On the secondary flow induced by spheres and discs rotating in elastico-viscous liquids

Abstract

Numerical methods have been employed to simulate the secondary flows of non-Newtonian materials caused by the rotation of spheres and thin discs for “finite” Reynolds and Weissenberg numbers. Previous analytic work has been confined to “small” values of these parameters. The numerical scheme of the present paper is used to solve thefull non-linear equations of motion for finite values of these global parameters for a fluid ofarbitrary viscosity characterisation, and so isnot restricted to the hierarchy constitutive equations used in previous analyses.