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Characterizations of the critical Stokes number for potential and viscous flows

Published online by Cambridge University Press:  26 February 2010

D. Lesnic ,
L. Elliott  and
D. B. Ingham
D. Lesnic
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
L. Elliott
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
D. B. Ingham
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
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Abstract

The impaction on symmetrical obstacles placed in uniform streams of aerosols is investigated. The governing equations of motion are nonlinear differential equations involving a parameter called the Stokes number. The study differentiates between the critical value of the Stokes number on the centre-line, kcr, below which no particles reach the stagnation point in finite time, and the critical value of the Stokes number on the obstacle, Kcr, below which no particles may be deposited on the obstacle in finite time. Based on the properties of the centre-line fluid velocity of the potential and viscous flows past a variety of symmetrically shaped obstacles, upper and lower bounds of Kcr and Kcr are established. Furthermore, using a numerical procedure for solving nonlinear differential equations with unknown parameters the critical values of Kcr and Kcr are obtained.

Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 277 - 292
Copyright
Copyright © University College London 1994

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