Linear Taylor-Couette stability of a transversely isotropic fluid

The presence of these fibres can significantly alter the rheology of the fluid, and hence must be incorporated in any modelling undertaken. A transversely-isotropic fluid treats these suspensions as a \chn{continuum} with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters.

We consider the axisymmetric linear stability of a transversely-isotropic viscous fluid, contained between two rotating co-axial cylinders, and determine the critical wave and Taylor numbers for varying gap width and inner cylinder velocity (assuming the outer cylinder is fixed). Through the inclusion of transversely isotropic effects, the onset of instability is delayed, increasing the range of stable operating regimes.