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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2018
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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. |
format | Online Article Text |
id | pubmed-6404120 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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