Brownian diffusion in concentrated suspensions of interacting particles

In this paper we set out to calculate the self-diffusivity of a Brownian particle in a concentrated suspension. The problem is treated by regarding the neighbours of a test particle as forming a ‘cage’. For short time t < tc, say, the particle is partially constrained by the cage and an equation is proposed to describe the coupled dynamics of particle and cage. The equation is shown to be asymptotically exact in some cases and acceptably accurate for other simple systems by comparing with Monte Carlo simulations. For times t > tc, the particle diffuses sufficiently far to escape its original cage (and finds itself in a new one). A quantitative estimate for tc is proposed and verified for a system of rod-like particles by numerical simulation. By combining these two ingredients an estimate of the long-time (t [Gt ] tc) self-diffusivity of a particle is made. For rod-like particles tc is the reptation time, and the result here is compared with the theory of Doi & Edwards (1978a, b), and with experiment. For a system of spheres comparison is made with the tracer light-scattering experiments of Kops-Werkhoven & Fijnaut (1982). In both cases good agreement is found when the particle concentration is sufficiently high.