Mathematical theory of diffusion in solids: solutions in the semi-infinite body and solution to a diffusion problem with a variable boundary condition

TL;DR

This paper reviews solutions to solid-state diffusion problems in semi-infinite bodies and discusses a two-step diffusion problem with changing boundary conditions, providing insights into diffusion behavior under different boundary scenarios.

Contribution

It introduces a detailed analysis of a two-step diffusion problem with variable boundary conditions based on existing solutions for semi-infinite bodies.

Findings

Solutions for diffusion with Dirichlet boundary conditions

Solutions for diffusion with Neumann boundary conditions

Analysis of diffusion behavior in two-step boundary scenarios

Abstract

A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step characterized by a Dirichlet constant concentration condition and the second step by a Neumann condition.