On molecular diffusion in nanostructured porous media: interfacial exchange kinetics and surface diffusion

Abstract

Water-vapour transport in nanostructured composite materials is poorly understood because diffusion and interfacial exchange kinetics are coupled. We formulate an interfacial balance that couples diffusion in dispersed and continuous phases to adsorption, absorption and interfacial surface diffusion. This work is motivated by water-vapour transport in cellulose fibre-based barriers, but the model applies to nanostructured porous media such as catalysts, chromatography columns, nanocomposites, cementitious structures and biomaterials. The interfacial balance can be applied in an analytical or a computational framework to porous media with any microstructural geometry. Here, we explore its capabilities in a model porous medium: randomly dispersed solid spheres in a continuous (humid) gas. We elucidate the roles of equilibrium moisture uptake, solid, gas and surface diffusion coefficients, inclusion size and interfacial exchange kinetics on the effective diffusivity. We then apply the local model to predict water-vapour transport rates under conditions in which the effective diffusivity varies through the cross section of a dense, homogeneous membrane that is subjected to a finite moisture-concentration gradient. As the microstructural length scale decreases from micrometres to nanometres, interfacial exchange kinetics and surface diffusion produce a maximum in the tracer flux. This optimal flux is flanked, respectively, by interfacial-kinetic- and diffusion-limited transport at smaller and larger microscales.