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Bidisperse filtration problem with non-monotonic retention profiles

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Abstract

During deep bed filtration of suspensions and colloids in a porous medium, some particles are retained in the pores and form a fixed deposit. A one-dimensional mathematical model of filtration with particles of two types is considered. Exact solution is derived. The existence and the uniqueness of the solution are proved by the method of characteristics, and a solution in the form of a traveling wave is obtained. The profiles of total and partial retained concentrations, showing the dependence of the retained particles concentrations on the coordinate at a fixed time, are studied. It is shown by Taylor expansions that the retained profiles of large particles decrease monotonically, while the retained profiles of small particles are non-monotonic. At a short time, the profile of small particles decreases monotonically; with increasing time, a maximum point appears on it, moving from the inlet to the outlet of the porous medium. When the maximum point reaches the outlet, the profile becomes monotonically increasing. The condition for the non-monotonicity of the total retained profile is obtained.

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No datasets were generated or analyzed for the results of this paper.

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Python program code for the numerical solution of the filtration problem.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Research University Higher School of Economics, 20, Myasnitskaya st., Moscow, Russia, 101000

    Liudmila I. Kuzmina

  2. Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University), 26, Yaroslavskoe Shosse, Moscow, Russia, 129337

    Yuri V. Osipov & Maxim D. Astakhov

Authors
  1. Liudmila I. Kuzmina
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  2. Yuri V. Osipov
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  3. Maxim D. Astakhov
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Correspondence to Yuri V. Osipov.

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Kuzmina, L.I., Osipov, Y.V. & Astakhov, M.D. Bidisperse filtration problem with non-monotonic retention profiles. Annali di Matematica 201, 2943–2964 (2022). https://doi.org/10.1007/s10231-022-01227-5

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