Diffusion between evolving interfaces

Abstract

Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.