Title: Telescopic shearing of non-Newtonian fluids with a saturation stress

Authors: Sergei Alexandrov; Elena Lyamina; Van Manh Dinh; Dinh Kien Nguyen

Addresses: Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, 119526 Moscow, Russia ' Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, 119526 Moscow, Russia ' Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam ' Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

Abstract: A closed form solution for quasi-static telescopic shearing of non-Newtonian fluids between two concentric cylinders is derived and then analysed. The paper focuses on qualitative features of the solution. In particular, it is shown that the qualitative behaviour of the solution in the vicinity of the inner friction surface is controlled by the dependence of the quadratic invariant of the stress tensor on the quadratic invariant of the strain rate tensor as the latter approaches infinity. In particular, no solution at sticking may exist if the quadratic invariant of the stress tensor approaches a finite value as the quadratic invariant of the strain rate tensor approaches infinity. In this case, it is necessary to construct the solution at sliding. This solution is singular, and the exact asymptotic representation of the quadratic invariant of the strain rate tensor in the vicinity of the friction surface depends on the exact dependence of the quadratic invariant of the stress tensor on the quadratic invariant of the strain rate tensor as the latter approaches infinity.

Keywords: sticking; sliding; singularity; saturation stress.

DOI: 10.1504/IJHM.2019.100773

International Journal of Hydromechatronics, 2019 Vol.2 No.2, pp.131 - 139

Received: 06 Feb 2019
Accepted: 04 Mar 2019
Published online: 17 Jul 2019 *

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