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Deep bed filtration with multiple pore-blocking mechanisms
Ch. 04003. P. 1–6.
Liudmila Kuzmina, Osipov Y.
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 pore throats. These poreblocking
mechanisms - size-exclusion and different types of bridging act
simultaneously. Exact solutions are obtained for constant coefficients, on
the concentrations front and at the porous medium inlet.
In book
Vol. 196. , EDP Sciences, 2018.
Kuzmina L., Osipov Y. V., International Journal for Computational Civil and Structural Engineering 2025 Vol. 21 No. 3 P. 135–147
Abstract: Particle transport by a fluid flow occurs in many applied construction problems, including pumping mortar into porous soil, creating watertight diaphragm walls, and constructing dams and underwater structures. A model of deep bed filtration of suspensions and colloids in a homogeneous porous medium with a finite number of vacancies for retained particles is considered. ...
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
Shvarts K.G., Russian Journal of Nonlinear Dynamics 2019 Vol. 15 No. 3 P. 261–270
This paper presents a derivation of new exact solutions to the Navier – Stokes equations in
Boussinesq approximation describing two advective flows in a rotating thin horizontal fluid layer
with no-slip or free boundaries in a vibrational field. The layer rotates at a constant angular
velocity; the axis of rotation is aligned with the vertical axis of coordinates. ...
Added: November 24, 2024
Shvarts K. G., Russian Journal of Nonlinear Dynamics 2023 Vol. 19 No. 2 P. 219–226
In this paper a new exact solution of the Navier – Stokes equations in the Boussinesq approximation describing advective flow in a horizontal liquid layer with free boundaries, where the vertical velocity component is a constant value, is obtained. The temperature is linear along the boundaries of the layer. Solutions of this kind are used ...
Added: November 16, 2024
Liudmila I. Kuzmina, Osipov Y., International Journal for Computational Civil and Structural Engineering 2024 Vol. 20 No. 3 P. 116–124
Strengthening of loose soil and creation of water-resistant underground walls are associated with filtration of small particles in a porous medium. Liquid solution pumped into a well under pressure spreads through hollow channels and strengthens the soil upon hardening. Many porous filters retain particles near the entrance. The particles deposited on the filter surface form ...
Added: October 31, 2024
L. I. Kuzmina, Osipov Y. V., Pesterev A. R., Applied Mathematics and Mechanics (English Edition) 2024 Vol. 45 No. 2 P. 355–372
Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition, namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based ...
Added: June 27, 2024
Liudmila Kuzmina, Osipov Y., , in: BIO Web of Conferences: Volume 107:19th International Conference Water and Wastewater: Transportation, Treatment, Management “Yakovlev Readings” (YRC-2024)Vol. 107.: EDP Sciences, 2024. Ch. 03003.
The formation of grout sediment in the pores of loose rock increases the water resistance of the soil and strengthens the foundation. A one-dimensional model of filtration in a porous medium considers the particles transport by the flow of a carrier fluid and the deposition of particles on the framework of a porous medium. The ...
Added: June 27, 2024
Kuzmina L., Osipov Y., , in: Proceedings of the 8th International Technical Conference on Frontiers of HCET 2023. Advances in Transdisciplinary Engineering, Volume 43.: IOS Press, 2023. P. 450–455.
Suspension and colloid filtration in porous rocks is encountered in problems of underground hydromechanics associated with construction. The formation of grout sediment in the pores of loose rock increases the water resistance of the soil and strengthens the foundation. A one-dimensional model of filtration in a porous medium considers the particles transport by the flow ...
Added: June 27, 2024
Liudmila Kuzmina, Osipov Y., Sosedka M., , in: Construction The Formation of Living Environment. Proceedings of FORM 2022. (LNCE, volume 282).: Cham: Springer, 2024. P. 21–31.
Filtering fluids with tiny particles in porous media occurs in many technological processes of environmental and civil engineering. To strengthen the foundation, a slurry is pumped into loose rock and, when hardened, strengthens it. Deep bed filtration is accompanied by the retention of particles. Various forces act on the particles and cause them to settle ...
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 I. Kuzmina, Osipov, Y., Pesterev, A., International Journal for Computational Civil and Structural Engineering 2023 Vol. 19 No. 3 P. 39–48
During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained ...
Added: October 31, 2023
L. I. Kuzmina, Osipov, Y. V., Shaidullina, A. M., , in: Proceedings of the II Scientific Conference “Modelling and Methods of Structural Analysis” 11–13 November 2021 Moscow, Russian Federation. Volume 2497Vol. 2497: Proceedings of the II Scientific Conference “Modelling and Methods of Structural Analysis”. Issue 1.: AIP Publishing LLC, 2023. 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 ...
Added: October 31, 2023
Mukhin S., Mukherjee A., Seidov S., Journal of Experimental and Theoretical Physics 2021 Vol. 132
Added: September 17, 2023
Mukhin S., Mukherjee A., Seidov S., Physical Review A: Atomic, Molecular, and Optical physics 2023 Vol. 107
Added: September 17, 2023
Seidov S., Mukhin S., Annals of Physics 2023 Vol. 456
Added: September 17, 2023
Abrashkin A. A., Journal of Physics A: Mathematical and Theoretical 2022 Vol. 55 No. 41 Article 415701
An analytical description of unsteady edge waves over a uniform slope is proposed. It is assumed that the waves are excited by time-harmonic external pressure with inhomogeneous spatial distribution. The problem is considered in Lagrangian variables. An exact solution of the hydrodynamic equations is obtained. It generalizes the stationary Gerstner–Constantin solution. The proposed model describes the dynamics of coastal splashes ...
Added: October 13, 2022
LIUDMILA I. KUZMINA, OSIPOV Y., International Journal for Computational Civil and Structural Engineering 2021 Vol. 17 No. 2 P. 43–49
During the construction of hydraulic and underground structures, a grout solution is pumped into the ground
to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The
mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through
the pores of ...
Added: October 18, 2021
Liudmila Kuzmina, Osipov Y. V., Tzariova V., , in: IOP Conference Series: Materials Science and Engineering 1030 (2021) VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, UzbekistanVol. 1030: VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, Uzbekistan.: IOP Publishing, 2021. Ch. 012109 P. 1–7.
Filtration problems arise in the design of tunnels and underground structures. A onedimensional
filtration model of a monodisperse suspension in a homogeneous porous medium
is considered. For a general nonlinear filtration function, an asymptotic solution is constructed
behind the concentrations front of suspended and retained particles. It is shown that the
asymptotics is close to the numerical solution. Comparison ...
Added: July 3, 2021
L I Kuzmina, Osipov Y. V., Astakhov M. D., , in: Journal of Physics: Conference Series 1926 (2021)Vol. 1926: Innovations and Technologies in Construction (BUILDINTECH BIT 2021) 9 th - 10th March 2021, Belgorod, Russia.: IOP Publishing, 2021. Ch. 012001 P. 1–7.
During the construction of underground storage of hazardous waste, it is necessary to create waterproof walls in the ground. The grout is filtered in the rock, fills the pores and, when hardened, creates a reliable barrier to groundwater. A one-dimensional model of the flow of inhomogeneous particles in a porous medium is considered. The retained ...
Added: July 3, 2021
LIUDMILA I. KUZMINA, Osipov Y., International Journal for Computational Civil and Structural Engineering 2020 Vol. 16 No. 4 P. 50–56
Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures.
A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration
problem – finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution ...
Added: July 2, 2021
Kuzmina, L.I., Osipov, Y. V., Gorbunova, T. N., Applied Mathematics and Mechanics (English Edition) 2021 Vol. 42 No. 1 P. 109–126
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 ...
Added: January 7, 2021