3 - Diffusion Through a Plane Membrane Layer

Abstract

This chapter deals with various cases of one-dimensional diffusion, perpendicular to the membrane surface, into a solid layer with a thickness of δ bounded by two parallel plane surfaces. A solution-diffusion model is applied for a description of this process. The results show that the transported component is adsorbed on the solid interface, transported by molecular diffusion through the membrane layer to its external surface, and to the bulk permeate phase through an external mass transfer resistance. The concentrations are in equilibrium at the interface and the sorption process is instantaneous. Most of the membrane modules used for separation are capillary membrane (hollow-fiber) modules. The conditions under which mass transport through a cylindrical membrane layer can be considered a plane layer are discussed. It is regarded as a plane interface when it takes place through plate-and-frame, tubular, and spiral-wound modules. Cases of steady-state and nonsteady-state diffusion are also discussed. Classic solution-diffusion theory is valid for governing permeation through essentially nonswollen membranes. Another key factor determining permeability in a membrane is the sorption coefficient. The sorption coefficient varies as a function of the concentration, but this dependency is much lower than that of the diffusion coefficient. The value of the variable diffusion coefficient can be changed as a function of concentration and/or space coordinate.