et al. 1999). As

a result, flow in small tubes or micro-channel has been studied by many researches over the

years for their novel applications (Chen et al. 2008). Rapid developments of micro-mechanic and

micro-system technology make researches in this field more important (Hetsroni et al. 2005).

The applications of fluid flow in micro-channel in micro-system technology include micro-

scaled cooling system of electronic devices, fuel cell system, advanced heat sink designs, and

other micro-devices (Kandlikar and Grande, 2003).

Furthermore, in recent years, the growing interest on biotechnology, drug discovery and

environmental monitoring is also encouraging the study on this microfluidic system for biology

and chemical analysis application. The driving factors of these devices are small size, low cost

easy to use and high through put. The concept of lab on chip (LOC) was introduced. By

shrinking a laboratorys function into a silicon chip, the miniaturized biological and chemical

analysis offers many advantages, such as small volume reagents or sample consumption,

reliability, automatic performance control and portability at the point of care (Chew et al. 2006).

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The concept of lab on chip (LOC) even increases the considerable attention received by the

technology of fluid flow in micro-channel.

In the system of fluid flow in micro-channel or also known as microfluidic system, it is

essential to precisely control the small amount of fluid flow. The large surface-to-volume ratio in

this system makes it possible to control the micro-fluid flow through the use of capillary forces

as a valve (Chen et al. 2008). In other words, these capillary forces are required to be overcome

by some pumping mechanism for the fluid to flow through the micro-channel.

One of the pumping mechanisms to trigger the flow through the micro-channel is by

applying centrifugal forces. The centrifugal forces are inertial forces produced due to angular

velocity when a body is rotating. By controlling the centrifugal forces exerted, the fluid flow

through the micro-channel can also be controlled. This is an example of passively designed

capillary micro-channel. This design can be achieved simply by making an abrupt change of

geometry in the micro-channels and the trigger of flow can be generated by a rotating system.

Besides centrifugal force, other forces such as electrics and pressure can also be used to initiate

the flow.

Passive capillary channels have been frequently used to regulate liquid flow in the

compact disk (CD) - based centrifugal microfluidics to which the ease of implementing channels

is vitally important. Centrifugal or rotational microfluidics has been demonstrated to provide

promising platforms for efficient mixing and high throughput screening, while its applications to

sensing and diagnostic tests require more severe technical challenges (Chen et al. 2008). In this

research, we present the analysis of two-dimensional (2D) model along with the numerical

simulation on the fluid flow in a micro-channel of a rotating system using Computational Fluid

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Dynamics (CFD). We choose water liquid as the fluid to be analyzed. This research can be

considered as a new research, as it involve the application of numerical flow simulation in this

rotational microfluidics field and the use of one of the most powerful engineering tools, the CFD

in solving the problems. Besides, this research also introduces the comparison of results obtained

theoretically against numerically, which is quite new in engineering research field as

traditionally, the comparison is often made between practical or experimental results with

theoretical results.

1.2 Statement of the Problems

It is important to precisely control the small amount of fluid flow in the system of fluid

flow in micro-channel. In this research, the flow is triggered by the centrifugal forces generated

due to rotation. As micro-channel exerts capillary forces on the fluid, there must be specific

magnitude of the centrifugal forces to be generated by the rotation in order to overcome the

capillary forces and allow the fluid to completely flow through the micro-channel. In other word,

the minimum rotational speed to overcome those capillary forces must be determined and it is

known as the burst frequency. This burst frequency is different for different diameter of micro-

channel and can be determined from certain equations or expressions which are yet inconclusive

as implied practically and theoretically by the existing researches. The expressions should thus,

be verified or tested by using new approaches.

In this research, the problem to be considered and solved is shown schematically in

Figure 1.1. The microfluidic system consists of two sections connected by a horizontal micro-

channel. The right hand side opened inlet section is filled with the mixture of air and water. The

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system is rotated about the y-axis to induce the centrifugal forces on the water to trigger the

water to flow through the micro-channel into the opened outlet section.

Figure 1.1: Schematic of problem specification

This research will focus on determining and analyzing the burst frequency for different

diameter of micro-channel of the system numerically, that is from simulation using the

Computational Fluid Dynamics (CFD) and comparing this numerically obtained value of the

burst frequency with the theoretical value calculated from the proposed expressions. From the

comparisons, the verification of the analytical expressions applied can be done. Besides, concern

will also be given in designing and fabricating practically this microfluidic system.

4

3.0mm

3.0mm

3.0mm

35.0mm

6.0mm

0.3mm

3.0mm

OutletInlet


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1.3 Objectives of the Research

There are four (4) objectives that need to be achieved from this research:

a) Determining and analyzing the burst frequency of the fluid flow in a micro-channel of a

rotating system using Computational Fluid Dynamics (CFD).

b) Comparing the numerical burst frequency with the theoretical value.

c) Verifying the existing analytical expressions in calculating the burst frequency

theoretically.

d) Designing and fabricating microfluidic system.

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CHAPTER 2

Literature Review

2.1 Fluid Flow

Fluid flow can be defined as the natural science of fluids in motion. Fluid flows are

encountered everyday often without being aware of it. The behavior of fluids, which refer to both

liquids and gases, can be observed in almost all areas of life ranging from simple situations of

daily life to more complex technical applications.

The simplest example of fluid flow in daily life even appear in the morning coffee cup

after adding milk and slowly stirring or the eddies and waves caused by water flowing in or

draining out of a bathtub. The smoke rising from a candle or cigarette and the bubbles ascending

in carbonated beverages are further examples. Furthermore, a flowing stream, a plummeting

waterfall and the transformation of puffy little white clouds into thunderstorm clouds are several

outdoor example of fluid flow.

The behavior of flows also plays a huge role in engineering applications. The drag

coefficient of a car, which represents the resistance the flowing air exerts on a moving vehicle, is

an important parameter. Similarly, the construction of modern aircraft would be impossible

without detail knowledge of the fluid flow around the wings.

All these phenomena are caused by various processes taking place within different fluids.

The main concerns are the interactions between the different fluid particles as well as the forces

between moving fluids and solid bodies at rest or between a moving solid body and a fluid at

rest. All experimental observations indicate that a fluid in motion comes to a complete stop at the

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surface, that is a fluid direct contact with the solid sticks to the surface. The source of this no

slip condition is a physical property of fluids known as viscosity, which generates frictional

forces acting on the fluid. For instance, the coffee in the cup does not take long time for the

rotation of the fluid to damp and dies down after stirring. The coffee has come to rest as the

result of internal friction.

For explanation of these phenomena, the fluid is imagined to be consisted by individual

layers which can slide over each other. These layers are set in uniform motion at the beginning.

If the bottom fluid layer that sticks to the surface suddenly stops, the above layers continue to

slide forward due to their inertial forces. These forces are opposed by the friction or viscous

forces between the fluid layers, which slow down the next layer and so on. In this way, the force

acting on the bottom layer is transferred to the other layers through viscous forces. This

idealization classifies the fluid flow into two different categories: laminar flow and turbulent

flow.

The flow adhering the above idealization is called laminar flow. Laminar flow can be

defined as a highly ordered fluid motion characterized by smooth layers of fluid or smooth

streamlines. The word laminarcomes from the movement of adjacent fluid particles together in

laminates. The flow of high-viscosity fluids such as oils at low velocities is typically laminar.

On the other hand, the highly disordered fluid motion with velocity fluctuations that

typically occurs at high velocities is called turbulent flow. In this flow, the particles belonging to

different sheets may become mixed. The flow of low-viscosity fluids such as the air at high

velocities is typically turbulent.

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As already mentioned, the motion of a fluid is determined by the two elementary

properties: viscosity and inertia. The relative magnitude of these two properties is measured by a

dimensionless parameter named in honor of the British physicist, Osborne Reynolds who

conducted exhaustive experiments in the 1880s. The parameter is the ratio of the inertia forces to

the viscous forces in the fluid and is called the Reynolds number. Reynolds number depends on

the velocity of the fluid, its viscosity and the size of the flow region. At large Reynolds number,

the inertia forces are large relative to the viscous forces and thus the viscous forces cannot

prevent the random and rapid fluctuations of the fluid. The flow in this case is turbulent. At small

or moderate Reynolds number, however, the viscous forces are large enough to suppress these

fluctuations and to keep the fluid in line. Thus, the flow in this case is laminar.

As explained earlier, when two fluid layers move relative to each other, a friction force

develops between them and the slower layer tries to slow down the faster layer. This internal

resistance to flow is quantified by viscosity. Viscosity is caused by cohesive forces between the

molecules in liquids and by molecular collisions in gases. There is no fluid with zero viscosity,

and thus all fluid flows involve viscous effects to some degree. Flows in which the frictional

effects are significant are called viscous flow.

However, in many flows of practical interest, there are fluids or regions where the

viscous forces are negligibly small compared to inertial or pressure force. The flow without

viscous term is called inviscid flow, which greatly simplifies the analysis but with much loss in

accuracy. For example in highly viscous fluids like honey, the frictional forces are strong, so that

the different layers come to rest earlier than for less viscous fluids such as water or air. This is

proven when more force is required to move a spoon through the honey compared to move the

spoon through the air. In gases, the internal friction is so small that it is often neglected in the

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description of their physical properties by mathematical equations. Thus, gases are regarded as

inviscid fluids.

For a long time during 18 th and 19th centuries, scientists in the field of hydrodynamics,

concerned with the mathematical description of fluid flows, believed that the internal friction in

water could be neglected. This assumption allowed the explanation of several phenomena such

as the formation of convection cells and the generation of waves. However, in the case of water

flow encountering an obstacle, the predictions of those scientists did not agree with the empirical

results of hydraulics, which dealing with the mechanical properties of the liquids. The German

physicist Ludwig Prandtl resolved this contradiction with his boundary layer theory described in

his groundbreaking paper, Fluid Flow in Very Little Friction in 1904. In his theory, friction is

only considered in a thin layer close to a wall, the so-called boundary layer. In this layer, the

viscous effects are significant and the inertial forces are smaller since the fluid is flowing

relatively more slowly than in the interior, coming to rest at the wall itself. The description of

flows given by the Navier-Stokes equations, which forms the basis of the mathematical treatment

in fluid flow, accounts for friction throughout the entire flow domain, and thus also modeling

more viscous fluids. Analytical solutions of these equations, however, can only be obtained

under strongly simplifying assumptions.

Besides the distinctions between laminar and turbulent flows, and viscous and inviscid

flows, fluid flows are also classified as being compressible or incompressible. Compressible

means that the fluid can be compressed and, thus the fluid of the same mass does not always

occupy the same volume. The occupied volume will only depend on the pressure, so the density

of the fluid varies during flow. Incompressible, on the other hand, means that the fluid cannot be

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compressed and the density remains nearly constant throughout the flow. Therefore, the volume

of every portion of incompressible fluid remains unchanged during the flow.

The densities of liquids are normally constant, thus the flow of liquids is typically

incompressible. For instance, a pressure of 210 atm causes the density of water at 1 atm to

change by just 1%. Thus, liquids such as water are usually referred to as incompressible

substances. Gases, on the other hand are highly compressible. A pressure change of just about

0.01 at, for example, causes a change of nearly 1% in the density of atmospheric air.

2.2 Navier-Stokes Equations

For simplicity, the fluid flows are normally assumed laminar, viscous and

incompressible. This type of fluid flow can be described by the Navier-Stokes equations, named

after Claude-Louis Navier from France and George Gabriel Stokes from England, who derive the

equations independently in early 1800s. The Navier-Stokes equations are a set of nonlinear

partial differential equations that describe the flow of fluid. They describe the relationship

between velocity, pressure, temperature, and density of a moving fluid. These equations arise

from applying the conservation principles and the Newtons second law of motion to the fluid

motion, together with the assumption that the fluid stress is the sum of a pressure term, with a

diffusing viscous term which is proportional to the velocity gradient. The equations are very

complex and too difficult to be solved analytically. Thus, they can only be solved using

Computational Fluid Dynamics (CFD) with the from high speed computers.

The Navier-Stokes equations consist of a time-dependent continuity equation for

conservation of mass, three time-dependent conservation of momentum equations, and a time-

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dependent conservation of energy equation. There are four independent variables: x, y and z-

coordinates, and the time t. On the other hand, there are six dependent variables: the pressure p,

density , temperature T, and three components of the velocity vector. The components of

velocity vector consist ofu component is in thex direction, the v component is in they direction,

and the w component is in the zdirection. All the dependent variables are functions of all four

independent variables. The Navier-Stokes equations are given as following,

Continuity :( ) ( ) ( )

0=

+

+

+

z

w

y

v

x

u

t

x-Momentum :

( ) ( ) ( ) ( )

+

+

+

=

+

+

+

zyxxz

uw

y

uv

x

u

t

u xzxyxx

Re

12

y-Momentum :( ) ( ) ( ) ( )

+

+

+

=

+

+

+

zyxyz

vw

y

v

x

uv

t

v yzyyxy

Re

12

z-Momentum :( ) ( ) ( ) ( )

+

+

+

=

+

+

+

zyxzz

w

y

vw

x

uw

t

w zzyzxz

Re

12

Energy :

( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

++

+++

+++

+

+

+

=

+

+

+

zzyzxzyzyyxyxzxyxx

zyx

wvuz

wvuy

wvux

z

q

y

q

x

q

z

w

y

v

x

u

z

wE

y

vE

x

uE

t

E

Re

1

PrRe

1

whereRe is the Reynolds number, Pris the Prandtl number, Eis the total energy, q is the heat

flux, and is the stress.

The Navier-Stokes equations focus not on position but rather velocity. A solution of the

Navier-Stokes equations is called a velocity field or flow field, which is a description of the

velocity of the fluid at a given point in space and time. Once the velocity field is solved, other

interested parameters such as the flow rate or drag force can be determined.

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The Navier-Stokes equations are very useful because they describe the physics of a lot of

applications. They may be used to model the ocean currents, weather, flow of water in a pipe and

air flow around an aircraft wings. The Navier-Stokes equations in their full and simplified forms

also contribute in the design of aircraft and cars, the study of blood flow, the design of power

stations, the analysis of pollution, and many more applications.

2.3 Micro-channel Fluid Flow

Micro-channel fluid flow has been studied by a many researches over the years due to its

vast applications in microfluidic devices. Research on microfluidic devices fabricated using

micro-machining technology originated about 20 years ago. A gas chromatograph was developed

at Stanford University, while ink jet printer nozzles were designed at IBM. With recent

improvement of micro-channel fabrication methods and the increasing number of fluidic devices

with complex microstructures, the knowledge in understanding the fundamentals of micro-

channel flow become more important. Nevertheless, published results have often been

inconsistent, with discrepancies between different researches.

Today, fluid flows in micro-channel are mostly analyzed using the Navier-Stokes

equations. However, one of the research paper entitled Micro-channel Fluid Behavior Using

Micro-polar Fluid Theory by I. Papautsky, J. Brazzle, T. A. Ameel, and A. B. Frazier in 1998

pointed out that a number of publications indicate that flows on the micro-scale are different

from that of the macro-scale and thus Navier-Stokes equations are incapable of explaining the

micro-channel fluid flows. In addition, it was also mentioned that experiments show that fluid

viscosity close to the channel wall is higher (50% to 80%) than the bulk viscosity of the fluid.

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Thus, the laws of hydrodynamic flow developed for a macro-scale continuum fluid which is the

Navier-Stokes Theory may no longer be applicable to micro-scale flow.

Another research paper, Fluid Flow in Micro-channels by G. Hetsroni, A. Mosyak, E.

Pogrebnyak, and L. P. Yarin in 2005, emphasized that in spite of the existence of numerous

experimental and theoretical investigations, a number of principal problems related to micro-

fluid hydrodynamics are not well studied. There are contradictory data on drag in micro-

channels, transition from laminar to turbulent flow and so on. These lead to difficulties in

understanding the essence of the phenomenon of fluid flow in micro-channel and are a basis for

questionable discoveries of special micro-effects. This paper then presented the comparison of

experimental data with predictions of conventional theory based on the Navier-Stokes equations.

The discrepancy between these data was interpreted as a display of new effects of flow in micro-

channels.

These two papers are among many other research papers which question the capability of

the Navier-Stokes equations to represent adequately the flow behavior in micro-channels (Liu &

Garimella, 2004). Thus, it is suggested that further research must be done in analyzing the fluid

flow in micro-channel using different approach other than the Navier-Stokes equations. However

in this research, the expressions used in calculating the theoretical burst frequency are still

obtained by applying the Navier-Stokes equations. The expressions are then verified from the

results of Computational Fluid Dynamics (CFD) simulations, and thus, the capability of the

Navier-Stokes equations in micro-channel fluid flows can be tested, this time with numerical

approach.

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2.4 Micro-channel Fluid Flow in a Rotating System

Centrifugal Microfluidic Flow

The flow through micro-channel can be triggered using many mechanisms, thus designed

actively or passively. Actively designed micro-channel requires an external force to function,

whereas a passively designed micro-channel works by itself (Chew et al. 2006).

Active micro-channel requires an external actuator to provide a mechanical action, to

move the fluid through the micro-channel. The actuation or activation principles used are

pneumatic, piezoelectric, electrostatic, shape memory alloy, electromagnetic. However, external

mechanical actuators usually lead to disadvantages such as high cost, difficulty in integration,

complex fabrication, complex assembly and complex circuitry.

On the other hand, passive micro-channel works by making use of the energy of the fluid

flow in the system. Passive micro-channel offer advantages such as no external power

requirement, ease of integration, low cost, and possibility of use without active control.

However, the challenges faced are that this passive microfluidic system cannot be easily

reconfigured and it is strongly dependent on variances in the fabrication process. Besides, it is

not suitable for a wide range of fluidic mediums. Despite these challenges, the advantages of the

passive control approach make it a viable approach for developing microfluidic platforms for

many applications.

One of the most promising passive control approaches is the centrifugal microfluidic

system. This system utilizes the centrifugal forces generated from rotation to initiate the fluid

flow through the micro-channel. A more advanced research was also done that is on micro-

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channel fluid flow in rotating system by Jerry M. Chen, Po-Chun Huang, and Mou-Gee Lin in

2007. This research paper, Analysis and Experiment of Capillary Valves for Microfluidics on a

Rotating Disk, presented an analytical expression of the pressure barrier in a capillary-burst valve

for flow regulation in centrifugal microfluidics. A simple expression that predicts the critical

burst pressure or rotational speed to overcome the capillary valve is derived. In this research,

practical experiments were carried out by using the image-capturing unit for capillary valves that

were integrated with micro-channels on a rotating disk having various cross-sectional

dimensions and wedge angles of sudden expansion.

From the results of this research, the measurements of burst rotational speeds for the

capillary valves are in good agreement, nearly only 10% lower with the predictions by the simple

expression. Besides, both the experiment and the theory consistently show that the burst

rotational speed is higher for the valve with a smaller channel width.

In our research, the micro-channel acts as the capillary and unlike the above research,

there is no additional capillary valve involved. Besides, our research will focus on the

comparison between theoretically calculated value of burst rotational speed or burst frequency

with the numerical burst frequency obtained from the try-an-error simulations of Computational

Fluid Dynamics (CFD). This whole new way of comparison is different from the above research

where practical experiment is conducted and the experimental values recorded are compared

with theoretical values. In addition, by applying CFD which is an example of numerical

approach methods, our research can be considered as a new research in this centrifugal driven

microfluidic field and is believed to give more accurate results. Even several researchers have

employed CFD in understanding the behavior of micro-fluidic components, both in pressure

driven flow (Olsson et al. 1999) as well as in electro-kinetics (Patankaret al. 1998, Ermakov et

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al. 1998). However, the theoretical value for our research is determined by referring to the

analytical theory or expression derived in the above research as this expression was proven to be

promisingly accurate. Another research paper published in 2000 by Jun Zeng, Ken B. Greiner,

Manish Deshpande, and John R. Gilbert entitled Fluidic Capacitance Model of Capillary-Driven

Stop Valves also apply the same expressions in analyzing the fluid flow.

Figure 2.1: Schematic configuration of microfluidic system in this research

Figure 1 show the schematic configuration of our microfluidic system where the capillary

micro-channel connects the two sections, inlet and outlet rotated about the y-axis. Theoretically,

when the microfluidic system is at rest, the liquid stored in the left hand-sided inlet section stops

at the inlet of the micro-channel. As the system is rotating, the centrifugal forces induce a

pressure at the liquid and push the liquid into the micro-channel until the fluid flows to the

suddenly expanded volume of the right hand-sided outlet section. The liquid flow is stopped by

the capillary pressure. From the one-dimensional (1D) Navier-Stokes equations with the

16

Inlet Outlet

r1

Dc

Capillary

Liquid

r2


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assumption that the liquid momentum is negligible, the centrifugally induced pressure, pc acting

on the static liquid can be derived as,

mc rrp =2

(1)

where is the liquid density, is the angular frequency, r = r1 r2is the length of the liquid

occupied with its fronts located r2 in the inlet section and r1 in the inlet of micro-channel from

the rotational center, and rm = (r1 + r2) / 2. When the rotational speed of the system exceeds a

critical value, the centrifugal force becomes larger than the capillary force causing the liquid to

burst into the expanded volume and flow into the outlet. This critical value of rotational speed is

known as the burst frequency. Thus, it is important to calculate these two forces for manipulating

the centrifugal microfluidic flow.

Despite the simple expression of the centrifugally induced pressure, the capillary pressure

on the other hand can be extremely complicated depending on the geometry and the liquid-air-

solid interfacial properties. For capillary with axisymmetric cross sections and a sudden opening

of 90, the maximum capillary pressure at the liquid front known as the burst pressure pb is

given by (Zeng et al. 2000),

c

cb

Dp

cos4 =

(2)

where is the liquid-air surface tension, c is the contact angle, andDc is the hydraulic diameter

of the capillary channel. This equation or expression of burst pressure can be derived from the

Young-Laplace equation,

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+=

21

11

RRpb

In our case, the meniscus of liquid is assumed circular, so

R =R1

=R2

Hence, the Young-Laplace Equation can be rewritten as,

=R

pb2

From the cross section and dimension of the capillary micro-channel,

R

Dc

c2cos =

c

cD

R

cos

2=

Substituting into the Young Laplace equation, the burst pressure can be expressed as,

=

c

cb

Dp

cos22

c

cbDp

cos4 =

where c

used is equal to (180c

).

18

c

Liquid Air

Dc/ 2

(180 - c)

R

Figure 2.2: Cross section of micro-channel


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To allow the fluid to completely flow through the capillary micro-channel, the centrifugally

induced pressure must be at least equal to the capillary burst pressure. Therefore, equating Eq.

(1) and Eq. (2), the theoretical burst rotational speed or burst frequency can be determined from

the expression below,

bc pp =

c

cm

Drr

cos42 =

mc

c

brrD

=

cos4

(3)

This equation or expression above in determining the burst frequency of the fluid flow in a

micro-channel of a rotating system is still inconclusive. Through our research, we will verify this

equation by comparing the theoretical value calculated from this equation with the numerical

value obtained from the simulation of Computational Fluid Dynamics (CFD).

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2.5 Numerical Flow Simulation Computational Fluid

Dynamics (CFD)

The central task in the natural science lies in describing the reality as accurately as

possible in order to understand better the natural phenomena and thus gain insight into the

behavior of objects under given conditions. In the past, there were two methodical approaches to

uncover the laws of nature: the practical approach and the theoretical approach. The practical

approach discovers the physical laws through observations aided by experiments using various

devices and measuring instruments. Galileo Galilei is regarded as the founder of experimental

physics. He conducted falling experiments from the leaning tower of Pisa and is said to have

discovered that the bodies of different weight fall to the ground with the same velocity. This

experiment became the first representative of the practical approach.

Another approach, theoretical approach converts the laws of nature to relationship

between mathematical quantities. This mathematical modeling often employs the language of

differential and integral calculus to describe how certain quantities or parameters change with

respect on others. According to the well-known anecdote, a falling apple suggested to Sir Isaac

Newton that the same force of gravity must govern the entire space. This leads to his

development of the theory of gravitation. Sir Isaac Newton also proposed that the motion of solid

bodies can be described by three laws that now bear his name: Newton Laws of Motion in his

published monograph Philosophi Naturalis Principia Mathematica, Latin for "Mathematical

Principles of Natural Philosophy" in 1687. James Clerk Maxwell on the other hand, discovered

the equations governing the electromagnetic in his published paperA Dynamical Theory of the

Electromagnetic Field in 1865. In 1916, Albert Einstein published his famous theory, General

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relativity or thegeneral theory of relativity which he developed while sitting at his desk. For the

mathematical treatment of fluid flow, the Navier-Stokes and Euler equations form the basis

which describes the dependence of velocity and pressure on space and time.

However, both practical and theoretical approaches have their shortcomings. In certain

areas, performing physical experiments to describe the law of nature are impossible for reasons

of safety. For instance, investigating the accident in a nuclear reactor or the effects of an oil spill

in the ocean. Furthermore, not all measurements can be carried out as there are sometimes the

experiments involve extremely long or short duration, or the parameters to be measured are too

small or too large.

On the other hand, mathematical equations that describe the physical nature with

reasonable accuracy are often so complex that analytical solutions are quite impossible to be

obtained by human power. Usually an exact solution can only be obtained for considerably

simplified models with a lot of assumptions.

In recent years, a third approach connecting the two traditional approaches has

established itself and is known as numerical simulation. Numerical simulation is characterized

by the following procedure. From observations of the real world, physicists derive mathematical

equations valid at infinitely many points in space and time. These equations are then discretized,

that is considered at only a finite number of selected points. At these points, the underlying

continuous equations are solved approximately. This implies that for more densely spaced

discretization points, the physical reality is simulated more accurately. Recent dramatic

improvements of computers allow more realistic simulations, so the experiments are reproduced

on a computer. Instead of costly and time consuming changes to an experimental apparatus

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previously, now modifications in these experiments can be made by just a few simple changes in

a computer program. Computed data are then followed by visualization techniques in order for

them to be interpreted and analyzed.

Numerical simulation has overcome many shortcomings of both experimental and

theoretical approach. Phenomena which previously could not be studied can be made by

numerical simulation, and costly experiments can be reduced. In addition, test series may be

optimized by quick repetitions with slightly varied parameters or geometries, and more data

become available than previous traditional experiments. Moreover, numerical simulation offers

at least approximate access to the solution of the equations governing the mathematical models.

Currently, numerical simulation is applied in many scientific and industrial areas. For

example, in mechanical engineering, the properties of elastic solids are studied by using

numerical simulation in order to design a safe vehicle with minimum amount of materials. In

civil engineering, numerical simulation is employed to analyze and improve the stability of the

structures of the buildings. In chemical applications, optimization of the reactions of different

substances occurring is done by numerical simulation, for instance in combustion process.

Further applications of numerical simulation include the crystal growth, the investigation of

melting and coating processes, the optimization of energy consumption by intelligent controlling

system, weather prediction and many more. On the other hand, in nuclear physics, the collision

of atomic nuclei and the bonding energy of electrons are computed, whereas in astrophysics,

scientists simulate the nuclear fusion processes taking place in the sun to predict the date it will

be extinguished, all by using numerical simulation.

Laws of Nature

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Figure 2.3:Approaches in uncovering and understand the laws of nature

For fluid flow numerical simulation, Computational Fluid Dynamics (CFD) appears to be

one of the most powerful engineering tools in this century. CFD is a branch of fluid mechanics

that uses numerical methods and algorithms to solve and analyze problems that involve fluid

flow. In other words, numerical methods are the heart of CFD process. It is used to generate the

simulation of fluid flow with the help of computers. CFD involves the solution of the governing

laws of fluid dynamics numerically through complex set of partial differential equations. Fluid

dynamics is a field of science which studies the physical laws describing the flow of fluids under

various conditions. Research in this field is complex yet theoretically strong as great effort is

required to understand the governing laws and the nature of fluids themselves. CFD has led

human to understand the world in new ways. Now, how blood flows through human arteries and

veins can be modeled, and even virtual worlds can be created. CFD enables simulation and

understanding on fluid flows without the help of instrument for measuring various flow variables

at desired locations. These prove how powerful and important CFD can be in engineering area.

Using the Navier-Stokes equations as the governing equations of fluid mechanics,

simulations of many fluid flow experiments in any engineering area can be carried out by CFD,

especially simulation on the flow around aircraft and other vehicles in order to investigate the

drag coefficient of different airfoil shapes of the wings or car body designs. CFD can also be

used to examine the effect a heating or air conditioning system has on the air circulation in a

room. Further applications of CFD include the simulation of flood waves from the breaking dam,

23

Practical ApproachTheoretical

Approach

Numerical

Approach


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the simulation of liquid movement in a moving container and even in more complex situation

such as the weather and climate modeling. In research field, CFD as an example of numerical

simulation provides quantitative analysis and significant insight into the physics present. The

simulation process is gaining acceptance amongst MEMS researchers and engineers and is given

regarded as means to interpret experimental data. Numerical simulation also provides a

mechanism of exploring the entire parameter space which is relatively difficult for an

experiment. Furthermore, simulation-based research is broadly recognized as a very cost-

effective approach (Zeng et al. 2000).

The vast applications of CFD are due to various reasons. Firstly, CFD allows numerical

simulation of fluid flows, results for which are available for study even after the analysis is over.

Secondly, CFD enables observation of flow properties to be made without disturbing the flow

itself, which is not always possible with conventional measuring equipment. Thirdly, CFD

allows observation of flow properties to be carried out at locations which may be harmful or may

not be accessible to measuring instruments. For instance, between the turbine blades or inside a

combustion chamber. Lastly, CFD can be used as a qualitative tool for narrowing down the

choices between various designs. In this case, designers and engineers can study prototypes

numerically, and then conduct experiment for testing only on those which appear to be

promising.

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Figure 2.4:Example of applications of CFD

Nevertheless, there are some weaknesses or shortcomings in CFD. CFD is not yet at the

level where it can be blindly used by any engineers without a working knowledge of numeric

involved. Besides, despite the increasing speed of computation available in this era, CFD has not

yet matured to a level where it can be used for real time computation. Generally, numerical

analyses like CFD require significant time to be set up and performed. For instance, in this

research, it takes about one whole day to complete a single simulation. In addition, CFD is still

an aid to other analysis and experimental tools such as wind tunnel testing, and is used in

conjunction with them.

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CHAPTER 3

Research Methodology

3.1 Procedure in Numerical Simulation

In this research, numerical flow simulation is carried out by Computational Fluid

Dynamics (CFD) in analyzing the fluid flow in a micro-channel of a rotating system. An outline

of the individual steps typically involved in numerical simulation is given in Figure 3.1.1.

26

Reality of physical process

Mathematical model

Treatment of non-linearity

Treatment of time-de endence

Discretization

Goal: Numerical experiments newinsights

Evaluation of computed solutions

with respect to continuous model and itsparameters

Fast solution of linear systems of

equations,

Iterative methodsEvaluation of discrete solution

Error estimation

Observation of experiments

Improvement

ImprovementParalleliza

tion

Time-stepping

Iteration


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3.2 Procedure in Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is one of the most powerful engineering tools used

in analyzing fluid flows. The fundamental basis of almost all CFD problems is the Navier-Stokes

equation, which defines any single-phase fluid flow. As CFD uses numerical methods and

algorithms to solve and analyze fluid flows problem, computer software are used to perform the

calculations required to simulate the interaction of liquids and gases with surfaces defined by

boundary conditions. CFD involves the solution of the governing laws of fluid dynamics

numerically through complex set of partial differential equations.

In analyzing the fluid flow in micro-channel of a rotating system, the fundamental

procedure for CFD is followed. Figure 3.2.1 below describes the procedure, which become the

basic experimental design that is used to achieve the objectives in this research.

27

Figure 3.1: Typical procedure in numerical simula

Defining the geometry (physical bounds) of the problem.


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3.2.1Meshing

The partial differential equations that govern the fluid flow involved in CFD are not

usually amenable to analytical solutions, except for some very simple cases. Therefore, in order

to analyze fluid flows, the flows domains are split into smaller subdomains in CFD, made up of

geometric primitives like hexahedra and tetrahedral in 3D and quadrilaterals and triangles in 2D.

The governing equations are then discretized and solved inside each of these subdomains.

Typically, one of three methods is used to solve the approximate version of the system of

equations: finite elements, finite volumes, or finite differences.

Proper continuity of solution must be ensured across the common interfaces between two

subdomains, so that the approximate solutions inside various portions can be put together to give

a complete picture of fluid flow in the entire domain. There are three types of mesh connectivity,

which describes how subdomains or cells are connected to one another. First is the structured

28

Preprocessing

Dividing the volume occupied by the fluid into discrete cells.

(Meshing)

Defining the physical modeling.

Defining the boundary conditions.

Simulation and equations solving

Analysis and visualization of the resulting solution

Figure 3.2:Fundamental procedure in Computational Fluid Dynamics (CFD)


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mesh. This type of mesh is characterized by regular connectivity that can be expressed as a two

or three dimensional array. Second is the unstructured mesh. This mesh on the other hand, is

characterized by irregular connectivity that is not readily expressed as two or three dimensional

array in computer memory. The third mesh is hybrid mesh. A hybrid mesh contains both

structured portions and unstructured portions. For the simulation in this research, the type of

mesh used is the unstructured mesh.

The accuracy of the simulation run to solve the problem depends highly on the mesh

generated. Theoretically, the finer the subdomains or cells, meaning the higher the number of

nodes or subdomains present, the more accurate the flow features is captured. Mesh Dependency

Test is carried out to determine the standard number of nodes where the simulations of the same

problem using different meshes result in relatively small differences. The modification of an

existing mesh to improve resolution of flow features without excessive increases in

computational effort is known as mesh adaption. Mesh adaption strategies can usually be

classified as one of three general types: r-refinement, h-refinement, or p-refinement. Refinement

is also applied in the meshing of the problem in this research in order to make sure more accurate

results can be obtained.

3.2.2Volume of Fluid (VOF) Method

In CFD, volume of fluid (VOF) method is a numerical technique for tracking and

locating the free surface or the fluid-fluid interface. As a result, the interface motion can be

simulated. In this method, an additional variable, the volume-of-fluid (F), that covers the entire

computational region of interest is introduced. For each control volume, Frepresents the fraction

of that volume that is occupied by liquid and varies with time and position to accurately trace the

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interface movement. Besides, the introduction of the volume-of-fluid function mathematically

formulates the surface tension force as a body force, and thus the interfacial boundary condition

becomes an additional forces term in the momentum equation (Zeng et al. 2000). The modified

Navier-Stokes equations, together with the volume-of-fluid function are then solved numerically

using the CFD to get the solution. The VOF method is also applied in the simulation in this

research.

3.3 Computational Fluid Dynamics (CFD) Simulation

Setup

In this research, the engineering simulation software used to perform the CFD isANSYS

12.0 Release developed by ANSYS, Inc. ANSYS Workbench is used to set up and solve a

two-dimensional fluid flow problem in micro-channel of rotating system using ANSYS

FLUENT fluid flow system. The geometry of the problem and the corresponding computational

mesh are created using the geometry and meshing tools within ANSYS Workbench. Then,

ANSYS FLUENT is used to set up and solve the CFD problem, followed by visualization of the

results.

3.3.1Step 1: Creating a Fluid Flow Analysis System in ANSYS

Workbench

1) ANSYS Workbench is started from the Start menu.

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2) A new fluid flow analysis system is created by double-clicking the Fluid Flow

(FLUENT) option underAnalysis Systems in theToolbox.

Figure 3.3:FLUENT analysis system

3) The project is saved.

3.3.2Step 2: Creating the Geometry in ANSYS DesignModeler

1) ANSYS DesignModeler is started by double-clicking the Geometry cell in

the analysis system.

2) The unit in ANSYS DesignModeler is set to millimeter (mm).

3) The two dimensional (2D) geometry of the microfluidic system consisting of two

sections connected by a horizontal micro-channel as shown in Figure 1.1is created.

4) The surface of the geometry sketched is generated.

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Figure 3.4: The geometry of microfluidic system createdinANSYS DesignModeler

5) ANSYS DesignModeler is closed.

3.3.3 Step 3: Meshing the Geometry in the ANSYS Meshing

Application

1) The ANSYS Meshing application is opened by double-clicking the Mesh cell

in the analysis system.

2) CFD is chosen for Physics Appearance.

3) The mesh is generated and the mesh statistics can be viewed by opening the

Statistics node in the Details view.

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4) The mesh statistics, especially the number of nodes can be changed by changing

the properties in Sizing. The properties in Sizing are set as shown in Figure 3.5.

Figure 3.5:Properties in Sizing settings

5) Refinement is also applied to the mesh and the settings are shown in Figure

3.6.

Figure 3.6:Refinement settings

6) The mesh is generated again.

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Figure 3.7: The computational mesh for the microfluidic system in ANSYS Mesh application

7) Named selections for the geometry boundaries are created for inlet, outlet and

capillary.

8) The ANSYS Meshing application is closed.

3.3.4Step 4: Setting Up the CFD Simulation in ANSYS FLUENT

1) ANSYS FLUENT is started by double-clicking the Setup cell.

2) 2D dimension and Double Precision option are ticked in FLUENT Launcher.

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3) Some General settings for the CFD analysis are set. The time is changed to

transient and the unit of length is changed to millimeter (mm) whereas the unit of

angular velocity is changed to rotation per minutes (rpm).

Figure 3.8: General settings

4) The Model for the CFD simulation is set to be Volume of Fluid (VOF) in

Multiphase. The Implicit Body Force is ticked.

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Figure 3.9:Models settings

5) The Materials are set up. New material which is the water-liquid is created

from Fluent Database.

Figure 3.10:Materials settings

6) The Phases are edited where air become the Primary phase and water as the

Secondary phase. For Phase Interaction, Wall Adhesion is ticked and the

Surface Tension value is inserted to be constant: 0.073

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Figure 3.11:Phases settings

7) The Cell Zone Conditions for the fluid zone are set to be in Moving

Reference Frame and the value of Rotational Velocity is inserted. For

Operating Conditions, the Operating Pressure is 101325 Pa and the value x is

35 mm.

Figure 3.12: Cell Zone Conditions settings

8) The Boundary Conditions are then set up. For capillary and wall, the

Contact Angle is set to be 115. For both inlet and outlet, the Gauge Total

Pressure is set to be 1 atm. For Operating Conditions, the Operating

Pressure is 101325 Pa and the value x is 35 mm.

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Figure 3.13:Boundary Conditions settings

9) The solution parameters for the CFD simulation are set up. For Solution

Methods, PISO is selected forScheme; Body Force Weighted is selected for

Pressure; First Order Upwind is selected for Momentum; and Geo-

Reconstruct is selected forVolume Fraction.

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Figure 3.14: Solution Methods settings

10) In Monitors, the convergence criteria for the continuity equation criteria are

changed. Plot is enabled. The value of continuity is set to be 1e-06, and 1e-05 is entered

for both x-velocity and y-velocity. New Surface Monitors are also created, one for

surface p-in and another one for surface p-out.

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Figure 3.15:Monitors settings

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11) The flow field is initialized using the boundary conditions settings at the inlet as a

starting point.

Figure 3.16: Solution Initializations settings

12) The region of fluid in the geometry is marked in Region Adaption by setting

the Input Coordinates. Then, Patch in Solution Initialization is clicked where

water is selected for the Phase. Volume Fraction is selected for Variable and

hexahedron is selected in Registers to Patch.

13) For visualization purpose, Solution Animations is created in Calculation

Activities. Filled contours of water phase are displayed on the geometry.

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Figure 3.17:Region Adaption and Patch settings

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Figure 3.18: Calculation Activities settings

14) In Run Calculation, theTime Stepping Method is set to Variable with

1e-15 Minimum Time Step Size. The calculation is then started.

Figure 3.19: Run Calculation settings

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15) The calculation is stopped once the contours of water fill the capillary and enter

the outlet section at the right hand side as shown in Figure 3.20 below, proving that the

burst frequency is achieved by the system.

Figure 3.20: Simulation stopping criteria

16) If this happen, the simulation is repeated by decreasing the rotational velocity in

the Cell Zone Conditions settings.

17) Otherwise, if the contours of water fail to enter the outlet section, the rotational

velocity is increased and the simulation is repeated.

18) This try-an-error simulation is carried on until the minimum rotational velocity

for the contours of water to completely flow through the capillary and flow into the

outlet is determined.

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19) Lastly for the results, the solution animation is saved in MPEG file for

visualization.

3.3.5Step 5: Changing the Geometry of the Capillary in ANSYS

DesignModeler

1) ANSYS DesignModeler is opened.

2) The diameter of the capillary micro-channel connecting the two sections is

changed.

3) ANSYS DesignModeler is closed.

3.3.6Step 6: Updating the Mesh in the ANSYS Meshing Application

1) The Mesh cell is right-clicked.

2) From the context menu, Update is selected. This will update the mesh for the

new geometry based on the mesh settings specified earlier without having to open the

editor to regenerate the mesh.

3.3.7Step 7: Calculating a New Solution in ANSYS FLUENT

1) ANSYS FLUENT is opened.

2) The settings specified earlier are repeated.

3) The solution is reinitialized.

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4) The solution is recalculated and the minimum rotational velocity for the water

contours to flow into the outlet (the burst frequency) is determined.

5) Lastly, the solution animation is saved in MPEG file.

3.4 Design and Fabrication of Rotating Microfluidic System

For the design element in this research, the basic fabrication of rotating microfluidic

system on a compact-disk (CD) is reviewed and performed. Most commonly, the CD consists of

multi-layer structures made of inexpensive polycarbonate plastic and pressure-sensitive

adhesives (PSA) to bind the CD layers (Siegrist et al. 2007). However, instead of the

polycarbonate plastic, Poly(methyl methacrylate) (PMMA) plastic is used for fabrication in this

research.

Using relatively simple CNC machines, venting holes and chamber holes are machined

on the PMMA CDs after the origin point is set. (ReferAppendix A) A computer controlled

cutter-plotter is used to cut the micro-channel in PSA. Once the appropriate pieces of CDs have

been designed and machined, they are aligned centrally and radially and laminated together using

the PSA layers by laminate machine to exert pressure.

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(a) (b)

Figure 3.21: (a) CNC machine. (b) Cutter-plotter

Figure 3.22:Machining chamber hole on PMMA CD by CNC machine

In our design, the most simple, standard microfluidic CD consists of five layers is

fabricated. The five layers are: 1) top PMMA CD with CNC-machined sample loading, sample

removal, and venting holes, 2) PSA layer with micro-channel features cut using a cutter-plotter,

3) middle PMMA CD with CNC chamber holes, 4) PSA layer with micro-channel features cut

using a cutter-plotter, 5) solid bottom PMMA CD to seal off the channels. (Figure 3.23)

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Figure 3.23: Schematic of 5-layer microfluidic CD

To transfer the design to the CD, the drawings of the design must be drawn on DWG file

and converted into machine language by some computer software. Thus, it is very important to

master the steps to convert the drawings into CNC language known as G-coding, and also into

cutter-plotter language before the fabrication of the CD with the desired design can be carried

out

3.4.1File Conversion Guide for CNC Machine

1) A new file is opened in CorelDRAW X3.

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Figure 3.24: CorelDRAW X3 software

2) The drawing file (.DWG file) is imported from AutoCAD.

3) The file is exported and saved asEPS Encapsulated PostScriptfile type.

4) The Simplified Chinese software is opened and CNC machine table size is set as per the

given parameters.

5) EPS file is imported from CorelDRAW X3.

6) The Conversion of Curves command is performed.

7) The drawing is selected and the Uncombine command is performed.

8) CAM Module is selected.

9) Cursor is used to select first group to be cut. In this case, all the venting holes are

selected.

10) Under Create Toolpaths > Available, 2D Cutting is selected. The file is saved if

prompted to do so. In the pop-up window, the cutting depth of the tool is ensured equal to

the thickness of the plastic to be cut, and internal cuttingis selected.

11) The second group to be cut is selected. In this case, the outer circle of the CD is selected.

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12) UnderCreate Toolpaths > Available, 2D Cuttingis selected.

13)Layer 1 is right-clicked at the Toolpath List on the right side of the display window, and

Simulation is selected.

14)Layer 1 is right-clicked at the Toolpath List again, andMachiningis selected.

15) The parameters for Machining are set up.

16)File is now saved into the thumb drive. The thumb drive is then connected to the

controller of the CNC machine. Drawing is now ready to be machined by the CNC.

3.4.1File Conversion Guide for Cutter-Plotter Machine

1) The Cutter Plotter machine is tuned ON.

2) The CorelDRAW X3 is started.

3) A new drawing sheet is opened.

4) The AutoCAD or SolidWorks file (.DWG file) is imported.

5) The drawing is right clicked and Ungroupis selected.

6) Shiftbutton is pressed and the surrounding circle of the drawing is clicked to exclude it

from the selected drawing parts.

7) The selected parts are kept. Creating new object that surrounds the selected object

button is selected.

8) The drawing is clicked and dragged from the center of the circle.

9) The perimeter only of the first drawing is selected, copied and pasted.

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10) The result drawing is selected and the Align and distribute button is clicked to make

sure that all the drawing parts are aligned.

11) The drawing is printed by choosing from the File list Print. The Cutter Plotter starts to

cut the drawing on the PSA.

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CHAPTER 4

Results and Discussion

4.1 Theoretical Results

The theoretical value of the burst frequency for different diameter of capillary micro-

channel can be calculated from the analytical expression derived earlier, Eq. (3).

4.1.1Properties

The properties of water at room temperature, 25C are,

Table 4.1:Properties of water

Density, 998.2 kg/m3

Surface tension between water and air, 0.073 N m-1

Contact angle, c 115

4.1.2Calculations

52

Referring Figure 2.1: r1 = 0.0378 m

r2 = 0.0360 m

2

0360.00378.0

2

21 +=+

=rr

rm = 0.0369 m

036.00378.021 == rrr = 0.0018 m


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The calculations to determine the theoretical value of the burst frequency of water flow in micro-

cannel of rotating system for different hydraulic diameter are performed as following.

ForDc = 0.05 mm = 0.00005 m

( )( ) ( ) ( ) ( )

sradb /9400.1920018.00369.02.99800005.0

115180cos)073.0(4=

=

rpmb 44.1842

2

609400.192 ==

ForDc = 0.10 mm = 0.00010 m

( )( ) ( ) ( ) ( )

sradb /4292.1360018.00369.02.99800010.0

115180cos)073.0(4=

=

rpmb 80.1302

2

604292.136 ==

ForDc = 0.15 mm = 0.00015 m

( )

( ) ( ) ( ) ( )sradb /3940.111

0018.00369.02.99800015.0

115180cos)073.0(4=

=

rpmb 73.1063

2

603940.111 ==

ForDc = 0.20 mm = 0.00020 m

( )( ) ( ) ( ) ( )

sradb /7400.960018.00369.02.99800020.0

115180cos)073.0(4=

=

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rpmb 22.9212

607400.96 ==

ForDc = 0.25 mm = 0.00025 m

( )

( ) ( ) ( ) ( )sradb /2854.86

0018.00369.02.99800025.0

115180cos)073.0(4=

=

rpmb 96.8232

602854.86 ==

ForDc = 0.30 mm = 0.00030 m

( )( ) ( ) ( ) ( )

sradb /7674.780018.00369.02.99800030.0

115180cos)073.0(4=

=

rpmb 17.7522

607674.78 ==

The theoretical value of burst frequency determined from calculations for each diameter of

capillary micro-channel is shown in Table4.2. These values predict at what minimum rotational

speed the microfluidic system must be rotated for the water to flow through the capillary micro-

channel into the outlet.

Table 4.2: Theoretical results table

Diameter of capillary

micro-channel,Dcmm 0.05 0.10 0.15 0.20 0.25 0.30

Theoretical

burst frequency, brpm

1842.4

4

1302.8

0

1063.7

3921.22 823.96 752.17

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4.2 Numerical Results - Computational Fluid Dynamics

(CFD) Simulation Results

The first task in the simulation setup is to create the problem geometry in ANSYS

DesignModeler. The example of outcome for this task is shown in Figure 4.1 below.

ForDc = 0.20 mm :

Figure 4.1: Geometry outcome for Dc = 0.20 mm

Meshing of the geometry is then generated. The example of meshing outcome is shown

in Figure 4.2. The mesh generated produces the grid with numbers of nodes of about ten

thousands (12,000). Besides, to resolve the flow field accurately in critical regions especially

within the micro-channel, the mesh is refined. A computational grid with eight (8) rows is

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obtained within the micro-channel. The mesh generated is believed to be able to analyze the fluid

flow and solve the problem with acceptable accuracy.

ForDc = 0.20 mm :

Figure 4.2:Meshing outcome for Dc = 0.20 mm

The numerical burst frequency, obtained from try-an-error CFD simulations for each

diameter of capillary micro-channel is shown in Table 4.3. The results from simulations are also

presented in flow visualizations which display the movement of the water in the microfluidic

system at their respective burst frequency.

Table 4.3:Numerical results table


micro-channel,Dcmm 0.05 0.10 0.15 0.20 0.25 0.30

Numerical

burst frequency, brpm 1400 930 700 650 520 470

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ForDc = 0.05 mm at 1400 rpm : For Dc = 0.10 mm at 930 rpm :

Figure 4.3:

Flow visualization for Dc = 0.05 mm at 1400 rpm

Figure 4.4:


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Figure 4.5:


Figure 4.6:



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Figure 4.7:


Figure 4.8:


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4.3 Results Comparison

A comparison of the theoretical calculated burst frequency of the water flow through the

capillary micro-channel of rotating system against the numerical burst frequency obtained from

numerical simulation of CFD is shown inTable 4.4. A graph showing both results is also plotted

as shown in Figure 4.9. For comparison of both results, the percentage difference between them

is determined from the formula given by,

Percentage difference,

%100%

= lTheoreticaNumericallTheoretica

Difference

Table 4.4:Results comparison


micro-channel,Dc

Burst frequency, b Percentage

differenceTheoretical Numerical

mm rpm rpm %

0.05 1842.44 1400 24.010.10 1302.80 930 28.62

0.15 1063.73 700 34.19

0.20 921.22 650 29.44

0.25 823.96 520 36.89

0.30 752.17 470 37.51

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Figure 4.9: Graph of comparison between theoretical results and numerical simulation results

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4.4 Design and Fabrication Outcome

After the design and fabrication process, the sample of 5-layer microfluidic CD produced

using PMMA plastic is shown in Figure 4.10.

(a)

(b)

Figure 4.10: (a) PMMA CD with chamber holes. (b) Complete model of 5-layer microfluidic CD which has been

tested ran using red liquid.

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4.5 Analysis and Discussion

In this research, analysis of the fluid flow in a micro-channel of a rotating system is

carried out by determining the burst frequency of water for different dimension of micro-

channel, applying two different approaches: theoretical and numerical. Burst frequency can be

defined as the minimum rotational speed that a microfluidic system must achieved to induce the

centrifugal pressure higher than the capillary pressure in order for the fluid to completely flow

through the capillary micro-channel.

In theoretical approach, the burst frequency is calculated from the analytical expression

derived using the modified Navier-Stokes equations and the Young-Laplace equation. It should

be noted that in derivation of the theoretical burst frequency expression, a lot of assumptions are

made for simplicity. The most important assumption that can affect greatly the theoretical results

is the liquid momentum is negligible. In reality, however, flow of liquid exerts significant kinetic

energy (Zeng et al. 2000). As a result, the viscous dissipation should also be taken into account.

Thus, the expression of capillary burst pressure,pb derived is not entirely true. Furthermore, the

existence of liquid momentum also has impact on the contact angle, c as the shape of liquid

meniscus may vary with time. The contact angle c is assumed constant throughout the flow in

deriving the burst frequency expression. Last but not least, the Navier-Stokes equations are only

proven to be obeyed on macro-scaled fluid flow (Papautsky et al. 1998). For micro-channel flow

involving different geometrical cross-section, the Navier-Stokes equations may not be entirely

correct. Due to reasons stated above, theoretical approach is believed may not be adequate in

analyzing fluid flow in micro-channel where much higher accuracy is desired. On the other hand,

numerical simulation intends to replicate the real physics and take into account most possible

factors, thus has the capability to supply quantitative analyses with much higher accuracy.

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In numerical approach, the burst frequency is determined using Computational Fluid

Dynamics (CFD), where try-an-error simulation is run repeated for each different diameter of

micro-channel in computational software, ANSYS 12.0 Release. First, the geometry of the

microfluidic system is created and meshing is generated. The mesh generated has a great

influence on the accuracy of the solutions calculated. The finer the mesh generated, the higher

the accuracy. Normally, the Mesh Independence Test is carried out to determine the standard

number of nodes required for a mesh so that the solution produced shows only slight changes

compared with another mesh. In this research, the Mesh Independence Test cannot be conducted

due to the time constraint. The solutions are then calculated and solved by the CFD software

package known as ANSYS FLUENT. The solutions are converted into flow visualization

animation, where the flow movement of water contour in the microfluidic system created at any

time can be displayed. Once the water from the flow animation passes through the micro-channel

and flows into the outlet section, the burst frequency is considered to be achieved by the system.

For all different diameter of micro-channel, it is observed from the flow animations that

the simulation at the respective burst frequency results in similar pattern of flow. From the

observation, there is a gap of air space appears that the inlet of the micro-channel when the

system is at stationary. The hypothesis or possible explanation for this is the existence of

capillary pressure acting on the water. As the system rotates, the centrifugal forces are induced,

pushing the water slowly into the micro-channel. The water flows inside the micro-channel until

it reaches the end of the micro-channel. The water then enters the sudden expanded volume of

the outlet section with much slower flow rate, opposing the increasing capillary pressure before

it floods quickly or burst into the outlet after some time. The burst of water shows that at

that moment, the centrifugally induced pressure has overcome the capillary pressure, allowing

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the water to flow quickly into the outlet without any significant resistance. Thus, only very little

centrifugal induced pressure is required by the water to maintain the flow. On the other hand, if

the flow is simulated at lower rotational speed than the burst frequency, the water flow stops at

the end of the micro-channel and unable to enter the expanded volume of the outlet section. This

is because centrifugal forces induced on the water are still not strong enough to overcome the

capillary pressure.

Both the theoretical and numerical burst frequencies for all diameter of the capillary

micro-channel are compared by plotting the graph as shown in Figure 4.9. From both the

theoretical results and numerical results, it is observed that as the diameter of the micro-channel

decreases, the burst frequency increases. The agreement on this burst frequency pattern between

the theory and numerical simulation is good. This pattern can be proven is correct because the

capillary pressure in narrower micro-channel is higher, resulting in faster rotation and higher

centrifugal pressure are required to overcome the capillary pressure. This satisfactory agreement

suggests that numerical simulation by CFD has been successfully employed in analyzing the

fluid flow behavior in the micro-channel of rotating system.

From Figure 4.9, it can also be observed that the numerical burst frequency is lower than

the theoretical burst frequency for all different diameter of micro-channel. The probable reasons

for the differences mostly come from the assumptions made in theoretical calculations such as

the neglect of liquid momentum and constant contact angle, besides other reasons including

human errors in simulation setup and limited time available for more simulations run to obtain

the exact numerical burst frequency with higher accuracy. Also, the differences between them

are all consistent, with the percentage difference range of about 20% to 40%. This consistency

indirectly implies that the analytical expressions derived from theoretical approach in this

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research fails to offer reliable and accurate predictions for the flow characteristics in micro-

channel of rotating system. In other word, the existing expression in calculating the burst

frequency theoretically cannot be verified. Therefore, further research should be conducted in

order to obtain the accurate analytical expressions in describing the fluid flow in micro-channel

of rotating system.

Through this research, the design and fabrication of microfluidic system is also

performed. A 5-layer microfluidic CD is managed to be produced. In fabrication process,

polycarbonate plastic is replaced by a more economical alternative, Poly(methyl methacrylate)

(PMMA) plastic as extreme strength is not necessary. This material selection is justified by the

absent of the potentially harmful bisphenol-A subunits which are found in polycarbonate in

PMMA, moderate properties of PMMA, easy handling and processing, and low cost. Indeed, the

microfluidic CD made up of PMMA plastic has been test ran before and no problem is faced.

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CHAPTER 5

Conclusion and Recommendations

5.1 Conclusion

In this research, the analysis of the fluid flow in a micro-channel of a rotating system has

been successfully carried out. The burst frequency of water flow in the capillary micro-channel

of the rotating system is determined and analyzed for different micro-channel diameter. Two

different approaches are applied to determine the burst frequency: theoretical and numerical

simulation. The theoretical burst frequency is determined from calculations using the analytical

expression derived from modified Navier-Stokes equations and the Young-Laplace equation. On

the other hand, the numerical burst frequency is determined from the Computational Fluid

Dynamics (CFD) simulation using ANSYS FLUENT. A comparison is made between the

theoretical burst frequency and the numerical burst frequency. Both theoretical and numerical

burst frequency shows a good agreement in the relationship of the diameter of micro-channel and

the burst frequency. It is shown that as the diameter of micro-channel decreases, the burst

frequency for respective system increases. This satisfactory agreement suggests that numerical

simulation by CFD has been successfully employed in analyzing the fluid flow in the micro-

channel of rotating system. Nevertheless, there are consistent discrepancy of 20% to 40% exist

between the theoretical and numerical simulation results. This consistency implies that the

analytical expressions of burst frequency derived from theoretical approach in this research fails

to offer reliable predictions and thus, cannot be verified. Lastly, the design and fabrication of 5-

layer microfluidic CD are performed. The CD fabricated in this research is different from

common microfluidic CD as PMMA plastic is used instead of polycarbonate plastic.

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5.2 Recommendations

This research presents only the fundamental and basic analysis in understanding the fluid

flow in micro-channel of a rotating system using Computational Fluid Dynamics (CFD). This

rotational microfluidic flow is believed to offer a promising technology to be applied in many

fields especially in biomedical engineering. Therefore, it is recommended that the research in

analyzing this rotational microfluidic flow should be conducted further with more improvements

especially in the research methodology or techniques. Before that, the knowledge of the

characteristics and behaviors of fluid flow must be studied and understand well. With enough

knowledge, the conclusive yet verified analytical expressions that able to provide reliable and

accurate predictions for the flow characteristics can be derived to be compared with the research

results. It is also suggested that the research should be carried out using numerical simulation

approach such as the Computational Fluid Dynamics (CFD) as its capability of supplying

quantitative analyses with higher accuracy is already proven.

One of the improvements that can be made in this research methodology is to run the

CFD simulation with the more accurate mesh generated on the model. To achieve this, the Mesh

Dependency Test must be carried out. The Mesh Dependency Test is used to determine the

standard settings of mesh, especially the number of nodes where the simulations of the same

problem using different meshes result in relatively small differences. In other word, a totally

good mesh is where the new mesh with finer settings produces results that only deviate slightly

than its results in the same problem. The CFD simulation should also be run on the more

advance computer with higher speed to minimize the time consumption in producing the results.

Besides, the practical experiments should also be conducted so that the experimental results can

be compared with the results from a particular simulation. This is done to verify whether the

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setup for the simulation is correct and agree with the problem conditions before further

simulation is run.

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