TY - JOUR

T1 - Analysis of the models of motion of aqueous solutions of polymers on the basis of their exact solutions

AU - Frolovskaya, Oxana A.

AU - Pukhnachev, Vladislav V.

N1 - Funding Information: Acknowledgments: This work was partially supported by the Russian Foundation for Basic Research (Project No. 16-01-00127). Authors thank Valery Yu. Liapidevskii and Andrey V. Zvyagin for useful discussions

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

KW - Dilute polymer solution

KW - Hereditary model

KW - Relaxation viscosity

KW - Second grade fluid

UR - http://www.scopus.com/inward/record.url?scp=85069825799&partnerID=8YFLogxK

U2 - 10.3390/POLYM10060684

DO - 10.3390/POLYM10060684

M3 - Article

C2 - 30966718

AN - SCOPUS:85069825799

VL - 10

JO - Polymers

JF - Polymers

SN - 2073-4360

IS - 6

M1 - 684

ER -