Study of non-linear mesoscopic diffusion with potential field effect

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).