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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

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Choosing mineral carrier of nanoscale additives for asphalt concrete

Vestnik MGSU 3/2014
  • Inozemtsev Sergey Sergeevich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, test engineer, Research and Educational Center on "Nanotechnology", Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7-499-188-04-00; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Korolev Evgeniy Valer'evich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Adviser, Russian Academy of Architectural and Building Sciences (RAACS), director, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7-499-188-04-00; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 158-167

At present time the operation life of the majority of roads is essentially shorter than required. The reason for it is the increase in traffic intensity and axle loads of automobile transport. The obvious reasons for early wear of roads are the low quality of the components used and low industrial standards while producing asphalt pavement. In this paper the mineral material was selected as a carrier of nanoscale additives for asphalt. The optimal modes for grinding mineral materials were identified, which provide correspondence of their structure parameters with the developed model. The influence of different mineral nanomodifier carriers on the structure formation processes was estimated. It is shown that among a number of mineral materials diatomite has high activity in relation to the bitumen, because it has a highly porous structure. It is also shown that as a result of lighter fractions of bitumen adsorption on the border of phase interface, diatomite and bitumen changes from the free state to the film, and solvate shell of bitumen is saturated with asphaltenes. With the help of IR spectroscopy the authors defined the nature of the diatomite and bitumen interaction and proved that in the process of their interaction there occurs physical adsorption with additional absorption of bitumen components into the pore space of diatomite grains.

DOI: 10.22227/1997-0935.2014.3.158-167

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