The stability of inelastic non-Newtonian fluids in Couette flow between concentric cylinders: a finite-element study

Abstract

The onset of axisymmetric (toroidal) vortices in flow between concentric cylinders of infinite length, the inner of which is rotating, is analysed for inelastic non-Newtonian fluids using finite-element techniques. Results are presented for thin and wide annuli of finite gap width and compared with literature values where possible. The shear-thinning behaviour of the fluid is shown to have a significant effect on both the critical Taylor number and the critical wavenumber. The former indicates the speed of rotation at which vortices appear while the latter describes the axial spacing of the vortices in terms of the number of gap widths. The effect of radial distribution of effective viscosity, present in any annulus having a finite gap width, is included. This variation is responsible for the occurrence of a maximum value of critical aspect ratio and a minimum value of critical Taylor number with respect to departure from Newtonian rheology.