?
Filtration of a highly concentrated suspension in a porous medium
Ch. 052001. P. 1–7.
Liudmila Kuzmina, Osipov Y.
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 a deposit. The concentration of
suspended particles injected at the porous medium inlet decreases when moving from inlet to
outlet. The mathematical model for a highly concentrated suspension in a porous medium
assumes a nonlinear dependence of the deposit growth rate on the concentration of suspended
particles. The exact solution to the filtration problem in implicit integral form and the Riemann
invariant relating the concentrations of suspended and retained particles are obtained. The
problem is solved for a linear filtration function and a general nonlinear concentration function.
An asymptotic solution is constructed near the concentrations front of suspended and retained
particles. It is shown that the asymptotics is close to the exact solution, the error decreases with
increasing order of asymptotic expansions. The asymptotic solution explicitly defines the
dependence of the solution on model parameters and can be used to solve the inverse filtration
problem.
In book
Vol. 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.
Yulia O. Koroleva, Alexander V. Korolev, , in: Proceedings of the 9th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2026). Irkutsk, Russia, June 22–26, 2026.: Irkutsk: ISDCT SB RAS, 2026. P. 132–133.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
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
Koroleva Y., https://arxiv.org/abs/2604.15410 2025 No. 1 P. 1–19
We study a model problem on the filtration of a conducting fluid through
a porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We show the dependence of
each flow parameter on the Debye radius which characterizes how far the influence of a
charge ...
Added: February 11, 2026
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
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
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
Yulia O. Koroleva, , in: Proceedings of the 7th International Conference on Nonlinear Analysis and Extremal Problems (NLA-2022), Irkutsk, Russia, July 15–22, 2022.: ISDCT SB RAS, 2022. P. 54–55.
We study a model problem on the filtration of a conducting fluid through a porous layer. A porous medium is presented as an assemblage of identical spherical cells. Each cell consists of a porous core and liquid shell. The common case of finite Debye radius in comparison to the cell radius is analyzed. We derive ...
Added: February 2, 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
Kuzmina L., Osipov Y., , in: The 7th International Technical Conference on Frontiers of Hydraulic and Civil Engineering Technology (HCET 2022). Volume 31.Vol. 31: of Advances in Transdisciplinary Engineering.: IOS Press, 2022. P. 40–48.
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
Koroleva Y., Khanukaeva D., Electronic Journal of Differential Equations 2021 Vol. 2021 No. 74 P. 1–16
We study a model problem on the filtration of micropolar fluid in the framework of a cell model technique. A porous medium is presented as an
assemblage of axially symmetric cells of an arbitrarily geometry. Each cell consists of a solid core, porous layer and liquid shell.
The influence of the neighboring cells is taken into account ...
Added: September 20, 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
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
L I Kuzmina, Osipov Y. V., , in: IOP Conference Series: Materials Science and EngineeringVol. 913: International Scientific Conference "Construction and Architecture: Theory and Practice of Innovative Development" (CATPID-2020) - Part 1 26-30 September 2020, Nalchik, Russian Federation.: IOP Publishing, 2020. Ch. 032066 P. 1–8.
Chemical reactions in a porous medium are found in many natural phenomena and
technological processes. Reactive substances dissolved in groundwater can significantly
change the soil strength. The precipitate formed as a result of the reaction changes the porous
medium structure and affects the porosity and permeability. A one-dimensional model of the
reaction of two reagents in a homogeneous porous ...
Added: January 7, 2021
Liudmila I. Kuzmina, Osipov Y., Zheglova Y., , in: Journal of Physics: Conference Series, Volume 1425, Modelling and Methods of Structural Analysis 13–15 November 2019, Moscow, Russian FederationVol. 1425.: IOP Publishing, 2020. Ch. 1425 P. 1–8.
Particle transport in a porous medium occurs in environmental, chemical and industrial technologies. The transport of suspended concrete grains in a liquid grout through porous soil is used in construction industry to strengthen foundations. When particles are transported by a fluid flow in a porous medium, some particles are retained in the pores and form ...
Added: July 2, 2020
Liudmila Kuzmina, Osipov Y., , in: IOP Conference Series: Materials Science and Engineering: XXVIII R-P-S Seminar 2019 9–13 September 20, 19, ŽilinaSlovakiaVol. 661: XXVIII R-P-S Seminar 2019 9–13 September 2019, Žilina, Slovakia.: IOP Publishing, 2019. Ch. 012122 P. 1–8.
Filtration problems in porous media are important for studying the movement of groundwater in porous formations and the spreading of liquid concrete injected into porous soil. Deep bed filtration of a monodisperse suspension in a homogeneous porous medium with two simultaneously acting particle capture mechanisms is considered. A mathematical model of suspension flow through porous ...
Added: July 2, 2020
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