On the selection principle for viscous fingering in porous media

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 2006-06, Vol.557, p.225-236
Main Authors: YORTSOS, Y. C., SALIN, D.
Format: Article
Language:English
Subjects:
Entropy
Exact sciences and technology
Flows through porous media
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Heterogeneity
Nonhomogeneous flows
Physics
Porous media
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112006009761