Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes

A theory of hyperfiltration, based on non-equilibrium thermodynamics, is presented, in which authors combine elements of their own previous work with important contributions of other investigators. The theory pinpoints criteria for salt-rejecting membranes; it does not deal with concentration polarization. The equations for water and salt flux across a differential membrane layer are derived from first principles, and integrated across the membrane, assuming constancy of three coefficients, viz. the specific hydraulic permeability, p1, the local solute permeability, P, and the reflection factor, σ. which is known to be a quantitative index of salt rejection, varying from zero to unity (for non-rejecting to perfect membranes respectively). This procedure is justified by considerations based on the friction model of membrane transport processes. It is shown that 1-σ is the product of an equilibrium term and a kinetic term. The first characterizes the static salt exclusion and hydrophilic properties of the membrane. The second is a quantitative expression for the kinetic characteristics of the membrane.