This article is cited in 2 papers

One-dimensional model of two-phase fluid displacement in a slot with permeable walls

S. V. Golovin^ab, M. Yu. Kazakova<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Novosibirsk, 630090, Russia

Abstract: A one-dimensional model is proposed for transportation of a two-phase fluid (sand-containing fluid and pure fluid) in the Hele–Shaw cell with permeable walls through which the pure fluid can escape as the sand concentration increases. The model describes the process of pure fluid displacement with the emergence of the Saffman-Taylor instability and extends the Koval' model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by the Koval' model, are discovered.

Keywords: Hele–Shaw cell with permeable walls, Saffman–Taylor instability, two-phase fluid, admixture transportation.

UDC: 532.54

Received: 01.12.2015

DOI: 10.15372/PMTF20170102

 English version: Journal of Applied Mechanics and Technical Physics, 2017, 58:1, 17–30

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