Transcript INTRODUCTION TO NANOTECHNOLOGY
INTRODUCTION TO NANOTECHNOLOGY
An Overview of Fluid Mechanics for MEMS
-Reni Raju
MEMS (Applications)
Accelerometers for airbags Micro heat exchangers Sensors Actuators Micropumps
NEMS (Application)
Nanostructured Catalysts Drug Delivery systems Molecular Assembler/Replicators Sensors Magnetic Storage Applications Reinforced Polymers Nanofluids
Fluid Mechanics of MEMS
Devices having a characteristic length of less than 1 mm but more than 1 micron.
10 -16 10 -14 Dia. Of Proton 10 -12 10 -10 10 -8 H-Atom Diameter
NEMS
10 -6 10 -4 10 Human Hair -2 10 0 Man 10 2
MEMS
FLUID MODELLING
Conventional Navier Stokes with no-slip boundary conditions cannot be used.
Pressure Gradient is non-constant along a microduct and flowrate greater than predicted.
Surface to volume ratio is high of the order of 10 6 micron.
m -1 for a characteristic length of 1 Other factors like thermal creep, rarefaction, viscous dissipation, compressibility etc.
For Gases
Fluid Modeling Molecular Modeling Deterministic Statistical MD Liouville DSMC Boltzmann Euler Continuum Models Burnett Navier Stokes
Either as a collection of molecules or as a continuum.
Mean Free path, Characteristic Length, 1 2
n
2
L
y
Knudsen Number,
Kn
L
2
Ma
Re
Kn=0.0001
0.001
0.01
0.1
1 10 100
Continuum Flow
(Ordinary Density Levels)
Slip-Flow Regime
(Slightly Rarefied)
Transition Regime
(Moderately Rarefied)
Free-Molecule Flow
(Highly rarefied) Local value of Knudsen Number determines the degree of rarefaction and the degree of validity of the continuum model.
CONTINUUM MODEL
Local Properties such as Density and Velocity are averages over elements large compared with the microscopic structure of the fluid but small enough to permit the use of differential calculus.
Conservation of Mass:
t
x k
k
0 Conservation of Momentum:
u i
t
u k
u
x k i
x k ki
g i
Conversation of Energy:
e
t
u k
e
x k
q
x k k
ki
u i
x k
Closure:
ki
p
ki
u i
x k
u k
x i
u
x j j
ki q i
k
T
x i
Flux
(
radiation
)
de p
c v dT
RT
Euler’s Equation: Fluid is invisicid and non-conducting,
t
x k
k
0
u i
t
u k
u
x k i
p
x k
g i
c v
T
t
u k
T
x k
p
u
x k k
Compressibility
DENSITY CHANGES DUE TO TEMPERATURE Strong wall Heating or cooling may cause density change.
DENSITY CHANGES DUE TO PRESSURE Pressure changes due to viscous effects even for Ma<0.3.
Continuity Equation:
D
Dt
u
x k k
0 1
D
Dt
Dp
Dt DT Dt
(
p
,
T
) (
p
,
T
) 1 1
p T
T p
For Adiabatic Walls;
T
*
T
Pr
u c T p
0 0 0 1 *
D
* 0
Ma
2
Dt
* *
Dp
*
Dt
* Pr
B
*
A DT
*
Dt
*
A
B
0 0
c p
0
T
0 ; 0
T
0
For Isothermal Wall;
T T w
T
0
T
0 1 *
D
* 0
Ma
2
Dt
* *
Dp
*
Dt
*
B
*
T w
T
0
T
0
D T
ˆ
Dt
*
Boundary Conditions
At the Fluid- Solid Interface No-slip and no-temperature jump is based on no discontinuities of velocity/temperature.
Continuum applicable for Kn<0.001
Tangential Slip velocity at wall,
u w
u gas
u wall
u
y w
For Real gases,
u w
u gas
u wall
2
v
v
u
y w
Slip velocity & Temperature Jump,
u
*
g a s
u
*
wa ll
2
v v
u
*
y
*
w
3 4 ( 1 )
Kn
2
Ec
Re
T
*
x
*
w T
*
gas
T
*
wa ll
2
T T
2 1
Kn
Pr
T
*
y
*
w
where
v
i i
r w
,
T
dE i dE i
dE r dE w
MOLECULAR BASED MODELS
Goal is to determine the position , velocity and state of all particles at all times.
DETERMINISTIC MODEL: Particle described in the form of two body potential energy and time evolution of the molecular positions by integrating Newton’s Law of motion.
Shortcomings: Need to choose a proper and convenient potential for a fluid & solid combination.
Vast computer resources.
STATISTICAL MODEL: Based on probability of finding a molecule at a particular position and state.
Six-dimensional phase space.
Assumption, for dilute gases with binary collision with no degrees of freedom.
Liouville equation, conservation of N-particle distribution function in 6N-dimensional space,
t
k N
1
k
.
x k
k N
1
F k
.
x k
0 Boltzmann equation for monatomic gases with binary collision, (
nf
t
)
j
(
nf
x j
)
F j
(
nf
x j
)
J
(
f
,
f
*)
j
1 , 2 , 3
Non-linear collision integral, describes the net effect of populating and depopulating collisions on the distribution.
J
(
f
,
f
*) 4 0
n
2 (
f
*
f
1 *
ff
1 )
r
d
(
d
) 1
LIQUID FLOWS
The Average distance between the molecules approaches the molecular diameter.
Molecules are always in collision state.
Difficult to predict.
Non-Newtonian behaviour commences,
u
y
2 1 Contradictory results in experimental data and modelling.
MD seems to be the best option available.
Based on MD, the degree of slip increases as the relative wall density increases or the strength of the wall-fluid coupling decreases.
Slip length,
L s
L o
1
c
SURFACE PHENOMENA
Surface to Volume ratio for 1 micron is 10 6 m -1.
High Radiative and Convective Heat transfer.
Increased importance to surface forces and waning importance of body forces.
Significant cohesive intermolecular forces between surface, stiction independent of device mass.
Adsorbed layer.
Surface tension and nonlinear volumetric intermolecular forces.
Fluid Mechanics for NEMS
Nanofluids - thermal conductivity fluids.
Possibility of applying Continuum Model for low Knudsen number.(?) Model applicability to Dense and rare gas.
Possible treatment of Liquids as dense gas at Nano scale.(?) Importance of Quantum Mechanics.
Importance of Surface Phenomenon's.
TASKS AHEAD
Modeling using the Continuum model for the Slip Flow Regime Knudsen Numbers.
Understanding the mechanics of Nano-scaled Domains.
Arriving at a suitable modeling technique comparable with the experimental data (if available.)