Statistical-mechanical theory of passive transport through partially sieving or leaky membranes

The basic equations for multicomponent transport through partially sieving or leaky membranes are discussed from a statistical-mechanical viewpoint. They have the same mathematical form as the corresponding equations for open membranes, but differ in a discontinuous way from the equations for semipermeable membranes (since a "leak" in a semipermeable membrane constitutes a discontinuous or singular perturbation). Partially sieving membranes can be made to mimic semipermeable behavior through the introduction of characteristic time scales. They may approximate semipermeable behavior at short times, but always deviate at longer times.