Gradient diffusion in dilute suspensions of hard spheroidal particles

The renormalization method proposed by Batchelor is used to derive gradient diffusion coefficients in Brownian suspensions of hard spheroidal particles with aspect ratio lambda in the range 1 <= lambda <= 3.5. The theory is based on pairwise steric and hydrodynamic interactions, and the results are therefore valid for dilute suspensions such that lambda(2)phi << 1, where phi is the particle volume fraction. The driving force for gradient diffusion, i.e. the gradient in chemical potential, is larger for suspensions of spheroidal particles than for spheres at the same volume fraction. The hydrodynamic resistance also increases with aspect ratio, but the increase is weaker than that in the driving force. Consequently, at the same particle volume fraction, the increases in rates of gradient diffusion are greater for spheroidal particles than for spheres. The concentration-dependent gradient diffusion coefficient D(phi, lambda) is shown to be closely approximated by D(phi, lambda) = xi D-m(0) {1 + 1.45 phi[1 + 0.259(lambda - 1) + 0.126(lambda - 1)(2)]}, which reduces to the result for spheres when lambda = 1. Here, D-0 is the Stokes-Einstein diffusivity of a spherical particle with its radius equal to the longer dimension of the spheroidal particle, and xi D-m(0) is the orientation-averaged diffusivity of an isolated spheroidal particle.