?
On the Electro-Hydrodynamical Boundary Value Problem for the Unit Cell of Cation-Exchange Membrane
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.
Language:
English
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
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
Koroleva Y., Mathematics and Statistics 2017 Vol. 4 No. 5 P. 143–150
The paper deals with study of Stokes-Brinkman system with varying viscosity that describes the fluid flow along an ensemble of partially porous cylindrical particles using the cell approach. Existence and uniqueness of the solution to the system is proved for an arbitrary varying viscosity. Some uniform estimates on the velocity of flow are derived. Moreover, ...
Added: October 8, 2021
Filippov A. N., Koroleva Y., Buletinul Academiei de Stiinte a Republicii Moldova. Matematica 2017 No. 3 P. 74–87
The paper deals with study of a Stokes-Brinkman system with varying viscosity that describes the fluid flow along an ensemble of partially porous cylindrical particles using the cell approach. We have proved the existence and uniqueness of the solutions as well as derived some uniform estimates. ...
Added: October 6, 2021
Filippov A. N., Koroleva Y., Applied Mathematics and Computation 2018 Vol. 338 P. 363–375
The paper considers a Stokes–Brinkman’s system with varying viscosity that describes the continuous flow of viscous incompressible liquid along an ensemble of partially porous cylindrical particles using the cell approach. The analytical solution for the considered system was derived and analyzed for a particular case of Brinkman’s viscosity which illustrates the presence of superhydrophobic surfaces ...
Added: September 26, 2021
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
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