can u mail me some of the models?i want to model a micropump and i want study the moving mesh example.thank u so much.my email is:mo.hg.eng20@yahoo.com
4.
MEMS – Micro Electro Mechanical System
• Micro – the devices are extremely tiny, in the order of micrometers
or smaller
• Electro – some electrical component is involved
• Mechanical – the system performs some mechanical motion
• Systems – all these and parts are combined in one package
6.
Individual physics interfaces (which include equations and boundary conditions for
modeling particular physical phenomena) are accessed from the model wizard
(shown below). The MEMS module adds new interfaces and extends those in the
base package, as shown below.
Electric Circuits interface
with SPICE import
Enhanced interfaces for
Electric Currents and
Electrostatics
Piezoelectric Devices
interface for modeling the
direct and inverse
Piezoelectric effects
Extended structural
mechanics capabilities
including geometric nonlinearity and viscoelasticity
Electromechanics interface
for modeling electrostatic
actuators
Individual physics interfaces (which include equations and boundary conditions for
modeling particular physical phenomena) are accessed from the model wizard
(shown below). The MEMS module adds new interfaces and extends those in the
base package, as shown below.
Interfaces for physical
models of damping and Fluid
Structure interactions. These
include: Fluid Structure
Interactions, Thin Film Flow
(for modeling gas and liquid
flow in thin layers via the
Reynolds Equations) and
Thermoelasticity
Interfaces for modeling
thermal structure interactions,
film stress and Joule heating
Piezoresistance interface
models fully anisotropic
piezoresistivity
7.
Electromechanics
Electrostatics coupled
together with moving mesh
and structural mechanics
for modeling electrostatic
actuators and sensors
Electrostatic attraction
between objects at
different potentials
causes structural
deformations
V=0
Cantilever beam fabricated
on silicon wafer
V+
Surrounding Air
Cantilever with
applied bias
Ground plane
Initial Mesh
COMSOL computes
electrical forces on
structure, both structure
and mesh deform
accordingly
Final result showing
deformed structure, axial
strain (color in beam) and
electric potential (contours)
Space dimensions supported: 3D, 2D Plane Strain, 2D Axisymmetric
Electromechanics: Structural Features
Full range of structural
boundary conditions available
including: Free, Fixed,
Boundary Loads, Follower
Loads, Advanced Perioidc
Conditions, Thin Elastic
Layers, Rollers, Spring
foundations, etc. Thin Film
Damping feature allows
complex damping models to
be easily added to the model.
y
Electrostatic forces and
mesh constraints are
automatically applied on the
surfaces of the structure.
Model electrics fields in
dielectric layers including
isotropic electrostriction.
Other material properties
(permittivity, elasticity) can
be fully anisotropic
If the field inside the material
is not important, solve only
the structural problem (the
material is assumed to be
conducting). Isotropic,
orthotropic, anisotropic and
viscoelastic materials can be
modelled
8.
Electromechanics: Structural Features
Arbitrary fictitious forces due
to a rotating or accelerating
reference frame, or any
combination of these can be
added using easy to enter
expressions for the body
force.
Add phenomenological
damping, thermal stresses
and a range of other options
to the model.
Model anchor losses using
perfectly matched layers or
low reflecting boundaries
Figure from: P.G. Steeneken,1, J.J.M. Ruigrok, S.
Kang, J.T.M. van Beek, J. Bontemps and J.J.
Koning,, “Parameter Extraction and Support-Loss in
MEMS Resonators”, COMSOL Users Conference,
Grenoble, 2007
Electromechanics: Electrical Features
Moving mesh automatically
accounts for contraction of
gaps due to structural
displacement
Full range of electrical
boundary conditions
available including Floating
Potentials, Ground, Thin
Capacitors, Thin Low
Permittivity Gaps, Dielectric
shielding, Zero Charge
(symmetry) etc.
Infinite Elements can be used
to account for electric fields far
away from the device, enabling
highly accurate capacitance
calculations
9.
Electromechanics: Electrical Features
Advanced perturbation
machinery: at different DC bias
points, the solution for the AC
voltage signal is computed at
the correct linearization point.
This unique functionality
enables straightforward and
accurate modeling of effects
such as spring-softening and
stress stiffening in the frequency
domain.
Terminal boundary
conditions make it
straightforward to couple
devices to a circuit and
automatically define lumped
parameters such as
capacitance to ground. For
high frequency applications
terminals can be used to
compute the S, Y or Z
parameters.
p
Displacement
VAC
VDC
Voltage
Electromechanics: Study Types
Prestressed Analysis,
Eigenfrequency:
First solve a stationary problem
with the applied DC bias. Then
compute the resonant modes of
the structure, accounting for all
the stresses induced by the DC
bias. Advanced solver
automatically includes coupling
between modes (as in
gyroscopes) and incorporates
spring softening etc.
Time dependent study
type for computing the
transient response to
arbitrary excitations.
Prestressed Analysis,
Frequency Domain:
First solve a stationary
problem with the applied DC
bias. Then account for the
effect of a (smaller) AC bias
(or perturbation) taking
account of the changes in
the system stiffness as a
result of the DC bias (spring
softening /stiffening).
Resonant
Frequency (Hz)
Stationary study type for
computing static
displacements and pullin voltages
Spring softening
DC Bias
(V)
10.
Electromechanics: Applications
Applications include:
•
•
•
•
•
•
•
•
•
Capacitive pressure sensors
Accelerometers
Gyroscopes
Combo sensors
Resonant sensors
MEMS oscillators / timing
Comb Drives
Parallel Plate Actuators
General capacitive sensors
Structural Mechanics
All the advanced features discussed in the slides entitled ‘Electromechanics:
Structural Features’ can be used in structural analysis. Additionally the following
extra features are available (which are not currently integrated into
Electromechanics).
Space Dimensions Supported:3D, 2D plane stress, 2D plane strain, 2D axisymmetric.
Compute effective
mass and spring
constants for the
structure using a
‘Modal Reduced
Order Model’ study
Support for frequency domain
analysis without prestresses.
Modal study types allow a
reduced set of vibrational
modes to be used in a
Frequency Domain or
Transient study,
dramatically increasing the
efficiency of the problem
Structural contact
Structural contact and friction problems (without electrostatic fields operating in the
t t l
t t
f
gap) can also be solved, as can linear buckling problems.
11.
Electrostatics and Electric Currents
All the advanced features discussed in the slides entitled ‘Electromechanics:
Electrical Features’ can be used in standalone electrical analyses. Additionally the
following extra features are available (which are not currently integrated into
Electromechanics).
•
Electric Currents
–
–
–
–
•
3D, in plane and axisymmetric
Metals and other conductive solids
Conductive Fluids
Enhanced boundary conditions such as: distributed impedance, floating potentials, contact im
pedance, terminals etc.
Lumped Parameters
–
–
–
Terminal features provide lumped parameters (e.g. capacitance) automatically
S, Y and Z parameter computation
p parameters in p
p
g
Conversion between lumped p
post-processing
Electric Circuits
Specify circuit using built
in components
Easily couple circuits to domain
models with the terminal
boundary condition
Import SPICE netlists
12.
Piezoelectric Devices
•
•
•
•
•
•
•
•
•
Similar range of boundary conditions and advanced structu
ral/electrical features to electromechanics
Fully coupled piezoelectric equations for linear piezoelectri
city
Direct and inverse effects
Stress-charge and strain-charge formulations
Material properties and orientation specified in a convenien
t manner – support for both stress and strain charge materi
al properties
Mixed material modeling: combine piezoelectric materials
with decoupled isotropic and anisotropic structural and elec
trical materials
Pre-defined coupling with acoustics
Static, modal, frequency-response and time-dependent an
alysis
Perturbations: ability to model in the frequency domain with
a DC signal bias.
Setting up Piezoelectric Materials
Easily specify material
orientation using Euler
angles
Strain charge and stress
charge forms of material
data included
Select co-ordinate system / material
properties in physics settings
13.
Piezoresistance
•
•
•
•
Similar range of boundary conditions and advanc
ed structural/electrical features to electromechani
cs
Piezoresistance(stress) or Elastoresistance(strain
) equation forms
Fully anisotropic equation formulation
3 interfaces allow flexibility in modeling conductin
g and structural layers
– Treat piezoresistors and conductors as thin layers (
surface features) and model structure in 3D
– Model both structure and piezoresistors in 3D, to c
apture effects such as non-uniform doping profiles
– Use the shell interface for the structure and treat th
e piezoresistors and conductors as thin layers withi
n the shell (requires the Structural Mechanics Mod
ule)
•
Static, modal, frequency-response and time-depe
ndent analysis
Setting up Piezoresisitive Materials
Select
Material from
Library
Simple definition of material co-ordinate axes using Euler
angles (similar to Piezoelectric Materials)
Specify a constant,
or even a spatially
varying dopant
density
14.
Thermal MEMS
•
Thermal stresses in structures can be comput
ed at a fixed temperature using the thermal e
xpansion feature
–
–
•
Thermal stress interface to compute the stres
ses in structures at non-uniform temperatures
–
•
Available in other interfaces such as Electromechanic
s and Piezoresistive Devices
Can be used to compute packaging/fabrication stress
es in devices held at a fixed temperature
Can be used to compute packaging/fabrication stress
es in devices with temperature gradients.
Joule heating and thermal expansion interfac
e to compute thermal stresses, generated by
electrical heating
–
Typical applications include thermal actuators
Thermoelasticity
• Dedicated interface to compute the damping
induced by thermoelastic effects in flexural re
sonators.
• Includes the entropy driven coupling between
structural mechanics and heat transfer autom
atically along with the structural and thermal
equations.
• Compute thermal and structural eigenvalues
together with quality factors. Can also be use
d for frequency domain, transient and freque
ncy-transient studies.
Temperature variation in a bending micro-beam
15.
Thin Film Flow
•
•
•
•
•
Interfaces solve for fluid flow in thin layers.
Two formulations of the Reynolds equation
available to model flow in thin-films of gases
or liquids.
2D planar, axisymmetric and 3D shell formul
ations available.
Features to model low pressure (rarefied) g
as in the gap, including accurate force comp
utation.
Film damping available as a feature in the st
ructural interfaces with automatically implem
ented two way coupling. Includes all the fun
ctionality of the stand alone Thin-film flow int
erfaces.
Fluid Structure Interactions
•
•
Based on the ALE moving mesh technolo
gy in COMSOL
Fully bidirectional coupling between fluid a
nd structure
–
–
•
•
•
•
Viscous, pressure and inertial fluid forces o
n the structure
Momentum transfer back to fluid
Small and large deformations
Highly accurate fluid load computation (we
ak constraints).
Predefined physics interface makes it eas
y to build models rapidly – no manual inter
facing between different solvers
Automatic segregated solver settings for t
he stationary and parametric analysis of la
rge 3D models
16.
MEMS Acoustic Devices / Microphones
u
T
Damped vibrations of a shell
above a thin air gap.
Deformation plot and two cross
sections depicting the acoustic
particle velocity and the
acoustic temperature field.
The Acoustics Module includes the thermoacou
stic interface for MEMS acoustics applications:
• Acoustics in small devices: mobile devices, t
ransducers, microphones, hearing aids, perf
orates, headsets, couplers etc.
• Includes thermal conduction and viscous los
ses explicitly
• Linearization of Navier-Stokes and energy e
quations
• Solves for acoustic variations in (p,u,T).
• Predefined interfaces to couple acoustics wi
th solid mechanics / shell interfaces (shell in
terfaces require the Structural Mechanics M
odule)
RF MEMS
T following application areas can be simulated with th
The
e MEMS Module:
• Silicon oscillators
• Variable capacitors
• Tunable filters
W
With the RF Module more advanced RF MEMS problems
c
can be solved:
• Cavity resonators / tunable cavity resonators
• Antennas / reconfigurable antennas
17.
Microfluidics
COMSOL offers a dedicated Microfluidics Module which in
cludes:
• Two Phase Flow
• Electrokinetic Effects
• Mixing and Diffusion
• Porous Media flow
eCAD import
(requires eCAD import module)
Import eCAD data in
GDS/NETEX-G or ODB++ format
Layers can be imported in 2D or
automatically extruded for a full 3D
import
18.
• MEMS
• MEMS
• MEMS
• MEMS
Capacitive Pressure Sensor
•
•
Pressure sensor example designed
to provide an introduction to
modeling techniques used in MEMS.
Shows how to set up a coupled
structural/electrical model using
important features of the MEMS
Module:
–
–
–
•
Electromechanics
Thermal Stress
Terminal Boundary Conditions
Shows how to compute the sensor
performance and the effects of
thermally induced packaging
stresses on the sensor response
19.
Biased Resonator
In this sequence of models, an electrostatically actuated
MEMS resonator is simulated. The device is biased with a
DC voltage. And then driven by a smaller AC voltage. A
series of models shows how to compute:
1. The biased displacement
2. The pull-in voltage
3. The biased resonant frequencies (shown below)
4. The frequency domain response
5. Transient response to an applied step function
Resonant mode shape
Resonant frequency vs
applied bias (showing
spring softening)
DC displacement of biased structure
showing electric potential contours
Electrostatically Actuated Cantilever
Mesh and structural
displacement
The elastic cantilever beam is
one of the elementary structures
used in MEMS designs. This
model shows the bending of a
cantilever beam under an applied
electrostatic load. The model
solves the deformation of the
beam under an applied voltage.
C-V curve
Electric field and
electric potential
20.
Electrostrictive Disc
Settings for linear elastic
dielectric
Electric potential and
structural displacement
Axial strain vs
electric field
Microresistor Beam
This model treats the movement of a beam
by conducting a current through it to
generate a temperature increase. This leads
to a displacement through thermal
expansion. The coupled thermal, electrical,
and structural analysis makes it possible to
estimate the current and temperature
increase needed to displace the beam.
This model shows how to compute the
electrostrictive strains and stresses in an
isotropic disc , using the electromechanics
interface.
21.
Thermal Stresses in a Layered Plate
A plate consisting of two layers (a coating and a substrate layer)
is stress and strain free at 800 C. The temperature of the plate is
reduced to 150 C, which induces thermal stresses. A third layer,
the carrier layer, is then added. The thermal stresses in the two
plates are included as an initial stress, and the temperature is
finally reduced to 20 C.
Prestressed Micromirror
This model shows the fundamentals of
how to set up and solve lift-off of a
prestressed plated micromirror. A
parametric study reveals how much
variations in the prestress affect the
displacements.
22.
Fluid-Structure Interaction
This model exemplifies how to model fluidstructure interactions (FSI) using the MEMS
Module. Viscous forces and the system's
pressure impose forces to the surface of a
structure. The deformation in the soft structure
is not small and the fluid regime will therefore
change. This means that changes in the
structure and the fluid dynamics are coupled.
Composite Piezoelectric Transducer
A quartz oscillator, operated
in the thickness shear
mode, is simulated. The
model shows how to set up
the co-ordinate system
correctly for AT cut quartz
and to model the response
of a device driven at
resonance. The resonant
frequency of the oscillator is
altered by the changing the
capacitance of a shunt
capacitor.
Displacement
Electric Potential
Mechanical response with
different shunt capacitors
23.
Composite Piezoelectric Transducer
A composite piezoelectric ultrasonic
transducer is analyzed. An
eigenfrequency analysis is followed by a
frequency response analysis to calculate
the input admittance as a function of the
excitation frequency.
Piezoceramic Tube
Displacement along
radial direction
This model performs a
static 2D axisymmetric
analysis of a piezoelectric
actuator. A radially
polarized piezoelectric
tube is simulated, with
two sets of boundary
conditions. The first case
illustrates the direct
piezoelectric effect (see
image), and the second
case shows the inverse
piezoelectric effect.
Induced voltage along
radial direction
Induced voltage
Displacement
24.
Surface Acoustic Wave Gas Sensor
This model analyzes the
eigenfrequencies of a surface acoustic
wave (SAW) gas sensor. In particular, the
model studies how the additional mass
load from an adsorbed gas lowers the
resonance frequency.
Piezoresistive Pressure Sensor
Electric current (arrows)
and electric potenial
(contours)
A piezoresistive pressure
sensor is simulated. This
model shows how to set
compute the stress induced
potential difference
produced by a four terminal
piezoresistor when the
membrane in which it is
embedded is deformed by
an applied pressure. Two
versions of the model are
available - the surface
currents model shown here,
and a model that uses the
shell interface which
requires the Structural
Mechanics Module.
Shear stress along
diaphragm edge in
local co-ordinates
Diaphragm displacement
25.
Gecko Foot
This model contains the
nano/micro hierarchy of synthetic
gecko foot hair, where cantilever
beams on different scales describe
the hairs. The analysis shows the
stresses and deflection of the
gecko foot caused by contact and
friction forces.
A Tunable MEMS Capacitor*
This is a model of an electrostatically tunable
parallel plate capacitor. The distance between
the plates is tuned via a spring, to which one of
the plates is attached. For a given voltage
difference between the plates, the distance of
the two plates can be computed, if the
characteristics of the spring are known.
* This Model is Part of the AC/DC Module Model Library, but the model can also be
set up and solved with the MEMS Module.
26.
Uniform Layer Waveguide*
In this model the thermoacoustic wave field in a
shallow uniform waveguide is modeled and
compared to an analytical solution. Because of
the small waveguide height (1 mm) the thermal
and viscous boundary layers are significant.
Detailed air or fluid damping for vibrating MEMS
devices may require accounting for
thermoacoustic damping effects. This can be
seen as a generalization of more conventional
gas-film damping.
* This model and analysis requires the Acoustics Module.
Nonlinear Magnetostrictive Transducer*
The magnetic field and displacement as
functions of the applied current are computed
for a magnetostrictive transducer where the BH
curve is nonlinear. This model considers the
case when the material is sufficiently prestressed so as to obtain the maximum
magnetostriction.
* This model is made with 2D axisymmetric magnetics available in the
COMSOL Multiphysics base package. For 3D magnetics modeling, the
AC/DC Module is required. This model is available in the Structural
Mechanics Module Model Library but also runs with the MEMS Module.
27.
Thermal Expansion in a MEMS Device*
This model analyzes the thermal expansion
in a MEMS device, such as a
microgyroscope, where the thermal
expansion should be as small as possible.
The model uses temperature-dependent
material properties from the Material Library.
* The Material Library is required to build the model.
Thermoelastic Damping
Settings for Linear
Thermoelastic
Material
Temperature
Axial stress
This model shows how to compute the
thermoelastic damping in a vibrating beam.
28.
Squeeze Film Disc
Pressure on the disc
Non-linear response
This benchmark model computes the forces on a vibrating
disc in for small (using the frequency domain) and large
(using a transient study) amplitudes.
Piezoelectric Shear-Actuated Beam
This model performs a static analysis of a
composite cantilever beam equipped with
a piezoceramic actuator. An electric field
is applied perpendicular to the poling
direction, thereby introducing a
transverse deflection of the beam.
29.
Piezoelectric Microgripper
This model shows the fundamentals of
how to set up a piezoelectric model with
mechanical contact. The microgripper
contains a stacked piezoactuator, which
operates in the longitudinal mode.
Simultaneous contraction in the
transversal direction and elongation in the
longitudinal direction closes the gripper
and moves objects.
• MEMS
• MEMS
• MEMS
• MEMS
30.
COMSOL is a Fully Integrated Software Suite
All modeling steps are available from a single unified
environment. The model tree (shown on the left)
provides quick and easy access to all the settings:
Geometry setup / CAD Import
User defined and built in material libraries
Simple and intuitive Mulitphysics Problem setup
Meshing
Solving
Visualization + Postprocessing
Data Import/Export
COMSOL is designed from the bottom up for arbitrary
combinations of physical equations and easy user
customization
Problem Definition
• Electrostatically biased cantilevered beam above ground
Infinite Free Space
300 um
V+
5 um gap
not to scale
2 um thick
31.
Electrostatics
• The electrostatic equation must be solved in and around the beam
0 r
V
0
V+
Forces on Beam
• Once the voltage field is computed, the Maxwell Stress Tensor is c
omputed
• These forces deflect the cantilever
32.
How do we couple electrostatics and solid m
echanics?
1. Solve for electrostatics
2. Calculate Maxwell stresses and add t
hem on the solid boundaries
3. Solve for the displacements in solids
4. Repeat the steps until solution conver
ges
All these steps are automated in COMSOL
What if solids undergo large deformation?
Linear strain (Cauchy strain)
Green-Lagrange strain
• COMSOL can account for large deformation in solids
• We cannot use the same computational mesh to solve for
the electrostatics problem anymore
33.
Reference mesh
• Mesh is “rigid” in the structural domain
• You solve the structural equation here
• We are using the Lagrangian (material) coordinate system
Moving Mesh
• Mesh is allowed to move in the air domain based on the structural
displacement
• You solve the electrostatics equation here
• We are using the Eulerian (spatial) coordinate system
34.
Lagrangian vs. Eulerian
• Lagrangian
– Mesh follows the material deformation
– Easier for representing structural mechanics
• Eulerian
– Mesh is fixed
– Continuum moves with respect to this grid
– Easier for most physics (fluids, EM, etc.) oth
er than structures
• Arbitrary Lagrangian Eulerian (ALE)
– Best of both worlds
– Moving mesh
What this means
• Solid mechanics
– I am sitting on the mesh that represents t
he beam and moving along with it
• Electrostatics
– I am sitting outside and seeing the mesh
that represents air get deformed as the b
eam moves
All this is automatically
taken care of in COMSOL
35.
Electric Potential
Displacement
You can also solve this in 3D
But…2D is faster, so
we will do that first
36.
Objectives
• Set up an electromechanical interaction problem
• How to mesh high aspect ratio 2D structures
• Vary the voltage on the beam and compute the capacitance
– Tunable capacitor!
Cantilever Beam 1
37.
Modeling steps
•
New > 2D
•
Structural Mechanics > Solid Mechanics ( Add Selected )
•
AC/DC > Electrostatics (Add Selected)
•
Mathematics > Deformed Mesh > Moving Mesh (Add
Selected)
•
Next
•
Stationary
•
Finish
Geometry – Change Units to Microns
• Highlight “Geometry 1”
• Change Length unit to “ m”
38.
Geometry - Beam
• Rt click on “Geom 1”
• Choose “Rectangle”
Size and Shape
• Width: 320
• Height: 2
Position: Corner
• x: 0
• y: 5
Geometry - Air
• Rt click on “Geom 1”
• Choose “Rectangle”
Size and Shape
• Width: 320
• Height: 25
Layers to the right
• Thickness: 20
39.
Materials – Set up Air and Polysilicon
•
•
•
•
Rt Click on “Materials”
Open Material Browser
Built-in > Rt Click on “Air”
Add to Model
•
•
•
•
•
Rt Click on “Materials”
Open Material Browser
Built-in > Rt Click on “Polysilicon”
Add to Model
Assign the beam (domain #2) to
Polysilicon
Solid Mechanics
• Pick “Solid Mechanics”
• Domain Selection > “Polysilicon”
• Thickness: 150[um]
• Rt Click on Solid Mechanics > Fixed
Constraint
• Choose Left End of Beam (#3)
40.
Structural – Electrostatic Load
•
•
•
•
•
•
Rt Click on “Solid Mechanics”
Choose “Boundary Load”
Select Bottom Boundary (#4, 6, 10)
Enter:
es.nTx_Fes
es.nTy_Fes
Set up Parameter for Applied Voltage
• Rt Click on “Global Definitions”
• Choose “Parameters”
• Enter Name as “Vdc”
• Enter Value as “20[V]”
41.
Specify the out-of-plane thickness
• Click “Electrostatics”
• In the “Thickness” section, set d as
150[um]
• This is used to calculate the capacit
ance
Electrical Boundary Condition – Ground
• Rt Click on “Electrostatics”
• Choose “Ground”
• Pick the bottom two boundarie
s (#2, 9)
42.
Electrical Boundary Condition – Terminal
• Rt Click on “Electrostatics”
• Choose “Terminal”
• Pick the far end, top and bottom of the
beam (#4, 6, 10)
• Terminal Type “Voltage”
• Enter Voltage as “Vdc”
Electrostatics Forces on Beam
•
•
•
•
Rt Click on “Electrostatics”
Choose “Force Calculation”
Select Domain: “Polysilicon”
Name the force “Fes”
43.
Moving Mesh – Specify Domain Motions
• Rt Click on “Moving Mesh”
• Add “Free Deformation”
• Choose Domain: “All Domains”
•
•
•
•
•
Rt Click on “Moving Mesh”
Add “Prescribed Deformation”
Pick Domain: “Polysilicon”
Set dx to “u”
Set dy to “v”
Free Deformation Boundary Conditions
•
•
•
•
Rt Click on “Moving Mesh”
Choose “Prescribed Mesh Displacement”
Choose Boundaries: “4, 6, 10”
Set to “u” and “v”
44.
Mapped Mesh
• Rt Click on “Mesh 1”
• Choose “Mapped”
• Highlight “Size”
• Change “Predefined” to “Extra Fine”
We are using 2nd order Lagrange elements…so
one element across the thickness of the beam is ok
Solve
• Rt Click on “Study 1”
• Select “Parametric Sweep”
• Set up the parametric sweep
to vary Vdc from 0 to 20 V at
a step of 2 V
• Rt Click on “Study 1”
• Hit Compute
Set up the model once but solve it for
multiple inputs
45.
Results: Electric Potential
Actual aspect ratio
Results: Displacement
Not to scale…but better
visualization for high aspect
ratio structures
46.
Plot Capacitance vs. Vdc
Capacitance is automatically
calculated when you use the
Terminal boundary condition
Cantilever Beam 2
47.
Modeling steps
• New > 2D
• Structural Mechanics >
Electromechanics
• Next
• Stationary
• Finish
Geometry – Change Units to Microns
• Highlight “Geometry 1”
• Change Length unit to “ m”
48.
Geometry - Beam
• Rt click on “Geom 1”
• Choose “Rectangle”
Size and Shape
• Width: 320
• Height: 2
Position: Corner
• x: 0
• y: 5
Geometry - Air
• Rt click on “Geom 1”
• Choose “Rectangle”
Size and Shape
• Width: 320
• Height: 25
Layers to the right
• Thickness: 20
49.
Materials – Set up Air and Polysilicon
•
•
•
•
Rt Click on “Materials”
Open Material Browser
Built-in > Rt Click on “Air”
Add to Model
• Rt Click on “Materials”
• Open Material Browser
• Built-in > Rt Click on
“Polysilicon”
• Add to Model
• Assign the beam (domain #2)
to Polysilicon
Specify the out-of-plane thickness
• Click “Electromechanics”
• In the “Thickness” section, set d as
150[um]
• This is used to calculate the capacit
ance
50.
Define What is Solid
• Expand “Electromechanics”
• Highlight “Linear Elastic Dielectric”
• Pick the Polysilicon Beam (#2)
Structural Boundary Conditions – Fixed
• Rt Click on “Electromechanics”
• Choose “Structural” >
Fixed Constraint”
• Pick the End of the beam
“
51.
Set up Parameter for Applied Voltage
• Rt Click on “Global Definitions”
• Choose “Parameters”
• Enter Name as “Vdc”
• Enter Value as “20[V]”
Electrical Boundary Condition – Ground
• Rt Click on “Electromechanics”
• Choose “Electrical” > “Ground”
• Pick the bottom two boundarie
s (#2, 9)
52.
Electrical Boundary Condition – Terminal
• Rt Click on “Electromechanics”
• Choose “Electrical” > “Terminal”
• Pick the far end, top and bottom of the
beam (#4, 6, 10)
• Terminal Type “Voltage”
• Enter Voltage as “Vdc”
Mapped Mesh
• Rt Click on “Mesh 1”
• Choose “Mapped”
• Highlight “Size”
• Change “Predefined” to “Extra Fine”
We are using 2nd order Lagrange elements…so
one element across the thickness of the beam is ok
53.
Solve
• Rt Click on “Study 1”
• Select “Parameteric Swe
ep”
• Set up the parametric sw
eep to vary Vdc from 0 to
20 V at a step of 2 V
• Rt Click on “Study 1”
• Hit Compute
Set up the model once but solve it for
multiple inputs
Results: Electric Potential
Actual aspect ratio
54.
Results: Displacement
Not to scale…but better
visualization for high aspect
ratio structures
Plot Capacitance vs. Vdc
Capacitance is automatically
calculated when you use the
Terminal boundary condition
56.
Modeling steps
• Start from the last model
• Rt click on the root node
• Select Add Study
• Select Prestressed Analysis, Eigenfrequency
• Finish
This solves a static problem to
evaluate the solution at the DC bias
point and then performs an
eigenfrequency analysis where it
uses the solution of the static
analysis to create the “shift”
Solve
•
•
•
Rt Click on “Study 2”
Select “Parameteric Sweep”
Set up the parametric sweep to v
ary Vdc from 0 to 20 V at a step
of 4 V
•
Click on Study 2 > Step 2: Eige
nfrequency
Set Desired number of eigenfr
equencies to 1
•
•
•
•
Click on “Study 2” and uncheck
Generate default plots
Rt Click on “Study 2”
Hit Compute
We will only calculate the first or
“fundamental” resonance
57.
Results: Resonant frequency vs.
DC bias voltage
• By using a DC bias voltage
you can tune:
– Capacitance
– Resonant frequency
• Now we have a tunable
resonator!
Frequency Domain
58.
Modeling steps
• Start from the last model
• Rt click on the root node
• Select Add Study
• Select Prestressed Analysis, Frequency Domain
• Finish
This solves a static problem to
evaluate the solution at the DC bias
The frequency domain problem is
then solved as a linearized small
perturbation around this bias point
Set up additional parameters
• Rt Click on “Global Definitions”
• Choose “Parameters”
• Enter Name as “Vac”
• Enter Value as “0.2[V]”
• Enter Name as “eta_s”
• Enter Value as “0.01”
59.
Add damping
•
•
•
•
Rt click “Electromechanics > Linear Elastic Dielectric 1”
Select “Damping”
Choose “Damping type” as “Isotropic loss factor”
Set it as a User defined value of eta_s
Add the AC input
• Rt click “Electromechanics > Terminal 1”
• Select “Harmonic perturbation”
• Set the Electric potential as Vac
• This is the magnitude of the AC signal
• This information will only be used for the frequency-domain pertu
rbation part of the study
60.
Solve
•
•
•
Rt Click on “Study 3”
Select “Parameteric Sweep”
Set up the parametric sweep to a
lter Vdc to 2 V and 6 V
•
Click on “Study 3 > Frequency-D
omain Perturbation”
Set up the frequency to vary fro
m 25 kHz to 35 kHz at a step of
0.2 kHz
•
Tweaking the solver settings
• Rt Click on “Study 3”
• Select “Show Default Solver”
• Click on “Study 3 > Solver Conf
igurations > Solver 1 > Stationa
ry Solver 2 > Direct”
• Expand the section on “Error”
• Set the Factor in error estimat
e as 50
• Rt Click on “Study 3”
• Hit Compute
Setting this factor as a small number
is helpful when we are solving a
linearized model but the geometry
has high aspect ratio and we are
using less mesh elements to save
memory and time
61.
Results: Displacement vs. Frequency
at different DC bias voltages
• By using a DC bias voltage
you can tune:
– Capacitance
– Resonant frequency
– Dynamic response
• Now we have a tunable
resonator!
63.
Microfluidic Processes –
Dimensionless Numbers
•
Pressure driven flow (Re): laminar flow or creeping flow, slip/no slip wa
ll, moving and leaking wall
•
Species transport with reaction (PeMT): dispersion, mixing and separ
ation, filtration, surface reactions, chaotic advection, electrokinetics
•
Interface tension and multiphase flow (Ca, We): free surface deform
ation, jet and droplet, drop dynamics, moving contact
•
Heat transfer (PeHT, Mg): heat transfer, heat of reaction, phase change
, evaporation, condensation, Marangoni effects
Reynolds number (Re): measure of the ratio of inertial
forces to viscous forces.
Peclet number (Pe): the ratio of the rate of
convection/advection to the rate of diffusion.
Capillary number (Ca): the relative effect of viscous
forces versus surface tension.
Weber number (We): fluid's inertia compared to its
surface tension.
Marangoni number (Mg): the ratio thermal surface
tension forces to viscous forces.
Re
U 0 L0
Pe MT
U 0 L0
D
Ca
We
U0
U 02 L
Pe HT
c pU 0 L0
Mg
d L T
dT
64.
Key Application Areas: Lab on a Chip
Microfluidic platforms /
Lab on a Chip Systems
Capillary Driven
Droplet Based
Droplet
production in
a T-junction
Electroosmotic
micropump
Pressure Driven
Electrokinetic
Magnetokinetic
Centrifugal
Pressure
Driven Micromixer
Key Application Areas
Inkjet printing
Drug delivery
Electrowetting
optical / display devices
Fuel cells
65.
• Microfludics
• Microfludics
• Microfludics
• Microfludics
Single Phase Flow
•
•
•
•
•
•
Laminar Flow (Re 1000)
Reynolds number:
U L
0 0
Re
Creeping Flow (Re«1)
Incompressible flow
Compressible flow (Ma<0.3)
Shallow channel approximation
Non-Newtonian Flow:
– Power law:
– Carreau model:
– User defined:
• look-up table or mathematical expression
• dependent on any physics variable: e.g. shear
rate variable, Temperature
66.
Multi-Phase Flow
Three complimentary methods available:
Moving Interface, Fixed Mesh
Level Set
Phase field
Moving Mesh
Multi-Phase Flow: Moving Interface, Fixed Mesh
Level Set and Phase Field Interfaces
•
•
•
•
Problem solved on a fixed mesh.
Level set/Phase Field function switch between a low value (LS:
0 PF:-1) in one phase and high value in the second phase (LS/
PF:1) – density, viscosity etc., is scaled accordingly.
Interface is diffuse and centered on the center value of these fu
nctions (LS:0.5 PF:0).
Level Set
–
–
•
Level set function is solved for in addition to the Navier-Stokes equations
Level set method usually represents surface tension more accurately than p
hase field method
Phase field
–
–
Both phase field and phase field helper functions are solved in addition to th
e Navier-Stokes equations
Phase field method is physically motivated, and is generally more numericall
y stable than the level set method. It can be extended to more phases (diffic
ult!) and is compatible with fluid structure interactions.
67.
Multi-Phase Flow: Moving Mesh
•
•
Problem solved on a moving mesh, using the ALE method.
Interface is sharp and corresponds to a boundary in the initial
geometry.
–
–
•
Since physical interfaces are usually much thinner than practical mesh res
olutions this technique offers the most accurate representation of the interf
ace.
The sharp interface means that different physics can be solved in the dom
ains either side of the interface – for example chemical migration can be a
dded to the model on one side of the boundary only.
The mesh must deform continuously, which means problems
involving topological changes cannot be solved.
Porous Media Flow
•
Darcy’s Law
– Viscosity dominated flow.
– Incompressible flow only
• Brinkman Equations
– Fluid inertia included (can be neglected b
y using Stokes-Brinkman option)
– Compressible/Incompressible flow
– Body forces can be added
• Free and porous media flow
– Pre-defined coupling between Brinkman
equations and the laminar flow interface.
Note: Porous media flow in COMSOL has been
applied to model intracellular transport
68.
Fluid Structure Interactions
(with MEMS or Structural Mechanics Module)
•
•
Based on the ALE moving mesh technolo
gy in COMSOL
Fully bidirectional coupling between fluid a
nd structure
–
–
•
•
•
•
Viscous, pressure and inertial fluid forces o
n the structure
Momentum transfer back to fluid
Small and large deformations
Highly accurate fluid load computation (we
ak constraints).
Predefined physics interface makes it eas
y to build models rapidly – no manual inter
facing between different solvers
Automatic segregated solver settings for t
he stationary and parametric analysis of la
rge 3D models
Species Transport
•
Enhanced interface for transport of diluted spec
ies
–
•
Diffusion, Convection & Migration of multiple species
Together with Chemical Reaction Engineering
Module:
–
–
–
Transport of concentrated species
Chemical reactions: Bulk / Surface
Reaction engineering interface
69.
Electrokinetics/Magnetohydrodynamics
•
•
Electrowetting
Electroosmosis
–
–
•
•
•
•
Explicit modeling of electric double layers on small lengt
h scales
On larger scales, the electroosmotic mobility can be spe
cified as part of a slip boundary condition.
Electrophoresis
Dielectrophoresis
Magnetophoresis (with AC/DC Module)
Electrothermal flows
Thermal Flows
•
•
•
•
•
•
•
Non-isothermal flows
Natural and forced convection
Conduction
Radiation (with Heat Transfer Module)
Joule Heating (extended with AC/DC Module)
Thermophoresis
Marangoni flows
70.
Rarefied Flows
Continuum
o n
Continuum
Flow
l
Flow
Degree of rarefaction characterized
by the Knudsen number, Kn:
Slip
Flow
Slip
Slip
Flow
Flow
Transitional
Flow
Transitional
s
Transitional
Flow
w
Flow
Molecular
c
Molecular
Flow Molecular
o
Flow
Flow
Continuum
Flow
Kn
L
Rarefied Flow Interfaces:
0.01<Kn<0.1: Slip Flow
0.1<Kn<10: Transitional Flow
Kn>10:
Molecular Flow
Transitional Flow and Molecular Flo
w interfaces are available in the Mol
ecular Flow Module
Slip Flow
Requires Microfluidics Module
•
•
•
•
Navier Stokes equations still apply except f
or a small region near the boundaries (the
Knudsen Layer).
COMSOL’s slip flow interface can be used t
o model laminar, isothermal or thermal flow
s in the slip flow regime.
Slip and temperature jump boundary conditi
ons are available to model the Knudsen lay
er.
Specifying the slip can be done in two ways
:
1. Through Maxwell’s model with arbitrary accommod
ation coefficients.
2. By specifying directly the viscous and thermal slip
coefficients along with the temperature jump coeffi
cient.
71.
Transitional Flow
•
•
The transitional flow interface can handle rarefied flows from the Navier
Stokes to the Free Molecular Flow limits.
It employs the discrete velocity method:
• A finite set of velocities are chosen to represent all the potential
velocities of the molecules (the more velocities that are chosen – the
better a rarefied flow will be represented).
• Atoms are assigned into these velocity bins and the interface solves for
the number density in each bin. A convection equation is solved in the
domains, along with a scattering term that moves the molecules between
the bins.
• Total accommodation is assumed on the boundaries
The transitional flow
interface uses a
discrete set of
velocities, similar to the
set shown, to model
the flow.
Molecular Flow
•
•
Molecules collide only with the chamber
walls – no collisions between molecule
s
Angular Coefficient Method
–
–
•
•
•
•
Molecules collide only with the chamber walls
– collisions between molecules are negligible.
Diffuse reflection only through Knudsen’s cosi
ne law (emitted flux intensity cos( ))
No thermal fluctuations.
Faster than DSMC for low velocity flows
– easier to perform parametric studies e
tc.
Stationary flows only.
Computation of pressure and number d
ensity is performed using correct results
from Kinetic Theory
–
More accurate than previously employed ‘radi
ation analogy’ modeling.
72.
• Microfludics
• Microfludics
• Microfludics
• Microfludics
Controlled Diffusion Micromixer
•
•
Micromixer example designed to provi
de an introduction to modeling techniq
ues used in microfluidics.
Shows how to set up a simple fluid flo
w problem using some of the core feat
ures of the Microfluidics Module:
–
–
–
•
Creeping flow
Species transport
Laminar inflow boundary conditions
Demonstrates how to use a range of p
ost-processing features including:
–
–
–
3D, 2D and 1D plot groups
Creating derived data sets such as a cut plan
e from the solution data sets generated auto
matically by COMSOL
Evaluating the numerical values of derived q
uantities such as the mean outlet concentrati
on.
73.
Other Micromixer Models – Enhanced Mixing
•
Key features:
– Import the geometry from industr
y-standard CAD – any level of co
mplexity is possible
– Moving mesh, rotating frame
– Moving/rotating parts
– Concentrated or diluted species c
onvection and diffusion
– Mixing index calculation
– Nonlinear effects and more physi
cs can be added: thermal, chemic
c
al, electric or magnetic field …
Inkjet Printing
•
•
•
•
Microfluidic technology
Propelling droplet onto paper
Pressure oscillation generated by
piezo or heater
Key Features:
– Interface tracked exactly; Interface
normal, curvature and physical qua
ntities can be computed
– Good mass conservation with reinit
ialization
– Mapped mesh
– Multiphysics coupling: electrostatic
s, heat transfer…
74.
Electroosmotic Pump
•
•
•
•
Essential components in microfluidic l
ab-on-a-chip devices
No moving parts
Easy to integrate in microfluidic circui
ts
Key Features:
– Flow field: momentum balance (S
tokes or Navier-Stokes)
– Electric field: current balance
– Using built-in boundary condition
– Parametric study on pressure find
s the strength of the pump
Transport in an Electrokinetic Valve
•
Key Features:
– Flow field: momentum balance (Stokes
or Navier-Stokes)
– Electric field: current balance
– Mass transport: diluted species, NernstPlanck
– Fully integrated
– Solved the model in sequence accordin
g to the actual device
– Yon can specify: charge number, mobili
ty, diffusivity (isotropic or anisotropic), n
onlinear material properties
75.
Capillary Filling
•
Key Features:
– Capillary driven two phase flow
– Surface tension and wall adhesive forc
es
– Built-in moving contact: interface movin
g along the wall, hydrophobic or hydrop
hilic
– Specify friction using wall slip length an
d contact angle
– Wettability gradients: thermal gradient (
built-in), electrowetting, optowetting
– Ready to couple with other physics
Electrophoresis
•
•
•
•
•
Coupling of
– Fluid flow
– Electric current
– Moving mesh
Walls and particle surfaces are rigid a
nd insulating
Walls and particle have uniform nega
a
tive zeta potential
Electric double layers not resolved
User’s model presented at COMSOL
2006 Conference
Model courtesy of Davison and Sharp, COMSOL
2006 Conference
76.
Dielectrophoresis
• how to model dielectrophoresis of particles
in an alternating currents (AC) field
• Two groups of particles are considered:
one group with positive DEP (pDEP : red)
and one group with negative DEP (nDEP :
blue).
• with Particle Tracing
High field region
V
fCM
AC Electrokinetically Enhanced Surface Re
actions
•
Key features:
– Coupling of electrostatics, heat transf
er with joule heating, species transfer
with surface reaction and laminar flow
– Electrothermal force generated by te
mperature gradient due to inhomogen
eous joule heating
– Swirling patterns in the fluid enhance t
he transport of the analyte to the react
t
ion surface
Model courtesy of Gaurav Soni, Marin Sigurdson,
and Carl Meinhart of the Department of Mechanical
and Environmental Engineering, University of
California, Santa Barbara.
77.
Surface Reactions in a Biosensor
• A flow cell in a biosensor contains an
array of micropillars coated with an
active
• Micropillars introduces passive mixing
• Adsorbtion of species produce a signal
• Surface Reactions coupled with mass
transport in a fluid stream
Drug Delivery System
• Drug delivery system that supplies a
variable concentration of a water soluble
drug.
• A droplet with a fixed volume of water
travels down a capillary tube at a
constant velocity.
• Part of the capillary wall consists of a
permeable membrane , as the drop
passes by the membrane, its contact
angle changes and drug dissolves into
the water.
• Modeling using Transport of Diluted
Species, Laminar Two-Phase Flow, and
Moving Mesh
78.
Split-Recombine Mixer Benchmark
• Fluid flow benchmark that computes
the lamination pattern in a complex
split and recombine mixer.
• Lamination patterns are computed in
the absence of physical diffusion.
• COMSOL compares well with the
results in the reference below.
T. Glatzel et al, Computational fluid
dynamics (CFD) software tools for
microfluidic applications - A case
study, Computers & Fluids, vol. 37,
pp. 218235, 2008.
.
Rotating Channel Benchmark
Pressure (Pa)
• Fluid flow benchmark that
computes pressure along the axis
of a rotating channel.
• Example showing how to
implement centrifugal and
centripetal forces – a good
starting point for a centrifugal
microfluidics model.
• COMSOL compares well with the
results in the reference below.
Distance along axis (mm)
T. Glatzel et al, Computational fluid
dynamics (CFD) software tools for
microfluidic applications - A case
study, Computers & Fluids, vol. 37,
pp. 218235, 2008.
79.
Tesla Microvalve Optimization
Requires Optimization Module
Fluid Velocity (m/s), Forward Flow
• Geometrical optimization of a Tesla
microvale, which inhibits
backwards flow on a fixed
geometry by utilizing friction forces
instead of moving parts.
• Model is optimized to minimize the
ratio of frictional losses in forward
flow to that of frictional losses in
reverse flow.
• Pressure drop across the valve for
forward flow is approximately 200
Pa, for reverse flow it is
approximately 380 Pa.
• Shows how to perform shape
optimization on a fluid flow
geometry.
Fluid Velocity (m/s), Reverse Flow
Ion Implanter
Number density along beam path for
different angles of the wafer to the beam
This model computes the number density of
outgassed hydrogen along the ion beam
path in an ion implanter. When the ion beam
strikes part of the wafer covered in
photoresist, the resist breaks down,
outgassing undesirable species (including
hydrogen) into the system. If the ions strike
these outgassed species along the beam
path they can become ionized and can be
accelerated into the wafer. The implantation
of these secondary species degrades the
process.
• A parametric study is performed to asse
ss the effect of altering the angle betwee
n the ion beam and the wafer.
• The number density along a line interior
to the flow domain is computed using th
e number density reconstruction feature.
80.
Evaporator
In an evaporator a metallic sample is heated
beyond its melting point. The liquid metal then
evaporates into the chamber, at a rate controlled by
the temperature of the sample. This model shows
how to compute the evaporated film thickness on a
wafer segment and on the walls of the system.
•
•
The deposition boundary condition is used to
compute the film thickness on the chamber w
alls as a function of time.
The evaporation feature is used to specify the
outgoing flux of evaporated metal from the so
urce. The surface temperature feature is also
used to specify an elevated temperature for th
e source.
Water Adsorption/Desorption
This model shows how to model the time
dependent adsorption and desorption of water in a
vacuum system at low pressures. The water is
introduced into the system when a gate valve to a
load lock is opened and the subsequent migration
and pumping of the water is modeled.
•
•
Illustrates how to model chamber pumpdown pro
blems.
Gives simple examples for the equations required
to specify sticking coefficients, desorption rates et
c. when modeling adsorption and desorption.
81.
Differential Pumping
Differentially pumped vacuum systems use a small
orifice or tube to connect two parts of a vacuum
system at very different pressures. Such systems
are necessary when processes run at higher
pressures and are monitored by detectors which
require UHV for operation. In this model the gas
flow through a narrow tube into a high vacuum
chamber is approximated using an analytic
expression for the flow rate down the tube.
•
Shows how to couple molecular flow to (isotherm
al) transitional flow down a small tube, using anal
ytic expressions for the flow rate through the tube
.
Analysis assesses the effect of molecular beamin
g in the tube in the molecular flow regime.
Model can be adapted to couple transitional flow t
hrough a narrow tube to any geometry.
•
•
Outgassing Pipes
Monte-Carlo
1D simulation
COMSOL
This benchmark model
computes the pressure in a
system of outgassing pipes
with a high aspect ratio. The
results are compared with a
1D simulation and a MonteCarlo simulation of the same
system from the literature.
82.
RF Coupler
(Requires particle tracing module)
This model computes the
transmission probability through
an RF coupler using both the
angular coefficient method
available in the Free Molecular
Flow interface and a Monte
Carlo method using the
Mathematical Particle Tracing
interface. The computed
transmission probability by the
two methods is in excellent
agreement, less than 1%
difference
Trajectories of molecules
computed by Particle
Tracing interface
Molecular flux computed
by Molecular Flow
interface
Rotating Plate
Number density on the surface of a rotating plate in a
molecular beam computed by different methods, as a
function of the angle of the plate to the beam
Radiation method
COMSOL: Total
number density
COMSOL: Outgoing
number density
COMSOL: Incident number
density
This model computes the particle flux,
number density and pressure on the
surface of a plate that rotates in a
highly directional molecular flow. The
results obtained are compared with
those obtained from the so-called
‘radiation method’, previously
employed for this type of
computation.
• The schematic (lower left) shows t
hat when a plate is perpendicular t
o a molecular beam the incident fl
ux goes to zero but the number de
nsity does not.
• The radiation method incorrectly p
redicts that the number density go
es to zero when the plate is perpe
ndicular to the flow.
83.
S-Bend Benchmark
Particle
trajectories
(Particle
Tracing)
Molecular
flux (Free
Molecular
Flow)
Number
density (Free
Molecular
Flow)
(requires the Particle Tracing Module)
This model computes the transmission
probability through an s-bend geometry
using both the angular coefficient
method available in the Free Molecular
Flow interface and a Monte Carlo
method using the Mathematical Particle
Tracing interface. The computed
transmission probability by the two
methods is in excellent agreement, less
than 1% difference.
• 2D example which shows how to co
mpute transmission probabilities with
the particle tracing and free molecul
ar flow interfaces
• Model also shows how to compute t
he number density on a domain..
Vacuum Capillary
Molecular flow down a
cylinder was one of the first
problems in the field to be
treated analytically. In this
benchmark model the
transmission probability is
computed for molecular
flow down a capillary tube
of variable length and the
results are compared with
the analytic solution.
86.
Molecular Flow Interface: Modeling Process
The COMSOL user interface presents simulation information in a compact, easy to
understand format.
Graphics Area: Used to
select geometric
features and to display
results
Active
Node
Model Tree: A
hierarchical list of all
the model properties
Settings Area: displays the
detailed settings for a node
in the model tree
Molecular Flow Interface: Modeling Process
1. Create the geometry.
Define the geometry Or use your preferred CAD
Directly in COMSOL tool and import the file or
dynamically link to COMSOL
using a LiveLink Product
87.
Molecular Flow Interface: Modeling Process
2. Set up materials and physics
COMSOL supports a
range of boundary
conditions to
conveniently specify
the flow.
Industry standard
units (e.g. torr, mBar,
litres/s, sccm) are
supported (SI units
are used by default
but others can be
entered in square
brackets)
1000 [l/s]
Molecular Flow Interface: Modeling Process
3. Mesh the geometry. A range of
options are available for the
mesh. It is possible to mesh just
the surfaces of the model or the
entire domain.
88.
Molecular Flow Interface: Modeling Process
4. Solve
A range of studies are available including:
• Stationary
• Time dependent (to study secondary
effects such as pump down, getters etc.)
• Parametric (parameterize geometry,
settings etc.)
• Optimization
COMSOL automatically suggests the best
settings for the study, but advanced users
have full flexibility to change all the solver
settings.
Molecular Flow Interface: Modeling Process
5. Post-Processing
COMSOL’s powerful post-processing tools are available to analyze the
results.
124.
Bring your ideas to life with COMSOL Multiphysics
(주)알트소프트 TEL: 02-547-2344 FAX: 02-547-2343 E-mail: comsol@altsoft.co.kr Homepage: www.altsoft.co.kr