Flow of a Johnson–Segalman fluid between rotating co-axial cylinders with and without suction

Abstract

The Johnson–Segalman fluid has a non-monotone relationship between the shear stress and velocity gradient in simple shear flows for a certain range of material parameters resulting in solutions with discontinuous velocity gradients for planar and cylindrical Poiseuille flow. This has been used to explain the phenomenon of “Spurt”. Rao and Rajagopal [ Acta Mechania, to be published] have shown that the addition of suction necessarily smoothens the solutions for planar Poiseuille and cylindrical Poiseuille flows. Here we study the effect of a different geometry on the flow of a Johnson–Segalman fluid. The problems of cylindrical Couette flow, cylindrical Couette flow with suction (or injection) and Hamel flow are studied and it is found that the boundary condition can have an interesting effect on the regularity of the solution. The presence of suction increases the regularity of the solution, i.e. solutions with discontinuous velocity gradients are not possible.