Model of lateral diffusion in ultrathin layered films

We consider the diffusion of markers in a layered medium, with the lateral diffusion coefficient being the function of hight. We show that the probability density of the lateral displacements follows one-dimensional Batchelor's equation with time-dependent diffusion coefficient governed by the particles' redistribution in height. For the film of a finite thickness the resulting mean squared displacement exhibits superdiffusion at short times and crosses over to normal diffusion at long times. The approach is used for description of experimental results on inhomogeneous molecular diffusion in thin liquid films deposited on solid surfaces.