Nonlinear Diffusion Equation with Diffusion Coefficient Directly Proportional to Concentration of Impurities

摘要

We analyzed a diffusion model based on the assumption that the sufficient condition for the mass flux at point x + L to be different from zero is a nonzero value of the impurity gradient and of impurity concentration at point x. In our model, the length of the jump of diffusing particles from one equilibrium position to another has a defined value L. By describing variation of impurity concentration with time when the frequency of the jumps depends on coordinates and L, the nonlinear diffusion equation was derived. We found that the diffusion coefficient in this nonlinear equation is directly proportional to the concentration of impurities, as it had been proposed in earliest papers. The derived nonlinear diffusion equation was solved numerically for the case of spherical symmetry.