• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Book chapter
  • Traveling Wave Solution to Filtration Model in Porous Medium
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
May 22, 2026
HSE Graduates AI Project Wins at TECH & AI Awards
Daria Davydova, graduate of the HSE Graduate School of Business and Head of the AI Implementation Unit at the Artificial Intelligence Department of Alfa-Bank, received a prize at the TECH & AI Awards. She was awarded for the best AI solution for optimising business processes. The winners were determined as part of the VII Russian Summit and Awards on Digital Transformation (CDO/CDTO Summit & Awards).
May 20, 2026
HSE University Opens First Representative Office of Satellite Laboratory in Brazil
HSE University-St Petersburg opened a representative office of the Satellite Laboratory on Social Entrepreneurship at the University of Campinas in Brazil. The platform is going to unite research and educational projects in the spheres of sustainable development, communications and social innovations.
May 18, 2026
The 'Second Shift' Is Not Why Women Avoid News
Women are more likely than men to avoid political and economic news, but the reasons for this behaviour are linked less to structural inequality or family-related stress than to personal attitudes and the emotional perception of news content. This conclusion was reached by HSE researchers after analysing data from a large-scale survey of more than 10,000 residents across 61 regions of Russia. The study findings have been published in Woman in Russian Society.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Traveling Wave Solution to Filtration Model in Porous Medium

P. 450–455.
Kuzmina L., Osipov Y.

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 of a carrier fluid and the deposition of particles on the framework of a porous medium. The purpose of the work is to study the concentrations of suspended and settled particles of a suspension over a long time. Exact and asymptotic methods are used to obtain a solution to the model. The exact solution is presented in an implicit integral form. A set of solutions in the form of traveling waves with an arbitrary initial condition and their asymptotics are constructed. An explicit second-order asymptotic solution for a long time is obtained as an expansion in decreasing exponents. Comparison of the asymptotic solution with the traveling waves makes it possible to choose a single traveling wave corresponding to the exact solution. The closeness of the traveling wave to the exact solution of the filtration model is verified numerically. The traveling wave found determines the explicit asymptotics of the concentration of deposited particles for a long time.

Language: English
Full text
DOI
Text on another site
Keywords: Deep bed filtration porous medium exact solutiontraveling wave solution

In book

Proceedings of the 8th International Technical Conference on Frontiers of HCET 2023. Advances in Transdisciplinary Engineering, Volume 43.
IOS Press, 2023.
Similar publications
PARTICLE TRANSPORT WITH FINITE FILTRATION TIME
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
ESTIMATES TO THE WEAK SOLUTION OF THE ELECTRO-HYDRODYNAMICAL BOUNDARY VALUE PROBLEM FOR THE UNIT CELL OF CATION-EXCHANGE MEMBRANE. THE CASE OF NONZERO DEBYE RADIUS
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
Advective Flow of a Rotating Fluid Layer in a Vibrational Field
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
Plane-Parallel Advective Flow in a Horizontal Layer of Incompressible Permeable Fluid
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
Inverse Filtration Problem of a Bidisperse Suspension
Liudmila I. Kuzmina, Osipov Y., , in: Proceedings of the 10th International Conference on Civil Engineering.: Singapore: Springer, 2024. P. 585–593.
Filtration problems of suspensions and colloids in porous media are considered when designing tunnels and underground structures. To strengthen weak soil, a liquid solution is injected into the rock, the particles of which are filtered in the pores and distributed far from the well. A deep bed filtration model of 2-particle suspension in a porous ...
Added: October 31, 2024
Model Of Cake Filtration In Porous Medium
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
Non-linear filtration model with splitting front
Liudmila I. Kuzmina, Osipov, Y., Pesterev, A., International Journal of Non-Linear Mechanics 2024 Vol. 167 Article 104905
We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the ...
Added: October 31, 2024
Deep bed filtration model for cake filtration and erosion
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
Long-term filtration of particles in a porous medium
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
Modelling of Filtration with Two Capture Mechanisms
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
On the Weak Solution of the Electro-Hydrodynamical Boundary Value Problem for the Unit Cell of Cation-exchange Membrane
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
CHARACTERISTIC METHOD FOR SOLVING FILTRATION PROBLEM
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
Filtration in Porous Medium with Particle Release
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
Dicke Model Semiclassical Dynamics in Superradiant Dipolar Phase in the “Bound Luminosity” State
Mukhin S., Mukherjee A., Seidov S., Journal of Experimental and Theoretical Physics 2021 Vol. 132
Added: September 17, 2023
Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top
Mukhin S., Mukherjee A., Seidov S., Physical Review A: Atomic, Molecular, and Optical physics 2023 Vol. 107
Added: September 17, 2023
“Bound luminosity” state in the extended Dicke model
Seidov S., Mukhin S., Annals of Physics 2023 Vol. 456
Added: September 17, 2023
Exact solution to non-linear filtration in heterogeneous porous media
L.I. Kuzmina, Osipov, Y. V., International Journal of Non-Linear Mechanics 2023 Vol. 150 Article 104363
Many technological processes of chemical and environmental engineering are associated with the filtration of fine particles in porous media, specifically in heterogeneous reservoirs. A one-dimensional model of deep bed filtration of suspensions and colloids in a heterogeneous porous medium is derived. The model includes the mass balance equation with variable porosity for the concentrations of ...
Added: May 19, 2023
Bidisperse filtration problem with non-monotonic retention profiles
Kuzmina L., Osipov, Y. V., Astakhov, M. D., Annali di Matematica Pura ed Applicata 2022 Vol. 201 No. 6 P. 2943–2964
During deep bed filtration of suspensions and colloids in a porous medium, some particles are retained in the pores and form a fixed deposit. A one-dimensional mathematical model of filtration with particles of two types is considered. Exact solution is derived. The existence and the uniqueness of the solution are proved by the method of ...
Added: October 26, 2022
ANALYSIS OF THE FILTRATION PROBLEM BY BITWISE SEARCH METHOD
Liudmila I. Kuzmina, Osipov Y., Astakhov M., International Journal for Computational Civil and Structural Engineering 2022 Vol. 18 No. 3 P. 86–94
During the construction of ground and underground structures, filtration of a liquid grout in loose soil makes it possible to strengthen the foundation and create underground waterproof partitions. A one-dimensional problem of filtering a bidisperse suspension in a homogeneous porous medium with size-exclusion particle capture mechanism is considered. The article is devoted to the calculation ...
Added: October 26, 2022
Unsteady edge waves generated by time-harmonic pressure: exact solutions
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
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit