Telescopic shearing of non-Newtonian fluids with a saturation stress
by Sergei Alexandrov; Elena Lyamina; Van Manh Dinh; Dinh Kien Nguyen
International Journal of Hydromechatronics (IJHM), Vol. 2, No. 2, 2019

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.

Online publication date: Wed, 17-Jul-2019

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