Reformulation of the solution-diffusion theory of reverse osmosis

Many transport concepts have been proposed for desalination by reverse osmosis; however, one of the most useful has been the solution diffusion mechanism as articulated mathematically by Lonsdale, Merten, and Riley in 1965. Their simple formulation has proved effective for describing desalination by reverse osmosis in spite of the many simplifying assumptions, either explicitly or implicitly, used in its development. The result is a linear model where the flux of solvent increases without limit and solute rejection approaches 100% as the pressure differential becomes large. There is good reason to expect that many of the simplifications in the classical theory for the solution-diffusion mechanism will not be appropriate for separation of organic systems. There are numerous opportunities for reverse osmosis-type separations involving organics that might become practical as suitable membrane systems become available. The development of such membranes will require an understanding of the issues that affect the transport of both the solute and solvent in the polymer membrane; for this, a suitable theoretical framework for analysis of experimental data in terms of fundamental parameters is needed. This paper revisits the formulation of the theory for pressure-driven processes where both solute and solvent transports occur exclusively by the solution-diffusion mechanism. This more rigorous treatment of the thermodynamic boundary conditions naturally leads to nonlinear responses where the flux of solvent must reach a finite value as the pressure differential becomes very large. The practical consequence of this becomes more important as the solvent molar volume increases. Likewise, the effects of pressure on solute rejection may not be negligible as its molar volume increases. Finally, the effects of solute-solvent coupling may become important and this is considered using the Maxwell-Stefan formulation for multi-component diffusion. Various approximate forms of the general formulation are given and illustrated by calculations. (C) 2004 Elsevier B.V. All rights reserved.