It was noted that the H chemical potential in metallic membranes was affected by self-stresses that were generated by interstitial transport within the lattice (stress-induced diffusion). Analytical and numerical evidence was provided which showed that, in the presence of stress-induced diffusion, H transport in thin metallic cylindrical membranes could exhibit macroscopic features that were qualitatively different to those observed in planar structures. This was a result of the differing ways in which diffusion-induced

stresses propagated in planar and cylindrical structures. The investigation was focussed upon the up-hill diffusion effect which was observed experimentally in Pd and Pd-alloy membranes. This was originally explained as being a consequence of a failure of Fick’s law for solid-state diffusion. It was shown that the classical stress-induced diffusion model, as applied to a cylindrical structure, led to a Fickian-type transport equation. This indeed exhibited the up-hill effect, simply as a consequence of the non-linear non-local time-dependent boundary conditions which corresponded to permeation experiments.

Stress-Induced Diffusion of Hydrogen in Metallic Membranes - Cylindrical versus Planar Formulation – I. A.Adrover, M.Giona, L.Capobianco, P.Tripodi, V.Violante: Journal of Alloys and Compounds, 2003, 358[1-2], 268-80