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Polymers 2018, 10(6), 684; https://doi.org/10.3390/polym10060684

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

Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk State University, 630090 Novosibirsk, Russia
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Received: 24 May 2018 / Revised: 15 June 2018 / Accepted: 15 June 2018 / Published: 19 June 2018
(This article belongs to the Special Issue Polymer Dynamics)
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Abstract

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. View Full-Text
Keywords: dilute polymer solution; hereditary model; relaxation viscosity; second grade fluid dilute polymer solution; hereditary model; relaxation viscosity; second grade fluid
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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 2018, 10, 684.

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