Theoretical formulation of the diffusion through a slab—theory validation

A new theoretical approach to diffusion through a slab and its convection out of the slab is developed. The resulted general model is based on the following assumptions. The transport is a one-dimensional. The diffusion coefficient, the membrane thickness and the temperature are constants. The fluxes in or out of the slab are proportional to concentration differences at the slab interfaces with the concentrations in the two volumes of both sides of the slab. No restrictions are set on the size of the two volumes, on the solute concentrations either in the slab or in the two volumes, as well as on the stirring intensity (natural to perfect forced convection) of the solutions in the two volumes. The formulation in general is exact, except the initial condition. It has been approximately satisfied using the residual approximation method. The general model is validated by its reduction to special cases covering the whole range of its parameters. The general model is reduced to existing analytical studies and well agrees to existing data covering other parts of the parameter ranges. The generality of the model is useful in a wide variety of applications such as separation technology, conducting diffusion experiments, membrane material selection, packaging, pharmaceutical and agricultural applications, as well as other applications which obey the above restrictions underlying the general model.