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Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are...

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Detalles Bibliográficos
Autores principales: Frolovskaya, Oxana A., Pukhnachev, Vladislav V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6404120/
https://www.ncbi.nlm.nih.gov/pubmed/30966718
http://dx.doi.org/10.3390/polym10060684
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author Frolovskaya, Oxana A.
Pukhnachev, Vladislav V.
author_facet Frolovskaya, Oxana A.
Pukhnachev, Vladislav V.
author_sort Frolovskaya, Oxana A.
collection PubMed
description The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are similar to those of motion of a usual viscous fluid. Other models can include weak discontinuities, which are retained in the course of fluid motion. Exact solutions are found by using the group analysis of the examined systems of equations. These solutions describe the fluid motion in a gap between coaxial rotating cylinders, the stagnation point flow, and the motion in a half-space induced by plane rotation (analog of the Karman vortex). The problem of motion of an aqueous solution of a polymer in a cylindrical tube under the action of a streamwise pressure gradient is considered. In this case, a flow with straight-line trajectories is possible (analog of the Hagen-Poiseuille flow). In contrast to the latter, however, the pressure in the flow considered here depends on all three spatial variables.
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spelling pubmed-64041202019-04-02 Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions Frolovskaya, Oxana A. Pukhnachev, Vladislav V. Polymers (Basel) Article The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are similar to those of motion of a usual viscous fluid. Other models can include weak discontinuities, which are retained in the course of fluid motion. Exact solutions are found by using the group analysis of the examined systems of equations. These solutions describe the fluid motion in a gap between coaxial rotating cylinders, the stagnation point flow, and the motion in a half-space induced by plane rotation (analog of the Karman vortex). The problem of motion of an aqueous solution of a polymer in a cylindrical tube under the action of a streamwise pressure gradient is considered. In this case, a flow with straight-line trajectories is possible (analog of the Hagen-Poiseuille flow). In contrast to the latter, however, the pressure in the flow considered here depends on all three spatial variables. MDPI 2018-06-19 /pmc/articles/PMC6404120/ /pubmed/30966718 http://dx.doi.org/10.3390/polym10060684 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Frolovskaya, Oxana A.
Pukhnachev, Vladislav V.
Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title_full Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title_fullStr Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title_full_unstemmed Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title_short Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions
title_sort analysis of the models of motion of aqueous solutions of polymers on the basis of their exact solutions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6404120/
https://www.ncbi.nlm.nih.gov/pubmed/30966718
http://dx.doi.org/10.3390/polym10060684
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