Study of non-linear mesoscopic diffusion with potential field effect

Abstract

The mass diffusion is affected with potential field, and this work theoretically studies the mesoscopic mass diffusion in various constant potential fields using a non-Fickian diffusion equation derived from the Kramers equation. For the practical interest the diffusion coefficient in the sample is assumed to depend either linearly or exponentially on concentration. A hybrid application of the Laplace transform method and a modified discretization formulation is developed to solve the non-linear governing differential equation. To evidence the rationality and reliability of the present numerical results, a comparison of them with the results in the literature is made. The results show the behavior of non-Fickian diffusion is affected by the potential gradient and is sensitive to the function form of D( C).