We study the stability of dilute suspensions of spheroids in Taylor Couette flow. We focus on axisymmetric perturbations and on the limiting cases of thin disks and long rods. It is found that in the non-Brownian limit, the rods have a negligible effect on the stability, while the disks are destabilizing. The instability is driven by a tilting of the disks, which draws energy from the base flow into azimuthal velocity fluctuations. The resulting instability mode has a wavelength which is smaller than the unstable Newtonian mode. These findings may serve to understand experiments using clay suspensions in the literature
