Effects of nonlinear diffusion in a two-phase system

In this paper we investigate a one-dimensional convection-diffusion model with nonlinear molecular diffusion for mass transfer in a two-phase system. The molecular diffusion depends nonlinearly on both the concentration and the concentration gradient. Numerical results are obtained by employing an explicit second order finite difference scheme. The numerical solutions are compared with analytic ones for certain particular cases. In all cases the results are interpreted from a physical point of view, and the effects of the convection and the nonlinear diffusion are emphasized.