Hydrodynamic interactions and the diffusivity of spheroidal particles

It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor [J. Fluid Mech. 74, 1-29 (1976) and J. Fluid Mech. 131, 155-175 (1983)] calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles, and Russel et al. [Colloidal Dispersions (Cambridge University Press, 1991)] and Brady [J. Fluid Mech. 272, 109-134 (1994)] treated nondilute (higher particle volume fraction) suspensions. Although most particles lack perfect sphericity, little is known about the effects of hydrodynamic interactions on the diffusivity of spheroidal particles, which are the simplest shapes that can be used to model anisotropic particles. Here, we calculate the effects of hydrodynamic interactions on the translational and rotational diffusivities of spheroidal particles of arbitrary aspect ratio in dilute monodisperse suspensions. We find that the translational and rotational diffusivities of prolate spheroids are more sensitive to eccentricity than for oblate spheroids. The origin of the hydrodynamic anisotropy is that found in the stresslet field for the induced-dipole interaction. However, in the dilute limit, the effects of anisotropy are at the level of a few percent. These effects have influence on a vast range of settings, from partially frozen colloidal suspensions to the dynamics of cytoplasm.