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Asymptotics for filtration of polydisperse suspension with small impurities

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Abstract

A model for deep bed filtration of a polydisperse suspension with small impurities in a porous medium is considered. Different suspended particles move with the same velocity as the carrier water and get blocked in the pore throats due to the size-exclusion mechanism of particle retention. A solution of the model in the form of a traveling wave is obtained. The global exact solution for a multiparticle filtration with one high concentration and several low concentrations of suspended particles is obtained in an explicit form. The analytic solutions for a bidisperse suspension with large and small particles are constructed. The profiles of the retained small particles change monotony with time. The global asymptotics for the filtration of a polydisperse suspension with small kinetic rates is constructed in the whole filtration zone.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, National Research University Higher School of Economics, Moscow, 101000, Russia

    L. I. Kuzmina

  2. Department of Applied Mathematics, Moscow State University of Civil Engineering (National Research University), Moscow, 129337, Russia

    Y. V. Osipov & T. N. Gorbunova

Authors
  1. L. I. Kuzmina
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  2. Y. V. Osipov
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  3. T. N. Gorbunova
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Correspondence to Y. V. Osipov.

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Kuzmina, L.I., Osipov, Y.V. & Gorbunova, T.N. Asymptotics for filtration of polydisperse suspension with small impurities. Appl. Math. Mech.-Engl. Ed. 42, 109–126 (2021). https://doi.org/10.1007/s10483-021-2690-6

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  • DOI: https://doi.org/10.1007/s10483-021-2690-6

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