SELF-DIFFUSION OF INTERACTING BROWNIAN PARTICLES IN A PLANE

We study self-diffusion of interacting Brownian particles confined to a plane. The system is idealized as a set of discs interacting via a pair potential. We analyze the time-dependent mean square displacement of a selected disc. For long times the displacement grows linearly with time, and this defines the long-time self-diffusion coefficient, but there are important logarithmic correction terms. We present an exact expression for the time-dependent displacement in a semidilute suspension of discs with square-well interaction. An approximate expression is proposed which should be valid at any concentration for systems with repulsive interaction. The approximation is characterized by a small number of parameters which in principle can be determined from experimental or computer-simulation data.