Reevaluating Analytical Approximations of Fick's Second Law: A Computational Perspective

Abstract

This study examines the limitations of classical analytical approximations of Fick's second law of diffusion and proposes a computational approach to determine the diffusion coefficient (D) using the entire diffusion process data. Traditional approximations rely on short-time diffusion data, potentially leading to misinterpretations. The computational method, validated with experimental data on liquid water diffusion in poly(lactic acid) and oxygen diffusion in poly(ethylene terephthalate), demonstrates higher accuracy and broader applicability. This approach challenges the common assumption that deviations from analytical approximations imply non-Fickian behavior, offering a more reliable method for diffusion analysis.