Stress-induced diffusion of hydrogen in metallic membranes: cylindrical vs. planar formulation. I

The hydrogen chemical potential in metallic membranes is affected by the self-stresses generated by the interstitial transport within the lattice (stress-induced diffusion). This article provides analytical and numerical evidence that, in the presence of stress-induced diffusion, hydrogen transport in thin metallic cylindrical membranes can exhibit macroscopic features qualitatively different from those observed in planar structures. This is a consequence of the different ways diffusion-induced stresses propagate in planar and in the cylindrical structures. We focus on the investigation of the uphill diffusion effect (observed experimentally in Pd and I'd alloy membranes) originally explained as a consequence of the failure of the Fick law for solid-state diffusion. We show that the classical stress-induced diffusion (SID) model applied to a cylindrical structure leads to a Fickian-type transport equation, which indeed displays the uphill effect solely as a consequence of the non-linear, non-local time-dependent boundary conditions corresponding to permeation experiments. (C) 2003 Elsevier B.V. All rights reserved.