The solution-diffusion model: “Rumors of my death have been exaggerated”

Abstract

The solution-diffusion (SD) model has been instrumental in the advancement of membrane science, due to its simplicity, transparency, and utility in process engineering. However, some doubts have recently been raised, concerning the fundamental validity of SD. These have largely been based on apparent discrepancies between molecular dynamics simulations and several features, deemed inherent to SD, that appeared in early reports — namely, the exact nature of the pressure and concentration distributions within the membrane. Herein, we re-visit the underlying physics of SD in the context of composite membranes, making no a-priori assumptions and, particularly, highlighting the role of polymer thermodynamics and the mechanics of a loaded, swollen film, supported by a porous substrate. The analysis provides a coherent view, linking the solvent concentration profile within the film and the resultant flux-pressure relations with the polymer rigidity and, importantly, the way in which the film is supported. It is shown that, although the flux may generally vary non-linearly with the feed pressure and depend on the film-support geometry, for rigid films – most common in real operations – SD predicts a linear behavior, virtually independent of specific geometry and pressure distribution. Moving forward, we stress the importance and need for further refinements of the SD model, driven by insight from molecular dynamics, thermodynamics and mechanics, while maintaining its applicability to process design.