The Gibbs-Duhem equation in membrane transport

It is argued that the Gibbs-Duhem equation alone cannot be used for deriving conclusions about the pressure gradient in membrane permeation. Statements regarding spatial variation of pressure in conjunction with chemical potential gradients of the components can legitimately be drawn from an equation that results from a combination of the G-D equation and the mechanical equilibrium equation. The derived equation has been applied here for explaining the mechanics of osmosis. In a further application, the frictional model has been improved here because the driving force also includes the membrane-solute potential interaction, thus allowing the solute partition coefficient to appear in the calculations naturally. By recognizing that because of the membrane-solution interaction, external forces of both potential and frictional character are present, the dissipation function is shown to depend explicitly on the centre-of-mass velocity. Thus the reference velocity for diffusive fluxes cannot be chosen arbitrarily, making Prigogine's theorem invalid in this approach to describing membrane permeation.