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A higher-order Hele-Shaw approximation with application to gas flows through shallow micro-channels

Published online by Cambridge University Press:  14 October 2009

A. D. GAT ,
I. FRANKEL  and
D. WEIHS
A. D. 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
*
†Email address for correspondence: gat@tx.technion.ac.il
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Abstract

The classic hydrodynamic Hele-Shaw problem is revisited in the context of evaluating the viscous resistance to low-Mach compressible viscous gas flows through shallow non-uniform micro-fluidic configurations. Our recent study of gas flows through constricted shallow micro-channels indicates that the failure of the standard Hele-Shaw approximation to satisfy the no-slip boundary condition at the sidewalls severely restricts its applicability. To overcome this we have extended the asymptotic scheme to incorporate an inner solution in the vicinity of the sidewalls (which, in turn, allows for the characterization of the effects of channel cross-section geometry) and its matching to an outer correction. We have compared the results of the present asymptotic analysis to existing exact analytic and numerical results for straight and uniform channels and to finite-element simulations for a 90° turn and a symmetric T-junction, which demonstrate a remarkably improved accuracy relative to the standard Hele-Shaw approximation. This suggests the present scheme as a viable alternative for the rapid performance estimate of micro-fluidic devices.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 638 , 10 November 2009 , pp. 141 - 160
Copyright
Copyright © Cambridge University Press 2009

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