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INTRODUCTION TO MEMS

EA C415

Dr. N.N. SHARMA

LECTURE 32

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Dimensionless Numbers

Reynolds No. 1ReMEMSIn;Re <<→= µ 

 LU 

Mach No.

All flows are laminar !

C U C 

U  M  <<→=  MEMSIn;

flows are in sub-sonic region !

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Dimensionless Numbers

Knudsen No. Characterizes Slip/No-Slip condition in

flow

1.0m.10pathfreeairroom-typical

 m,1gap MEMSIn

flowslip 1.0~slipno 1.0

channelsflowtheof gap

moleculesof pathfreeMean

=⇒

=

≈

><<

=

kn

knkn

kn

 µ 

 µ 

In effect structure is too small to allow many collisions close

to the walls which is the requirement for no-slip condition

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Rate of change of momentum

( )

( ) ( ) ∫∫∫∫

∫∫

++•−=•+

•+=

vssv

sv

gdvdsnPdsnU U Udvdt d 

dsnU U Udvdt 

d 

dt 

dP

 ρ τ  ρ  ρ 

 ρ  ρ 

equation)(GoverningStokesNavier

Net pressure force

Net shear tangential to surface

Body forces

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Navier Stokes Equation

( )( ) ( )

4 4 4 34 4 4 21

∫

•∇∇+∇++−∇=•∇+

s

ds

U U gPU 

dt 

U d 

τ 

 µ  ρ  ρ 

3

2

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( )

n

U knU U  w y

∂

∂−=−

σ 

σ 2

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ELECTROKINETIC-DRIVEN FLOW

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Electrolytes & Electrokinetic effects:

Near the wall:

( )

 =

→

−=∝

−=∇

∑

−

i

ii

 B

e

d 

d 

 L

 x

e

C  Z T k 

q

 L

 L

e d 

0,

22

0z

2

1

LengthDebye

ˆ ;ˆ

ε 

φ φ φ φ 

ε 

 ρ φ 

00,  ispotentialthehereposition wreferenceaationconcentratis re,temperatuabsoluteisT

constantBoltzmanis field,electricis where

φ 

ε 

i

 B

C 

k 

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Ionic Double Layer:

Motion of diffusion layer drags the fluid and results in

electro-osmotic flow

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Ionic Double Layer:

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ELECTROPHORESIS

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ELECTROPHORETIC SEPARATION with

ELECTRO-OSMOTIC FLOWAssume +ve diffusion layer

Flow is in the direction of applied voltage

Electro-osmosis (sample

plug carried down the sep.

channel

Different components separated

according to ep

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DIFFUSION EFFECT:

Infinitesimal slab of sample will spread out in width due

to diffusion

 D xw

ss

S

S

 L E 

 DL

U 

 L DW 

 Dt 

U 

 Lt 

U  L

σ 

 µ ==

=

=

0

.min

0

0

 possiblebandNarrowest

sampleof Width

bygivenisesition timthen tranSpeed, channelseparationof Length

TO HAVE SHARPEST BAND

Short column

Large Electric field

Large LD (Low ionic strength)

Small sample width (possible

by MEMS technology)

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PRESSURE EFFECTS IN MICROFLUIDIC

SEPARATION CHANNELS

In microfluidic separation channels, two differentionic species travels with two different speeds

Different velocities results in pressure drop

and consequently a Poiseullie like flow and

characteristic curved profile

So in case of extreme differences (upcoming highthroughput Microfluidic devices) the pressure driven

flow must also be accommodated in analysis