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The velocity field about a sphere of radius a rotating in a Brinkman fluid is derived and the hydrodynamic torque is calculated. The effect of the Darcy permeability (k) on the torque is O(a2/k), compared to O(a/k1/2) for the translational drag. The Brinkman effect on rotation is substantially weaker than on translational motion for any value of a/k1/2. Measurements of hydrodynamic torque and drag on spheres of different size could be used to determine the length scale at which the Brinkman model fails, thus providing insight into the microstructure of the fluid.
Solomentsev et al. (Mon,) studied this question.