Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

Abstract

The diffusion is the result of Brownian movement and occurs with a finite velocity. We consider the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. In this case of diffusion from the constant source, the maximum displacements of diffusing particles are proportional to the square root of diffusion time. This result coincides with Brownian movement theory. The obtained analytically solutions were successfully applied for describing the diffusion and superdiffusion experiments' in solids. After theoretical consideration of application of this equation for diffusion in gases, we are investigating here the binary nonlinear diffusion in gases. We obtained the nonlinear interdiffusion equation, for the spherical symmetric case, and presented the approximate analytical solutions.