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On the selection principle for viscous fingering in porous media

Published online by Cambridge University Press:  12 June 2006

Y. C. YORTSOS  and
D. SALIN
Y. C. YORTSOS
Affiliation:
Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1211, USA
D. SALIN
Affiliation:
Laboratoire FAST, Fluides Automatique et Systèmes Thermiques, Université P. M. Curie, Université Paris Sud, CNRS UMR 7608 Bât. 502, Campus Universitaire, F-91405 Orsay Cedex, France
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Abstract

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Viscous fingering in porous media at large Péclet numbers is subject to an unsolved selection problem, not unlike the Saffman–Taylor problem. The mixing zone predicted by the entropy solution is found to spread much faster than is observed experimentally or from fine-scale numerical simulations. In this paper we apply a recent approach by Menon & Otto (Commun. Math. Phys., vol. 257, 2005, p. 303), to develop bounds for the mixing zone. These give growth velocities smaller than the entropy solution result $(M-1/M)$. In particular, for an exponential viscosity-concentration mixing rule, the mixing zone velocity is bounded by $(M-1)^2/(M\ln M)$, which is smaller than $(M-1/M)$. An extension to a porous medium with an uncorrelated random heterogeneity is also given.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 557 , 25 June 2006 , pp. 225 - 236
Copyright
© 2006 Cambridge University Press