On the rotation of porous ellipsoids in simple shear flows

We study theoretically the dynamics of porous ellipsoids rotating in simple shear flows. We use the Brinkman–Debye–Bueche (BDB) model to simulate flow within and through particles and solve the coupled Stokes–BDB equations to calculate the overall flow field and the rotation rate of porous ellipsoids. Our results show that the permeability has little effect on the rotational behaviour of particles, and that Jeffery’s prediction of the angular velocity of impermeable ellipsoids in simple shear flows (Proc. R. Soc. Lond. A, vol. 102, 1922, pp. 161–179) remains an excellent approximation, if not an exact one, for porous ellipsoids. Employing an appropriate scaling, we also present approximate expressions for the torque exerted on ellipses and spheroids rotating in a quiescent fluid. Our findings can serve as the basis for developing a suspension theory for non-spherical porous particles, or for understanding the orientational diffusion of permeable ellipses and spheroids.