# Hydrodynamic interactions and the diffusivity of spheroidal particles

## TL;DR

This paper investigates how hydrodynamic interactions affect the translational and rotational diffusivities of spheroidal particles with arbitrary aspect ratios in dilute suspensions, revealing small anisotropic effects relevant to various scientific fields.

## Contribution

It provides the first calculation of hydrodynamic interaction effects on spheroidal particle diffusivity, extending prior spherical particle models to anisotropic shapes.

## Key findings

- Hydrodynamic interactions cause a few percent anisotropy in diffusivity.
- The stresslet field is the origin of anisotropic effects.
- Results are applicable to colloidal suspensions and cytoplasm dynamics.

## Abstract

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 (1976,1983) calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles and Russel et al.(1991), and Brady (1994) treated non-dilute (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. The origin of the hydrodynamic anisotropy is that found in the stresslet field for the induced-dipole induced-dipole interaction. However, in the dilute limit the anisotropy effects are at the level of a few percent. These effects have influence in a vast range of settings, from partially frozen colloidal suspensions to the dynamics of cytoplasm.