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This article is cited in 11 scientific papers (total in 11 papers)
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.
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, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 176–189; Proc. Steklov Inst. Math., 300 (2018), 168–181
Linking options:
https://www.mathnet.ru/eng/tm3857https://doi.org/10.1134/S0371968518010144 https://www.mathnet.ru/eng/tm/v300/p176
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