Boundary Conditions
Most of the boundary conditions either constrain the flow into the system by prescribing a fluid velocity or constrain the pressure at the boundary. The border flow condition is slightly more complex, requiring the gradient of the pressure to be set by specifying the value of the gradient of the pressure in the anti-normal direction such that:
The Border flow type selection list enables four ways that the value of Γ can be specified:
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The User defined option allows the value of Γ to be directly entered as an expression in a text field. This allows for arbitrary normal pressure gradients.
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The two Acoustic elongation options assume a linear gradient in the pressure outside the domain away from the boundary. The pressure gradient is calculated by dividing the pressure at the boundary, pf, by an elongation length, ΔL. The elongation length can either be specified as an absolute length or as a fraction of the domain width, such that:
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The Out-of-plane motion option calculates the pressure gradient at the boundary using a model detailed in Ref. 9. This model is suitable for including the effects of gas damping when fluid in a thin gap is subjected to out-of-plane motion of the walls or base (for example, when a microbeam is oscillating above an extended surface). When this option is selected, text fields are provided to specify the required coefficients (ζ,η,χ) and the pressure gradient is defined according to
where U is the out-of-plane velocity, Λ is the slip length at the walls, and p∞ is the ambient pressure far from the boundary away from the domain.