Generalized solution of interdiffusion problem: Optimal approach for multicomponent bounded systems
Marek Danielewski, Robert Filipek · Journal of Computational Chemistry · 1996
Darken's phenomenological scheme for diffusion in binary systems is used for a description of interdiffusion in multicomponent (r ≥ 2) mixtures. The mathematical model of interdiffusion in the bounded mixture (i.e., layer of finite thickness) showing constant concentration (e.g., in solid or liquid solutions) and variable diffusivity of the components is formulated. We derive, with the use of idea of generalized solution, an exact expression for the evolution of components distribution. Also, we consider an asymptotic approximation of the exact expression which can be simply applied to a variety of initial conditions. We show, in an elementary case of interdiffusion in a two-component mixture with constant diffusion coefficients, the analytical results and the complete algorithm of finding the density profiles. The experimental and theoretical results for a Cu(SINGLE BOND)Ni solid solution are presented. © 1996 by John Wiley & Sons, Inc.