Evaluation of S-Entropy Production in a Single-Membrane System in Concentration Polarization Conditions

Abstract

S-entropy source of membrane system was described based on linear non-equilibrium thermodynamics. The volume and diffusive fluxes of non-electrolyte solutions and osmotic and hydrostatic forces in this system were considered. Formulas describing the intensity of S-entropy production were derived for concentration polarization conditions and for homogeneous solutions. To show the influence of concentration polarization on the value of the S-entropy source, the expressions for the quotient and difference of S-entropy source were used in conditions of concentration polarization and homogeneous solutions. On the bases of elaborated formulas, the S-entropy sources as functions of osmotic and hydrostatic forces for homogeneous solutions and for solutions with concentration polarization of the membrane were calculated. Two-dimensional surfaces presented in this paper characterize second-order form of entropy source as a function of forces on the membrane.