The Solution–Diffusion Model: A Unified Approach to Membrane Permeation

Abstract

Over the last 40 years membrane technology has grown from a few analytical applications to a widely used industrial and medical process. Membrane sales are in the multibillion-dollar per year range. Our understanding of the underlying theory and science of membrane processes has also grown during these years. This paper covers the solutiondiffusion model, the most widely used description of permeation through reverse osmosis, pervaporation and gas separation membranes. In the past, these different processes were often treated as completely separate entities. The solution-diffusion model allows these processes to be described in a single, unified way, as we will show.Our approach is first to derive the base equations of the solution-diffusion model for a one-component fluid, and to illustrate the overall unity of the model. We then apply the model to multicomponent mixtures and explain the behavior of membranes when used to perform practical separations. At a number of points, rather than deriving the analytical solution to a specific problem, we simply present the basic equations and show the results of a computer calculation in graphical form. This approach avoids long, tedious derivations and reflects the reality of modern research. Even with the use of computers, this paper has more than 100 equations.A subject like this requires a balance between rigor and clarity. Too much rigor produces a paper only a handful of theoreticians will read. Too much clarity at the expense of rigor and the paper is clear but superficial. This paper is the collaboration of coworkers with different backgrounds. We have tried to present our combined thinking in a way that will be accessible to all, yet solid. 'May the Force be with you'! The Solution-Diffusion ModelThe most easily understood description of a membrane is a porous structure containing a network of tiny pores that separate large from small molecules in a manner similar to a filter. This is a reasonably accurate description of a microfiltration membrane, with pores in the 1000 Å diameter range. Even ultrafiltration membranes, in which the pores are small enough to separate dissolved polymer molecules from water, are best described as 'ultrafine' filters. However, the pore model of membrane transport breaks down when the pore diameter falls to 5 Å or less. The pore diameter is then within the range of the thermal motion of the polymer chains from which the membrane is made. Permeation is no longer a pressure-driven flow through tiny pores but a diffusive process controlled by the motion of the polymer chains.In the past, the transition point between pore flow and molecular diffusion, based on pore diameter, was an assumption. During the last

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