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Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 176–189 (Mi tm3857)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Voitkunskii–Amfilokhiev–Pavlovskii model of motion of aqueous polymer solutions

V. V. Pukhnachevab, O. A. Frolovskayaab

a Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Lavrent'eva 15, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00127
Ministry of Education and Science of the Russian Federation НШ-8146.2016.1
This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00127) and by a grant of the President of the Russian Federation (project no. NSh-8146.2016.1).


DOI: https://doi.org/10.1134/S0371968518010144

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 168–181

Bibliographic databases:

Document Type: Article
UDC: 532.13+517.958
Received: September 8, 2017

Citation: V. V. Pukhnachev, O. A. Frolovskaya, “On the Voitkunskii–Amfilokhiev–Pavlovskii model of motion of aqueous polymer solutions”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 176–189; Proc. Steklov Inst. Math., 300 (2018), 168–181

Citation in format AMSBIB
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\by V.~V.~Pukhnachev, O.~A.~Frolovskaya
\paper On the Voitkunskii--Amfilokhiev--Pavlovskii model of motion of aqueous polymer solutions
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 176--189
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3857}
\crossref{https://doi.org/10.1134/S0371968518010144}
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\jour Proc. Steklov Inst. Math.
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    This publication is cited in the following articles:
    1. Frolovskaya O.A., Pukhnachev V.V., “Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions”, Polymers, 10:6 (2018), 684  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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