Generalization of Matano's method: interdiffusion in solutions with volume change

Abstract

We present the formalism of Matano's method and an effective expression for the Matano plane position in finite systems. The flux formula for mixtures with volume change avoids the specific assumptions of Sauer and Freise. The classical case of diffusion between two semiinfinite media, with a concentration discontinuity as the initial condition is extended to finite diffusion couple and can also be applied if a volume change occurs. The formulae related to the diffusion coefficient and Matano plane position are independent of the origin of the coordinate system. The paper explains which assumptions are important and natural in this theory.

Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models

“… Is it possible to apply the small parameter method to a derivation of interfaces, e.g. via Matano’s method [ 32 ]? If indeed replacing Neumann boundary conditions by Stefan free boundary conditions is easy to conduct?…”

“…Is it possible to apply the small parameter method to a derivation of interfaces, e.g. via Matano’s method [ 32 ]?…”