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7/29/2019 Microfluidics-NEW [Compatibility Mode]

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INTRODUCTION TO MEMS

EA C415


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Dimensionless Numbers

Reynolds No. 1ReMEMSIn;Re


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Dimensionless Numbers

Knudsen No. Characterizes Slip/No-Slip condition in

flow

channelsflowtheofgap

moleculesofpathfreeMean=kn

1.0m.10pathfreeairroom-typical

m,1gapMEMSIn

flowslip1.0~slipno1.0

=

=

>


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FLUIDS (DIFFICULT)

Like solids they dont stay where they are put

Under shear forces, fluids deforms without

limits

Many regimes Many Models

Governing equations are partial and non-

linear

Fluids possess elasticity and inertia

In most MEMS application involving liquid

compressibility of liquid is neglected


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FLUIDS: CONCEPTS/MODELS1. VISCOCITY

Viscosity is the resistance encountered when a materialchange shape

Viscosity can be thought of as an internal friction

The amount of clingingness between the two moleculesgives rise to what is known as viscosity

In micro-domains more no. of available molecules per unit

area and larger clingingness increases viscous resistance

fluid)(Newtoniandy

du = u

y


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FLUIDS: CONCEPTS/MODELS2. Continuity equation (Conservation of mass)

U =

=

dsndt

dm

dvmv

( )

( ) equation)y(Continuit0U

0t

theoremdivergenceUsing

).VolControl(;0U

=+

=

+

=+

t

dvU

fixdsndvt

v

sv


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SCALING EFFECTS

# Ex 1 MICROCHANNEL

( )25050 m

!4000

10501050cm1.0

100bloodofdropOne

443

cmL

Lcmcm

LAV

l

=

=

=

=


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SCALING EFFECTS# Ex 2 Laminar Tubular Flow

84a

lQP =

!gchallanginisdomains-microinflowFluid

1

tubeofdiameteroverun t eroppressurerate,owvo .

4

a

P

a

=

==


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SCALING EFFECTS

# Ex 3 Surface tension-Pressure relation

( )

2

22

rPr

=

PDrop

( )

!eunfavorablllyenergeticaaredropsSmall

13

34

4

Volume

energySurface

surfaceunitacreatetorequiredenergyis;//

;

3

2

2

rrr

r

mJmN

r

=

=

=


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SCALING EFFECTS

# Ex 4 Surface tension-Pressure relation

BUBBLE

Attachment to surfaces

creates large localized

orces

Collapse of bubble causes cavitations and damage to

surface results

Smaller bubbles, comparatively with larger bubbles, have

higher P (P 1/r)

More damage from small bubbles due to cavitations


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SCALING EFFECTS

# Ex 5 Laminar Flow

forceViscous

forceInertiaNo.)(ReynoldRe =

In MEMS, inertia forces are negligible

But viscous forces are increased

Hence, Low Reynolds No., Very Laminar

flow


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SCALING EFFECTS

# Ex 5 Laminar Flow

Fluid mixing in micro-

domains is a problem

Passive Solution:

Bends and Turns

Active Solution: Induce

Chaos via pumping


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FLUIDS (DIFFICULT)

Like solids they dont stay where they are put

Under shear forces, fluids deforms without

limits

Many regimes Many Models

Governing equations are partial and non-

linear

Fluids possess elasticity and inertia

In most MEMS application involving liquid

compressibility of liquid is neglected


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FLUIDS: CONCEPTS/MODELS

1. VISCOCITY

Viscosity is the resistance encountered when a materialchange shape

Viscosity can be thought of as an internal friction

The amount of clingingness between the two moleculesgives rise to what is known as viscosity

In micro-domains more no. of available molecules per unit

area and larger clingingness increases viscous resistance

fluid)(Newtoniandy

du = u

y


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FLUIDS: CONCEPTS/MODELS

2. Continuity equation (Conservation of mass)

U =

=

dsndt

dm

dvm v

( )

( ) equation)y(Continuit0U

0t

theoremdivergenceUsing

).VolControl(;0U

=+

=

+

=+

t

dvU

fixdsndvt

v

sv


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Rate of change of momentum

( )

+=

sv

dsnUUUdvdt

d

dt

dP

equation)(GoverningStokesNavier

( ) ( ) ++=+ vssv gdvdsnPdsnUUUdvdt

Net pressure force

Net shear tangential to surface

Body forces


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Navier Stokes Equation

( )( ) ( )

+++=+

s

ds

UUgPUdt

Ud

3

2


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Energy Conservation

K.E from motion, P.E. from gravitation

Frictional dissipation due to shear at boundary

Internal dissipation due to viscous forces

Heat eneration heat flow

UtDt

Du

QJDt

DP

Dt

uD

ndissipatio

fluxheat

Q

+

==

+=

s;energy/masinternal

function


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( )n

UknUU wy

=

2


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Types of flows (No Slip condition)

Incompressible

=

0t

stokes)(Navier

equation)y(continuit0

2UgP

dt

dU

U

++=

=

Coutte flow (steady viscous flow between moving plates

LINEAR!stokes)(Navier0

neglecting

0

2

2

=

+

=

dy

UdgP

U


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Types of flows (No Slip condition)

Poiseulle flow (Pressure driven flow between stationary plates)

stokesNavier

(constant)let

2 kUd

kdxdP

=

=

( )[ ] !Parabolic2

1

kyhyU

dy

x =

Stokes flow

(Viscous)forcesshear

2 6

forceviscous

rUgPU

dtdu

++=


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MICROFLUIDIC PUMPING

1.Electro hydrodynamic using electrophoresisand electro-osmosis (Electrokinetically driven flow)

2.Piezoelectric pumping (uses surface forceinstead of body forces)

ELECTROKINETIC DRIVEN FLOW


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ELECTROKINETIC-DRIVEN FLOW


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Electrolytes & Electrokinetic effects:

Electrolytes are solutions of ionic species

They have special fluidic properties that arise because

of possibility of coupling electric field with flow

Consider Ci the concentration of ionic specie i, Zi the,

given by:=i

ieie CqZ

In normal electrolytes, far away from bounding

surface, the charge density is zero

Electrostatics obeys Laplace equation 02

=


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Ionic Double Layer:

Electrolyte-Solid surface interacts: Chemical-

electrostatic Interaction

Contact layers are produced due to adsorption

Layers are called Inner/outer Helmoltz

planes

Inner Layer polarity (+/-) is a function of

specific material and composition of electrolyte


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El t l t & El t ki ti ff t


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Electrolytes & Electrokinetic effects:

As the ionic strength increases Debye length

decreases

=

length = 0.3 nm 1 molar solution of monovalent

salt.

Fluid flow channels in Lab-on-chip (MEMS)

have width ~ 10 m 1 mm which is >> LD

Ionic Double Layer:


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y

Motion of diffusion layer drags the fluid and results in

electro-osmotic flow

Ionic Double Layer:


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Ionic Double Layer:


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ELECTROPHORESIS:


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ELECTROPHORESIS:

In addition to electrolyte, low concentration

ionic species (like aminoacids/proteins etc.)

does not effect basic electroosmotic flow

But drift with velocity:

mobilityreticelectrophois; epxepep EV=

Ionic Double Layer:


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Ionic Double Layer:


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ELECTROPHORESIS

ELECTROPHORETIC SEPARATION with


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ELECTRO-OSMOTIC FLOWAssume +ve diffusion layer

Flow is in the direction of applied voltage

Electro-osmosis (sample

.

channel

Different components separated

according toep

DIFFUSION EFFECT:


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Infinitesimal slab of sample will spread out in width dueto diffusion

S

S

Lt

U

L

=

0 bygivenisesition timthen tranSpeed,

channelseparationofLength

Dxw

ss

LE

DL

U

LDW

Dt

==

=

0

.min

0

possiblebandNarrowest

sampleofWidth

TO HAVE SHARPEST BAND

Short column

Large Electric field

Large LD (Low ionic strength)

Small sample width (possible

by MEMS technology)

PRESSURE EFFECTS IN MICROFLUIDIC


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PRESSURE EFFECTS IN MICROFLUIDIC

SEPARATION CHANNELS

In microfluidic separation channels, two different

ionic species travels with two different speeds

Different velocities results in pressure drop

and consequently a Poiseullie like flow andcharacteristic curved profile

So in case of extreme differences (upcoming high

throughput Microfluidic devices) the pressure driven

flow must also be accommodated in analysis

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