J. Phys. II France
Volume 3, Numéro 7, July 1993
Page(s) 955 - 959
DOI: 10.1051/jp2:1993175
J. Phys. II France 3 (1993) 955-959

Fingering in the fast flow through porous medium

A.P. Ershov, A.L. Kupershtokh and A.Ya. Dammer

Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, Siberian division, Lavrentyev pr. 15, 630090, Novosibirsk, Russia

(Received 8 January 1993, revised 14 May 1993, accepted 18 May 1993)

The displacement of dense liquid from the pore space, e.g. by injected gas, is considered. For fast flow regimes the drag law is non-linear. The resulting nonlinear boundary problem can be solved by methods similar to dielectric-breakdown models. The gas jets form fractal structures. In the plane geometry the fractal dimension D exceeds the known linear Laplace value D1, but it is less than D0.5 obtained in the model with a growth parameter $\eta=1/2$.

47.55 - 47.55M - 47.20

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