A Comparison of Critical Time Definitions in Multilayer Diffusion

Abstract

There are many ways to define how long diffusive processes take, and an appropriate "critical time" is highly dependent on the specific application. In particular, we are interested in diffusive processes through multilayered materials, which have applications to a wide range of areas. Here we perform a comprehensive comparison of six critical time definitions, outlining their strengths, weaknesses, and potential applications. A further four definitions are also briefly considered. Equivalences between appropriate definitions are determined in the asymptotic limit as the number of layers becomes large. Relatively simple approximations are obtained for the critical time definitions. The approximations are more accessible than inverting the analytical solution for time, and surprisingly accurate. The key definitions, their behaviour and approximations are summarized in tables.