ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

Vestnik MGSU 11/2017 Volume 12
  • Kuzmina Ludmila Ivanovna - National Research University Higher School of Economics Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, National Research University Higher School of Economics, 20 Myasnitskaya st., Moscow, 101000, Russian Federation.
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 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 in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

DOI: 10.22227/1997-0935.2017.11.1278-1283

Download

RESOLUTION OF THE PROBLEM OF TREATMENT OF WASTE WATER GENERATED BY CAR WASHES AND TRANSPORT ENTERPRISES

Vestnik MGSU 12/2012
  • Gogina Elena Sergeevna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Professor, Department of Water Disposal and Aquatic Ecology, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Salomeev Valeriy Petrovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Professor, Department of Waste Water Treatment and Water Ecology; +7 (495) 730-62-53, Moscow State University of Civil Engineering (MGSU), Room 318g 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Pobegaylo Yuriy Petrovich - Moscow State University of Civil Engineering (MGSU) Researcher, Department of Waste Water Treatment and Water Ecology; +7 (495) 730-62-53, Moscow State University of Civil Engineering (MGSU), Room 318g 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 166 - 176

The authors argue that development of car service companies has caused a new environmental problem: waste water produced by transport enterprises. Their number multiplies day to day in
big cities of Russia. At the same time, the quality of the waste water treated by local water treatment stations fails to meet the present-day standard requirements. Moreover, potable water shall not be used for the purpose of washing transport vehicles.
Within the recent 10 years, MGSU has developed a number of research projects aimed at the resolution of this problem. The concept developed by the MGSU specialists is to attain the highest quality of treated waste water generated by car washes and transport enterprises using the most advanced technologies of water treatment rather than to design new water treatment plants. Various methods may be applied for this purpose: restructuring of water treatment facilities, advanced feed, updated regulations governing the operation of water treatment plants.

DOI: 10.22227/1997-0935.2012.12.166 - 176

References
  1. Federal’nyy zakon Rossiyskoy Federatsii «Ob okhrane okruzhayushchey sredy» ot 10.01.2002 g. ¹ 7-FZ. [Federal Law of the Russian Federation “On Environmental Protection” of 10.01.2002. ¹ 7-FZ]. 13 p.
  2. SanPiN 2.1.5.980—00. Gigienicheskie trebovaniya k okhrane poverkhnostnykh vod ot zagryazneniya [Sanitary Norms and Regulations 2.1.5.980—00. Hygienic Requirements Applicable to Protection of Surface Waters from Pollution]. Moscow, Federal’nyy tsentr Gossanepidnadzora Minzdrava Rossii [Federal Centre for State Sanitary and Epidemiological Supervision of Ministry of Healthcare of the Russian Federation], 2000, 14 p.
  3. Timonin A.S. Inzhenerno-ekologicheskiy spravochnik [Reference Book of Engineering Ecology]. Kaluga, 2003, vol. 1, 917 p.
  4. Kunakhovich A.A. Ustanovki dlya ochistki dozhdevykh stochnykh vod [Rainwater Treatment Facilities]. Ekologiya proizvodstva [Ecology of Production]. 2007, no. 6, pp. 45—51.
  5. Fel’dshteyn G.N., Fel’dshteyn E.G., Moraru N.V. Vodooborotnaya sistema dlya moyki transporta [Water Circulation System for Car Washing Purposes]. Ekologiya proizvodstva [Ecology of Production]. 2008, no. 5, pp. 65—72.
  6. Serpokrylov N.S., Getmantsev S.V. Intensifi katsiya ochistki poverkhnostnykh stochnykh vod [Intensifi cation of Surface Wastewater Treatment]. Ekologiya proizvodstva [Ecology of Production]. 2009, no. 6, pp. 54—64.

Download

Results 1 - 2 of 2