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.