Slow axisymmetric rotation of a sphere in a transversely-isotropic fluid

The creeping flow engendered by the steady axisymmetric rotation of a sphere in a transversely-isotropic Newtonian fluid is investigated in the limiting case when the material properties of the fluid are unaffected by the fluid motion. By introducing an appropriate coordinate transformation, the problem is reduced to that of a spheroid rotating about its axis of symmetry in an isotropic fluid. Closed-form results are obtained for both the velocity field and the couple required to maintain the rotation.