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Deep bed filtration rate in porous media
Ch. 030011.
Filtration problems are investigated when calculating foundation fortifying in free soil, when planning tunnels and underground structures to make watertight dividers in porous rock. Amid the filtering of a liquid with tiny particles through a porous frame, some of the particles are trapped in the little pores and form immovable sediment. A 1D model of filtration of similar particles transported by the carrier fluid in a homogeneous porous structure is considered, the filtration function is presumed to be nonlinear. A suspension or colloid is injected into a porous sample filled with clean water and gradually displaced. The growth rate in time of the particles concentrations at a given point of the porous sample is studied. Depending on the particle size, the growth rate of the trapped particles concentration either decreases monotonically with time, or first increases and then decreases. For the nonlinear filtration function, the conditions for the existence of an inflection point on the graphs of the suspended and trapped particles dynamics are obtained.
In book
Vol. 2497: Proceedings of the II Scientific Conference “Modelling and Methods of Structural Analysis”. Issue 1. , AIP Publishing LLC, 2023.
Pochinka O., Shmukler V., Yakovlev E., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Keykhosravi A., Rehman S., Osipov Y. et al., GEOENERGY SCIENCE AND ENGINEERING 2026 Vol. 261 Article 214375
Injectivity decline due to injection of colloidal suspensions and emulsions occur in numerous areas of geo-energy production, geo- and environmental engineering. This phenomenon is attributed to colloidal capture by porous media resulting in permeability decrease. The shortcoming of the traditional analytical model predicting injectivity decline is the assumption of constant filtration coefficient (probability of the capture) leading ...
Added: February 25, 2026
Nozdrinova E., Pochinka O., Shmukler V. et al., Russian Journal of Mathematical Physics 2025 Vol. 32 P. 129–140
One of the constructions for obtaining flows on a manifold is the construction of a suspension over a diffeomorphism. S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. The converse is not true in the general case. A classic illustration of this fact are examples of non-conjugate diffeomorphisms of a circle whose suspensions ...
Added: May 6, 2025
Kuzmina L., Osipov, Y. V., Astakhov, M. D., Mathematical Methods in the Applied Sciences 2024 Vol. 47 No. 11 P. 8319–8341
A one‐dimensional deep bed filtration model of a polydisperse suspension or colloid in a porous medium is considered. The model includes a quasilinear system of 2n equations for concentrations of suspended and retained particles of n types. The problem is reduced to a closed 3 × 3 system for total concentrations of suspended and retained ...
Added: June 27, 2024
Arzhantsev I., Zaitseva Y., Research in Mathematical Sciences 2024 Vol. 11 No. 2 Article 27
An algebraic variety X is called a homogeneous variety if the automorphism group Aut(X) acts on X transitively, and a homogeneous space if there exists a transitive action of an algebraic group on X. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we ...
Added: March 23, 2024
Liudmila Kuzmina, Osipov Y., , in: IOP Conference Series: Materials Science and Engineering Volume 869, 2020 XXIII International Scientific Conference on Advance in Civil Engineering: "CONSTRUCTION - THE FORMATION OF LIVING ENVIRONMENT" (FORM-2020) 23-26 September 2020, Hanoi, VietnamVol. 869: XXIII International Scientific Conference on Advance in Civil Engineering: "CONSTRUCTION - THE FORMATION OF LIVING ENVIRONMENT" (FORM-2020) 23-26 September 2020, Hanoi, Vietnam. Issue 5: RELIABILITY OF BUILDINGS AND CONSTRUCTIONS.: IOP Publishing, 2020. Ch. 052001 P. 1–7.
The problems of filtration in porous media are in demand when strengthening
foundations and building waterproof walls in rocks. Deep bed filtration of a highly
concentrated monodisperse suspension in a homogeneous porous medium with size-exclusion
particle retention mechanism is considered. When filtering a suspension in a porous medium,
some solid particles get stuck on the porous frame and form ...
Added: January 7, 2021
Байгушева Ю. В., Закон 2020 № 10 С. 50–59
The article analyses Art. 183 of the Civil Code of the Russian Federation, which refers to the contract of obligation by representative without authority. The author believes that the rights and obligations stipulated by this agreement arise only with the approval of the person represented. In relation to the contract, approval is a suspensive condicio ...
Added: November 12, 2020
Dmitriev V. V., Kutuzov M. S., Soldatov A. A. et al., JETP Letters 2019 Vol. 110 No. 11 P. 748–749
We present results of nuclear magnetic resonance (NMR) experiments in superfluid 3He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples the superfluid ...
Added: November 21, 2019
Lyudmila I. Kuzmina, Osipov Y., Zheglova Y., International Journal for Computational Civil and Structural Engineering 2019 Vol. 15 No. 2 P. 77–85
Filtration of the suspension in a porous medium is important when strengthening the soil and creating
watertight partitions for the construction of tunnels and underground structures. A model of deep bed filtration
with variable porosity and fractional flow, and a size-exclusion mechanism of particle retention are considered.
A global asymptotic solution is constructed in the entire domain in ...
Added: July 7, 2019
Liudmila Kuzmina, Osipov Y., Zheglova Y., , in: E3S Web of Conferences Volume 97 (2019) XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019)Vol. 97: XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019).: EDP Sciences, 2019. Ch. 05002 P. 1–8.
Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The ...
Added: July 7, 2019
L I Kuzmina, Osipov Y., , in: VII International Symposium Actual Problems of Computational Simulation in Civil EngineeringVol. 456.: IOP Publishing, 2018. Ch. 012052 P. 1–6.
Filtration describes a variety of the construction complex problems: strengthening
loose soil to create a solid foundation, the movement of groundwater with solid impurities near
underground structures, and many others. A model of two-sized deep bed filtration particles
moving with different velocities in a porous medium with three-size pores is considered. The
competition of pores and various size particles ...
Added: January 18, 2019
L I Kuzmina, Osipov Y., Zheglova Y., , in: VII International Symposium Actual Problems of Computational Simulation in Civil EngineeringVol. 456.: IOP Publishing, 2018. Ch. 012051 P. 1–6.
The solution of the filtration problem allows calculating the injection of the grout
into a loose ground to create a solid foundation. The basic deep bed filtration model of a
monodisperse suspension in a porous medium is considered. Based on the synthesis of the
standard asymptotic solution for a short time and the asymptotics of the filtration problem ...
Added: January 18, 2019
Dmitriev V. V., Kutuzov M. S., Soldatov A. A. et al., JETP Letters 2018 Vol. 108 No. 12 P. 827–828
Magnetic materials generate demagnetizing field that depends on geometry of the sample and results in a shift of magnetic resonance frequency. This phenomenon should occur in porous nanostructures as well, e.g., in globally anisotropic aerogels. Here we report results of nuclear magnetic resonance (NMR) experiments with liquid 3He confined in anisotropic aerogels with different types of ...
Added: November 23, 2018
Dmitriev V. V., Kutuzov M. S., Melnikovsky L. A. et al., JETP Letters 2018 Vol. 108 No. 11 P. 772–773
We report the results of theoretical and experimental investigation of spin diffusion in the normal phase of liquid 3He confined in planar aerogel: a material consisting of nanostrands which are almost parallel to a specific plane and randomly oriented in this plane. Using spin echo technique we measure the spin diffusion coefficients in the directions perpendicular ...
Added: November 23, 2018
Liudmila Kuzmina, Osipov Y., , in: IOP Conference Series: Materials Science and Engineering, Volume 365, Safety in Construction XXI International Scientific Conference on Advanced in Civil Engineering "Construction - The Formation of Living Environment" (FORM 2018)Vol. 365.: IOP Publishing, 2018. Ch. 042003 P. 1–7.
Modelling of the suspended particles transport in a porous medium is used in the analysis of methods for strengthening foundations. To strengthen the porous soil, a low concentration cement-based grout is pumped into it under pressure. The suspension is filtered in a porous medium and fills the cavity of the soil. Grains of the grout ...
Added: November 2, 2018
Liudmila Kuzmina, Osipov Y., , in: XXVII R-S-P Seminar, Theoretical Foundation of Civil Engineering (27RSP) (TFoCE 2018)Vol. 196.: EDP Sciences, 2018. Ch. 04003 P. 1–6.
A one-dimensional model for the deep bed filtration of a
monodisperse suspension in a porous medium with variable porosity and
permeability and multiple pore-blocking mechanisms is considered. It is
assumed that the small pores are clogged by separate particles; pores of
medium size, exceeding the diameter of the particles, can be blocked by
arched bridges, forming stable structures at the ...
Added: October 29, 2018
Osipov Y., Kuzmina L., , in: Procedia Engineering, 153 (2016), XXV Polish – Russian – Slovak Seminar “Theoretical Foundation of Civil Engineering"Vol. 153.: Elsevier, 2016. P. 366–370.
Problems of deep bed filtration of the suspension in a porous soil are important for the design and construction of tunnels and hydrotechnical structures. A size-exclusion model of solid particle capture in a porous media is considered. For deep bed filtration equations an asymptotic solution for the concentrations of suspended and retained particles is constructed ...
Added: June 22, 2018
L.I. Kuzmina, Osipov Y. V., Вестник Московского государственного строительного университета 2017 No. 11 P. 1278–1283
Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck ...
Added: January 6, 2018
Ludmila I.Kuzmina, Osipov Y., Galaguz Y., International Journal for Computational Civil and Structural Engineering 2017 Vol. 13 No. 3 P. 70–76
The study of filtration as one of the problems of underground hydromechanics is necessary for the design and construction of tunnels, underground and hydraulic structures. Deep bed filtration of suspension in a porous medium with variable porosity and permeability and with an initial deposit is considered. An asymptotic solution to a model with small limit ...
Added: January 6, 2018
Л.И. Кузьмина, Осипов Ю. В., International Journal for Computational Civil and Structural Engineering 2017 Т. 13 № 1 С. 63–68
Filtration of the suspension in a porous medium with a geometric particle capture mechanism is considered. The porous medium has an initial deposit unevenly distributed across the filter. The nonlinear model of deep bed filtration suggests that the porosity and permeability of the porous medium depend on the deposit. The asymptotics of the movable boundary ...
Added: January 6, 2018
Kuzmina L., Osipov Y., , in: MATEC Web of Conferences. 5th International Scientific Conference “Integration, Partnership and Innovation in Construction Science and Education”. Moscow, Russia, October 16-17, 2016Т. 86.: [б.и.], 2016. Ch. 01005 P. 1–5.
Added: March 3, 2017