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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