Linear Taylor-Couette stability of a transversely isotropic fluid

Fibre-laden fluids are found in a variety of situations, whilst Couette devices are used for flow spectroscopy of long biological molecules, such as DNA and proteins in suspension.
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.
This effect is felt most strongly through incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes.
The changes to the rheology induced by the presence of the fibres therefore significantly alter the dynamics of the system, and hence should not be neglected.