The conventional equations describing mass transport through membranes predict proportionality between flux and driving force. Experimental results inconsistent with this prediction are usually attributed to a concentration dependency of the diffusion coefficients of the species involved. It has now been found that, in addition to this effect, simplifications in the models and the neglect of crystallinity and swelling of the membrane material contribute in no small way to the noted deviations. On the basis of the well-known "solution-diffusion" theory a new permeation rate equation has been derived, which accounts for the various shortcomings mentioned and which is capable of predicting the large effects of crystallinity and swelling of the membrane material on permeability. This equation also expresses the mutual effects of permeants on their separation without the introduction of an arbitrary coupling coefficient, which is required in the conventional equations.
A simplified procedure is proposed for calculating membrane separation of multicomponent mixtures, which is based on the assumption of an exponential concentration gradient inside the membrane in accordance with reported experimental observations. The exponential form, which differs for each composition and set of conditions, can be calculated from the boundary conditions of the membrane.