Excluded-volume effects in the diffusion of hard spheres

Excluded-volume effects can play an important role in determining transport properties in diffusion of particles through crowded environments. Here, the diffusion of finite-sized hard-core interacting particles is considered systematically using the method of matched asymptotic expansions. The result is a nonlinear diffusion equation for the one-particle distribution function, with crowding effects enhancing the overall diffusion rate. Stochastic simulations of the full particle system are shown to compare well with the solution of this equation for two examples