Alternative analytical analysis for improved Loschmidt diffusion cell

To measure gas phase diffusion coefficients across porous media, an apparatus called a Loschmidt diffusion cell is often utilized. In previous studies with such an apparatus, an infinite-length assumption is used to simplify the analytical solution. Experimentally, cell lengths must be quite long and measurement time is very brief to fulfill this assumption. In this study, Fick's second law is applied, and separation of variables with shifted homogeneity technique is performed for data analysis to enable design of a more compact experimental apparatus with extended measurement times and improved precision. The analytical solution is proved by both the inverse-matrix method and finite-volume discretization. Finally, using the new analytical solution obtained, the effective diffusion coefficient is determined for porous media used in fuel cell applications.