nmems-16a
TRANSCRIPT
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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