... variables.
15. 10.1 Well-Posedness
Based on the extensive mathematical literature on the Navier–Stokes equation, Abergel and Temam (1990)
established the well-posedness of the mathematical framework ... Systems • Other Applications
16.5 Conclusions 1 6-3 1
16.1 Introduction
Many important applications of micro-electro-mechanical systems (MEMS) devices involve the control of
co...
... LLC
5
Integrated Simulation
for MEMS: Coupling
Flow-Structure-
Thermal-Electrical
Domains
5.1 Introduction 5-1
Full-System Simulation • Computational Complexity of MEMS
Flows • Coupled-Domain Problems • A ... and
σ
T
are the tangential momentum and thermal accommodation coef-
ficients respectively. The accommodation coefficients model the momentum and energy exchange of gas mol-...
... of the Navier–Stokes equations, as well as the molecular interaction models of the MD and the
DSMC methods. Although it may seem that the molecular simulation methods are more fundamental, they
require ... particularly important for simulation of gas flows in MEMS components.
If we consider a micromotor or a micro-comb-drive mechanism, gas flow in most of the device can be
simul...
... Taylor & Francis Group, LLC
1 1-2 MEMS: Introduction and Fundamentals
attention of MEMS researchers since the early days of MEMS development, and there have been several
demonstrations of micromotors ... gradients in the microchannel. Probably the most common cause of this is a mis-
match in the height of the fluid level at the reservoirs. Although there may not be...
... used for MEMS. This alleviates many of the reservations and costs that might
inhibit their adoption. Because the MEMS constraint is the minimum gap dimension, the wave bearing
in a MEMS machine ... shows the measurements (from a 26:1 scaled-up experimental rig) along with the
theoretical predictions based on the assumed geometry. The right-hand frame shows the same meas...
... indeterminate set of equations. The continuum model is easier to handle mathematically (and
is also more familiar to most fluid dynamicists) than the alternative molecular models. Continuum mod-
els ... listed in the comments columns of the tables.
The question of the effect of size on the strength of MEMS materials often arises. This is because
MEMS structural components ca...
... process. The present section discusses molecular-based models and their relation to
the continuum models previously considered.
The most fundamental of the molecular models is deterministic. The motion ... illustrate
other ramifications of the large surface-to-volume ratio unique to MEMS and provide a molecular view-
point to surface forces.
U
ᎏ
h ϩ 2L
o
s
4-2 8 MEMS: Intro...
... and Ducts at Micro and Nano
Scales,” Microscale Thermophys. Eng. 3, p. 43.
Beskok, A. (2002) “Molecular-Based Microfluidic Simulation Models,” in Handbook of MEMS, 1st ed.,
M. Gad- el- Hak, ed., CRC ... on the molecular distribution function of the surrounding gas, the ther-
mophoretic force can be calculated by integrating the momentum flux imparted by the molecules strik-
i...
... obey the desired con-
tinuum equations of fluid dynamics. Thus LBM is based on the particle dynamics governed by a simpli-
fied model of the Boltzmann equation; the simplification is usually to the ... region 0 Յ x Յ 1 m. The first-order
8-2 8 MEMS: Introduction and Fundamentals
y/y
max
0.0
0.5
1.0
0.0 1.0 2.0 3.0 4.0 5.0
x/y
max
FIGURE 8.29
Microchannel geometry and grid....