TRANSPORT-EQUATION FOR A MEMBRANE-BASED ON A FRICTIONAL MODEL

We propose transport equations for a membrane bounded by binary soluti ons based on a frictional model. Several general transport equations i n a differential form have been previously proposed, for example, the frictional model, Stefan-Maxwell and Nernst-Plank equations. However, further knowledge, e.g. the relationship between the chemical potentia l and the concentration of the solution in the membrane, is necessary in order to integrate these equations. Transport equations with an int egrated form (finite-difference form) have been developed by Spiegler, Kedem, and Katchalsky on the basis of the frictional model, and these are widely used for the analysis of membrane transport. These equatio ns are obtained on the assumption that the solution in a membrane is i n equilibrium with an imaginary free solution. The reflection coeffici ent for the volume flux is equal to that for the solute flux in these equations. We have improved these equations by eliminating this assump tion. These equations show that the reflection coefficient for the vol ume flux depends on the volume flux. Two reflection coefficients for t he solute flux were derived. One is independent of the volume flux and the other is equal to that for the volume flux. The difference betwee n the two reflection coefficients becomes larger with an increase in t he volume flux.