Asymptotics for filtration of polydisperse suspension with small impurities
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-021-2690-6
Asymptotics for filtration of polydisperse suspension with small impurities∗ L. I. KUZMINA1 , Y. V. OSIPOV2,† , T. N. GORBUNOVA2 1. Department of Applied Mathematics, National Research University Higher School of Economics, Moscow 101000, Russia; 2. Department of Applied Mathematics, Moscow State University of Civil Engineering (National Research University), Moscow 129337, Russia (Received May 4, 2020 / Revised Sept. 21, 2020)
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. Key words deep bed filtration, suspension, colloid, porous medium, particle size distribution, analytical model Chinese Library Classification O368 2010 Mathematics Subject Classification
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74N15, 82D80
Introduction
The filtration of colloids, suspensions, and nanoparticles in a porous medium is important in many areas of science and technology. The movement of small particles in a porous rock can significantly reduce the productivity of oil and artesian wells[1–2] . The disposal of industrial wastes in aquifers can lead to environment contamination[3–4] . The filtration of liquid industrial waste and municipal wastewater serves to purify water[5–6] . In a classical filtration model, the identical solid particles are transported by a carrier fluid in a porous medium. The capture of particles by pores is due to electrical and gravitational forces, diffusion, viscosity and so on[7] . The long-term filtration process, which takes place in the entire porous medium, not just in its surface layer, is called deep bed filtration[8] . If the particle and pore sizes are close, the main retention mechanism is size-exclusion[2,4,9]. The ∗ Citation: KUZMINA, L. I., OSIPOV, Y. V., and GORBUNOVA, T. N. Asymptotics for filtration of polydisperse suspension with small impurities. Applied Mathematics and Mechanics (English Edition) (2021) https://doi.org/10.1007/s10483-021-2690-6 † Corresponding author, E-mail: [email protected] ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2021
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L. I. KUZMINA, Y. V. OSIPOV, and T. N. GORBUNOVA
particles pass freely through large pores, and get stuck in the pore throats, which are smaller than the diam
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