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Structure of the interface between phases moving toward a sink. (English. Russian original) Zbl 0792.76084

Sov. Phys., Dokl. 37, No. 11, 534-536 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 327, No. 2, 201-204 (1992).
The nonstationary two-dimensional problem of the displacement of an initially horizontal layer of viscous fluid by a second fluid which is inviscid, toward a sink located in the lower right-hand corner of a vertical container with a porous medium, is examined. The inertial effects and interphase tension are neglected. The Laplace equation in a domain with a complicated boundary was solved numerically using the boundary element method. The dynamics of the formation of fjords and protuberances in the interphase boundary is considered. In addition to the large-scale dendritic structure of the interphase surface, a microrelief may develop and lead to the appearance of fractal properties.

MSC:

76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
76M15 Boundary element methods applied to problems in fluid mechanics
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