Method of evaluation of the transport properties in polymeric membrane systems using the N? hybrid form of Kedem-Katchalsky-Peusner formalism

In this paper, the N (R) hybrid version of the Kedem-Katchalsky-Peusner (K-K-P) formalism for concentration polarization conditions is developed. For ternary non-electrolyte solutions, this formal-ism includes the hybrid Peusner coefficients (N-ij (R), i, j is an element of {1, 2, 3}, r = A, B), which determine the trans-port properties of the membrane, the N-ij (R) coefficients which determine the degree of coupling, and the energy conversion efficiency coefficient (e(ij)(R)). Besides, K-K-P formalism is the basis for a method to evaluate the conversion of internal energy (U-energy) into free energy (F-energy) and dissipated energy (S-energy) in a membrane system containing ternary non-electrolyte solutions separated by a polymer membrane. Moreover, it is shown that the Peusner coefficients are proposed as a flux-induced version of the modified Peclet number for concentration polarization conditions. The present paper is a continuation of several previous papers, of which the L (R), R (R), H (R), K (R) versions of the Kedem-Katchalsky-Peusner formalism are presented. The formalism using the N (R) form of the hybrid Kedem-Katchalsky-Peusner equations can be a useful tool to study the transport properties of artificial membranes for environmental engineering.