A continuum mechanical approach to the flow equations for membrane transport. I. Water flow

A concept is presented for modeling flows through membranes using continuum mechanics. Viscous interactions (due to velocity gradients) are explicitly incorporated and position-dependent local water-membrane interactions are taken into account before obtaining slab averages. This is in distinction to other treatments where strictly one-dimensional force balance equations are written using slab average friction coefficients which are really composite functions of local interactions. It is shown that the viscous and other frictional interactions do not simply form linear combinations in the solutions to the equations of motion. Flow profiles for pressure-driven flows ranging from Poiseuille's flow to "diffusion" flow are obtained depending on the strength and extent of the water-membrane interaction. The model is also applied to self-diffusion flows and the measurement of "equivalent pore size." It is shown that for a fixed pore size the ratio of filtration flow to self-diffusion flow for equal driving forces is able to vary over a wide range depending on the water-membrane interaction.