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Global instability of viscous fingering in a Hele–Shaw cell: formation of oscillatory fingers

Published online by Cambridge University Press:  16 July 2009

Jian-Jun Xu
Jian-Jun Xu
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
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Abstract

This work deals with the global instability mechanism of viscous fingering in a Hele–Shaw cell with the inclusion of surface tension. We investigate the interaction and propagation of travelling waves in the system, and obtain two discrete sets of global wave modes: symmetrical modes and anti-symmetrical modes. We call the instability mechanism determined by these global modes the global trapped wave (GTW) instability. A unique global, neutrally stable state of the system is found; it explains the formation of the narrow, oscillatory fingers discovered by Couder el al. (1986) and by Kopf-Sill & Homsy (1987).

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 2 , June 1991 , pp. 105 - 132
Copyright
Copyright © Cambridge University Press 1991

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