A comparison between linear and non linear thermodynamic models of membrane water and solute transport

The linear thermodynamic description of membrane transport, although successfully employed for small flows, has some known limitations. Patlak, Goldstein and Hoffman suggested that the linear practical equations by Kedem and Katchalsky may be written as a function of the local forces driving-water and solute flows and integrated across the membrane thickness. By such a procedure the resulting solute flow equation, non linearly related to the driving solute concentration difference is formally identical to the one obtained by Bresler and Wendt from the Hertzian continuity equation. The same procedure may be used for studying series arrays of membranes, which are necessary for the coupling of water flow to a chemical reaction driven solute flow. It can be shown that, in particular flow conditions, the results coincide with those obtained by means of linear thermodynamic network models or with a different system structure. The behaviour of the inner compartment concentration is analogous to the one obtained by a non linear thermodynamic network model. The locally linear model thus appears to be an extension of other linear models.