nmems-3a [compatibility mode]-scalig laws

7/29/2019 Nmems-3a [Compatibility Mode]-Scalig Laws

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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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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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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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Paschen Effect: Breakdown of continuum theory

airHg

Vb

P, d

P: pressure

d: distance between plates


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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


The scale model using the vertical bracket isgiven as:

[ ]

==

4

3

2

L

L

LL

LFF


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TRIMMERS NOTATION


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


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


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


In vertical bracket notation , time is given as:

5.1

=

0

5.0

1

L

L

Lt


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TRIMMERS NOTATION


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


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


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

nmems-3a [compatibility mode]-scalig laws

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