Fundamental aspects of the solution-friction model for ion and water transport in membranes

The solution-friction model is the state-of-the-art transport model for reverse osmosis, nanofiltration, and electrodialysis. To underpin and extend this broadly applicable theory in the most precise and effective manner, we discuss the latest developments in three fundamental topics of importance to mass transport modeling in solutions and membranes.

Firstly, we discuss activity coefficients in solution and membranes, related to the ion-ion Coulombic forces that underpin it which for a 1:1 salt leads to a cube-root dependence on salt concentration. We discuss how to implement these activity effect in a membrane model.

Secondly, we discuss the basics of the Soret effect which describes how ions move in a temperature gradient, which sometimes is to lower, and sometimes to higher temperatures. The existence of such a change in sign is one of the outstanding puzzles in the field of physical chemistry. Temperature effects are of great importance in membrane technology because we may attempt to use them for cheaper desalination.

Thirdly, we discuss how the simple Flory-Rehner theory for polymer expansion and compaction can be improved to include finite stretching of the polymer network (of which most membranes are made), charge efects, and how flow of water through a membrane leads to compaction, the more so at the low-pressure side.