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INTRODUCTION TO MEMS
EA C415
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SCALING
NATURE
FORCES
ELECTROSTATIC
V/S
ELECTROMAGNETIC
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Favorable
Small devices tend to be fasterConsume less power.
SCALING DOWN
ess avora eSmall actuators exerts less force;
Smaller power sources harness less power.Powering miniaturized devices is challenging
Miniaturizing powering devices is difficult
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SCALING IN NATURE
EXISTENCE: LARGE v/s SMALL
Huge animal: African Elephant 3.83m. very few
Macro animals: small variety
Small Virus : Few micro to nanometers
large variety
Uncountable number (billion-trillion)
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SCALING IN NATURE
SURFACE TO VOLUME RATIO
Heat loss (surface effect L2
)/Heat Generation(volume effect L3)
NATURES REMEDY:Small animals are
Evaporation (surface effect L2)
NATURES REMEDY: Sea based small
animals are more Skin friction (Surface Effect L2)
NATURES OBSERVATION: Large
animals swim faster
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SCALING IN NATURE
SURFACE TO VOLUME RATIO
Low Inertia (Volume Effect L3)/Large skin
friction Surface effect L2 )
NATURAL OBSERVATION: Small animals
easily float; Difficult to drag.
Surface Tension (Linear Effect L1)
NATURAL OBSERVATION : Spilling from cup
is easy in comparison to spilling from capillary
tube.
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SCALING ANALYSIS
DIMENSIONAL (MLT)/SCALING (Ln)L: Length/Size n: scaling index
n
.
ex: mass scales as 3L
PRELIMINARY INFORMATION
Without doing involved mathematics, simplistic
qualitative interpretation between physical qty. and
size is obtained.
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SCALING ANALYSIS
#ex 1 Rate of heat transfer (conduction mode)
1
1
020
LLLLL
dTA
tQ ===
#ex 2 Flow through circular conduit (Hagen-
Poiseullie) 400
044
8L
LL
LL
L
PdQ ==
=
#ex 3 Resistance
1
2
10
===LL
LL
A
l
R
#ex 4 Reynolds No. 20
110
Re LL
LLLvl===
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ELECTRICAL
MAGNETIC FLUIDIC
FORCES (Used in Micro Actuation)
CHEMICAL
ELECTROCHEMICAL
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SCALING OF FORCES
ELECTROSTATIC
Electrically charged material can exert an
attractive force on oppositely charged objects or a
.
To appreciate scaling issues in electrostatic
devices, Trimmers analysis of isometric scaling of
the maximum stored energy in a simple parallelplate capacitor is considered.
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SCALING OF FORCESELECTROSTATIC
dw
vSay w, v, d scales as L1
MAXIMUM ELECTROSTATIC POTENTIAL ENERGY STORED
d
wvvCVE br
b
22
12
02 ==
eCapacitanc
2
0==C
d
wvr
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SCALING OF FORCESELECTROSTATIC
Permitivity of vacuum and relative permitivityremains unchanged with scaling
b
effect range)( ) 31
2111
ll
lllE
2
1
32
2l
l
l
x
CV
x
EFx ==
=
=
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SCALING OF FORCESELECTROSTATIC
ELECTROSTATIC FORCES FOUND TO
SCALE AS SQUARE OF L.
FORCES SCALE AS CUBE OF L,
ELECTROSTATIC ACTUATORS ARE
ADVANTAGEOUS IN SCALED DOWN
SIZES.
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SCALING OF FORCESELECTROSTATIC
Paschen Effect: Breakdown of continuum theory
airHg
Vb
P, d
P: pressure
d: distance between plates
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SCALING OF FORCESELECTROSTATIC
Paschen Effect: Breakdown of continuum theoryVb scales non linearly in Paschen effect range
Higher Vb implies higher storage of energy and
so larger force.
Without Paschen Effect
With Paschen effect
E Vb/m
3J/m40
35 J/m104
v/m103 6
v/m103 8
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SCALING OF FORCESELECTROMAGNETIC
In the macro world, electromagnetic forcesdominate the development of actuators such
as conventional motors.
A GOOD STARTING POINT TO UNDERSTANDSCALING IN MAGNETICS IS AMPERES
CIRCUITAL LAW, USED TO CALCULATE THE
MAGNETIC INDUCTION
IdAJdLB 00 . ==
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SCALING OF FORCESELECTROMAGNETIC
1 '
JdensitycurrentconstantforBJdABidlF
==
41120asscalesF
LLLLL
Inertia scales as L3 ; Electromagnetic actuator force
scales as L4
TRY FINDING SCALING OF ELECTROMAGNETIC
FORCE USING STORED ENERGY!!!
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SCALING OF FORCESELECTROMAGNETIC v/s ELECTROSTATIC
3D 2D
Difficult to make Fabrication Compatible with planar technology
Scaling disadvantageous Scaling favorable
Less friction (Gap is large) Comparatively large friction
Large force (absolute) Comparatively Less force
35 J/m109~ E
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
Trimmer proposed a unique matrix torepresent force scaling with related
parameters of acceleration (a), time (t) and
power density that is required for scaling ofmotion of system.
This matrix has the generic name of forcescaling vector or Trimmers vertical bracket
notation
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
The scale model using the vertical bracket isgiven as:
[ ]
==
4
3
2
L
L
LL
LFF
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
The interpretation of equation is that as forces (The interpretation of equation is that as forces (FF))scales as first second, third or fourth power of scalescales as first second, third or fourth power of scale
size (size (LL). The acceleration in dimensional form is). The acceleration in dimensional form is
g ven as:g ven as:
[ ][ ]3
3
=== LLL
L
m
F
aF
F
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
The denominator term mass (m
) scales as thirdpower of size. So from previous equations, the
acceleration of micromachines in vertical bracket
=
1
0
1
2
L
L
L
L
a
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
Similarly time in dimensional form is:Similarly time in dimensional form is:
[ ][ ][ ][ ] [ ][ ] 21
22
1312
1
2 =
=
FFLLLLL
F
xmt
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
In vertical bracket notation , time is given as:
5.1
=
0
5.0
1
L
L
Lt
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
On similar lines, the vertical bracket notation forpower density can be obtained as:
=
2
5.0
1
5.2
L
L
L
L
VP o
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
So if the size of the component reduces by ten times, its
weight reduces by 1000 times.
The forces (weight), which scales as third power do not
vertical bracket .
but will reduce the time to complete the motion by
and same amount of reduction in power
the reduction in power consumption is therefore
5.010
oVP 16.3=
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TRIMMERS NOTATION
SCALING IN RIGID BODY DYNAMICS
Different forces scales differently: for example electrostatic forces scales as
power of two.
e ec romagne c orces as power o ree orfour
and surface tensile forces as power of one.
most advantageous scaling: surface tensionforces but it is a begging question to scientificcommunity to harness these forces as motiveforces.
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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
84
a
lQP =
!gchallanginisdomains-microinflowFluid
1
tubeofdiameter
overun t eroppressurerate,owvo .
4
a
P
a
=
==
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SCALING EFFECTS
# Ex 3 Surface tension-Pressure relation
( )
2
22rPr
=
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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SCALING EFFECTS
What happens to:
Friction
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