One-Dimensional Model of Two-Phase Fluid Displacement in a Slot with Permeable Walls
S. V. Golovin1,2, M. Yu. Kazakova1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: ячейка Хеле-Шоу с проницаемыми стенками, неустойчивость Саффмана-Тейлора, двухфазная жидкость, перенос примеси, Hele-Shaw cell with permeable walls, Saffman-Taylor instability, two-phase fluid, admixture transportation
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.
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