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Gas flows through constricted shallow micro-channels

Published online by Cambridge University Press:  25 April 2008

A. GAT ,
I. FRANKEL  and
D. WEIHS
A. GAT
Affiliation:
Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
I. FRANKEL
Affiliation:
Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
D. WEIHS
Affiliation:
Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
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Abstract

We study the viscous compressible flow through micro-channels of non-uniform cross-section. A lubrication approximation is applied to analyse the flow through shallow configurations whose gap width is small in comparison with the other characteristic dimensions. Focusing on channels with a symmetric constriction (or cavity) we obtain the solution to the problem by means of a Schwarz–Christoffel transformation. This analytic solution is verified by examining the convergence of numerical simulations with diminishing Reynolds number and gap width. Explicit closed-form expressions for the pressure-head and mass-flow-rate losses in terms of the geometrical parameters characterizing the constriction are presented and discussed in the context of experimental data existing in the literature.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 427 - 442
Copyright
Copyright © Cambridge University Press 2008

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