Filtration with sediment erosion in a porous medium

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Models of transport and filtration of small particles in porous media are used in the construction industry when designing foundations and underground structures. A liquid with particles moves through the channels of a porous soil. When particles are transported, some of them are locked in the pores and form a sediment. If the fluid flows slowly, the sedimented particles, retained on the walls of wide pores or in the throats of narrow pores, remain motionless. The liquid and suspension cannot tear the sedimented particles away from the sedimentation sites. When the flow rate of the suspension or colloid increases, part of the sediment is washed out by the carrier fluid and is transferred through the pores. A one-dimensional model of particle transport in a homogeneous porous medium is considered, taking into account the sedimentation of suspended particles on the framework and the erosion of the sediment. The model specifies the relationship between suspended and sedimented particles and the balance of sedimentation and erosion of the sediment. At low suspension concentration, the intensity of sediment formation and rise depends on the filtration function and the concentration of suspended particles; sediment erosion is determined by the number of particles deposited on the framework of the porous medium. Analytical solutions to the model and asymptotics in the form of a traveling wave are obtained. The maximum concentration of sediment with simultaneous action of particle retention and lifting is found.

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Sobre autores

L. Kuzmina

National Research University Higher School of Economics

Autor responsável pela correspondência
Email: lkuzmina@hse.ru

Candidate of Sciences (Physics and Mathematics), Associate Professor

Rússia, 20, Myasnitskaya Street, Moscow, 101000

Yu. Osipov

National Research Moscow State University of Civil Engineering

Email: yuri-osipov@mail.ru

Candidate of Sciences (Physics and Mathematics), Associate Professor

Rússia, 26, Yaroslavskoe Highway, Moscow, 129337

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2. Fig. 1. Traveling wave S(w) at s0=0.5; S*=1

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3. Fig. 2. Particle concentrations before the front: a – suspended C; b – retained S

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4. Fig. 3. Concentration of deposited particles behind the front at the porous medium inlet

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