Asymmetric diffusion in heterogeneous media

Diffusion in heterogeneous media (i.e., layers with discontinuous values of the diffusivity parameter) is found in different situations, including geology, catalyst, physiology and separation processes. This work considers an array of rectangular layers of different diffusivity as a simple model for studying diffusivity in heterogeneous media. Random walk simulations adapted for transport across interfaces between different materials are used for showing that heterogeneous media exhibit asymmetric transport in the sense that the diffusive flux depends of the transport direction. It is shown that Brownian particles run preferentially along the direction of decreasing diffusivity. An uphill diffusion effect is found when particles move from high to low diffusivity layers. In terms of Fick's modeling, asymmetric transport is explained from the presence of a jump in the particle density at layer interfaces.