# R Version of the Kedem–Katchalsky–Peusner Equations for Liquid Interface Potentials in a Membrane System

## TL;DR

This paper presents a new R version of the Kedem–Katchalsky–Peusner equations to model energy conversion in membrane transport processes.

## Contribution

The paper introduces a novel transformation of K-K equations into the R variant for membrane systems.

## Key findings

- Peusner coefficients were calculated from K-K coefficients for a dialyser membrane system.
- Energy conversion efficiency increased nonlinearly with solute concentration in the membrane.
- Energy fluxes were analyzed as functions of ionic current density for constant solute fluxes.

## Abstract

Peusner’s network thermodynamics (PNT) is an important way of describing processes in nonequilibrium thermodynamics. PNT allows energy transport and conversion processes in membrane systems to be described. This conversion concerns internal energy transformation into free and dissipated energies linked with the membrane transport of solutes. A transformation of the Kedem–Katchalsky (K-K) equations into the R variant of Kedem–Katchalsky–Peusner (K-K-P) equations was developed for the transport of binary electrolytic solutions through a membrane. The procedure was verified for a system in which a membrane Ultra Flo 145 Dialyser separated aqueous NaCl solutions. Peusner coefficients were calculated by the transformation of the K-K coefficients. Next, the coupling coefficients of the membrane processes and energy fluxes for electrolyte solutions transported through the membrane were calculated based on the Peusner coefficients. The efficiency of energy conversion in the membrane transport processes was estimated, and this coefficient increased nonlinearly with the increase in the solute concentration in the membrane. In addition, the energy fluxes as functions of ionic current density for constant solute fluxes were also investigated for membrane transport processes in the Ultra Flo 145 Dialyser membrane.