Pressure effects in nonporous membranes

The solution-diffusion theory for membranes is used as a basis for the formulation and consideration of three models which can describe the mass transfer of solvents through nonporous polymer membranes. Two types of solvent mass transfer processes are considered: the transport of solvent through a membrane immersed in a pure solvent and the osmotic mass transfer of solvent in a solvent–solute-semipermeable membrane system. For the first mass transfer process, the most general of these three mass transfer models (Model III) includes both thermodynamic effects at the solvent–membrane interfaces and pressure diffusion effects inside the membrane. Model I includes only pressure diffusion effects, and Model II includes only thermodynamic effects at the solvent–membrane interfaces. For each model, equations are derived for the solvent mass flux through the membrane and for the mass fraction distribution of solvent inside the membrane. The predictions of each of the models are compared with available mass transfer data for solvent–polymer membrane systems. A similar analysis is used to describe osmotic effects and reverse osmosis. It is concluded that Model III should be the preferred choice for analyzing mass transfer processes for solvents in nonporous polymer membranes. •Three models considered for solution-diffusion theory for nonporous membranes.•Solvent mass flux expressions derived for solvent–polymer membrane systems.•Solvent flux equations can describe reverse osmosis and negative reverse osmosis.•Solvent flow driven by pressure diffusion.•Solvent flow driven by thermodynamic effects.