If Border flow is selected, select an Elongation type—Relative or Absolute.

•If Relative is selected, enter a Relative border elongation Lr (unitless). The default is

•If Absolute is selected, enter a Border elongation L (SI unit: m). The default is

0.7m.

Inlet

Use the Inlet feature to set the inlet condition to normal inflow velocity, pressure, or

zero pressure.

B O U N D A R Y S E L E C T I O N

From the Selection list, choose the boundaries to define the inlet.

P A I R S E L E C T I O N

If Inlet is selected from the Pairs menu, choose the pair to define. An identity pair has to be created first. Ctrl-click to deselect.

I N L E T S E T T I N G S

Select an Inlet condition—Normal inflow velocity (the default), Pressure, or Zero

pressure.

•If Normal inflow velocity is selected, enter a Normal inflow velocity U0 (SI unit: Pa). The default is 0.

•If Pressure is selected, enter a Pressure pf,0 (SI unit: Pa) to define pf pf,0 on the edge/point. The default is 0.

•If Zero pressure is selected, this defines pf 0 on the edge/point.

Outlet

The Outlet feature includes a set of boundary conditions describing fluid flow

conditions at an outlet.

B O U N D A R Y S E L E C T I O N

From the Selection list, choose the boundaries to define the outlet.

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P A I R S E L E C T I O N

If Outlet is selected from the Pairs menu, choose the pair to define. An identity pair has to be created first. Ctrl-click to deselect.

O U T L E T S E T T I N G S

Select an Outlet condition—Normal outflow velocity, Pressure, or Zero pressure.

•If Zero pressure is selected, this defines pf 0 on the edge/point.

•If Pressure is selected, enter a Pressure pf,0 (SI unit: Pa) to define pf pf,0 on the edge/point. The default is 0.

•If Normal outflow velocity is selected, enter a Normal outflow velocity U0 (SI unit: Pa). The default is 0.

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T h e o r y f o r t h e T h i n - F i l m F l o w I n t e r f a c e s

The following sections describe the underlying theory for The Lubrication Shell Interface and The Thin-Film Flow Interface and includes these topics:

•Conditions for Film Damping

•The Reynolds Equation

•Structural Loads

•Gas Outflow Conditions

•Rarefaction and Slip Effects

•Geometry Orientations

•References for the Thin-Film Flow Interfaces

Conditions for Film Damping

Figure 5-1 shows an example system where film damping or hydrodynamic lubrication is expected to appear: a thin channel of fluid located between two moving structures. The upper structure is here referred to as the moving solid, whose damping or lubrication is of interest, and the lower one is referred to as the channel base. Damping or lubrication pressure operates on the boundaries of the moving wall, that is, on the solid walls.

Both structures can be in arbitrary motion, but there is typically a distinction between squeezed-film damping for mostly normal movements and slide-film damping or lubrication for mostly tangential movements. Furthermore, damping usually results from operation of compressible gas where as (nearly) incompressible liquids are often used for lubrication.

The fluid film poses two kinds of forces to the moving solid. Initially both structures are surrounded by gas with a constant pressure pa, and the fluid can freely move into and out of the gap. Due to the movements (normal displacement and tangential velocity) of the structures, an additional and usually time-dependent pressure component, the film pressure pf, appears in the gas inside the gap. Thus an effective force equal to Fn = npf affects the moving solid wall in the normal direction (n is the normal unit vector from the structure to the fluid). Another force that affects the

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moving solid wall is the viscous drag force of the fluid Ft, which resists the tangential movement of the structure.

a

Channel base

x0 x0 0 d0, u0 dx0 dt

Figure 5-1: Squeezed-film damping takes place when a narrow gas film is located between a fixed and a moving structure.

In MEMS devices the aspect ratios are very large, which means that the relative dimensions of the system are such that the horizontal dimension, a, is always much larger than the gap, or film thickness, h. It follows that the inertial effects in the fluid are negligible compared to the viscous effects (below MHz frequencies), the pressure is constant over the film thickness, and the velocity has a parabolic profile. Also, it can be assumed that the curvature of the channel is small and that the channel boundaries are almost parallel. Furthermore, owing to the small thickness of the gas film, the fluid is practically always isothermal.

Given these assumptions, solving the full fluid flow problem—described by the Navier-Stokes equations in the gap—reduces to solving the Reynolds equation in the channel boundary. The classical Reynolds equation is valid for large-scale problems. In microsystems, where the continuum assumption often is not valid, the non-continuum effects can be incorporated through so called relative flow rate coefficient Qch. Also, for gas film damping a modified Reynolds equation can be used that also covers the rarefied gas effects taking place at the microscale.

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