Highlighting multiplicity in the Gilliland solution to the Maxwell-Stefan equations describing diffusion distillation

Abstract

This article investigates the separation of ethanol/water and 2-propanol/water liquid mixtures of azeotropic composition by allowing diffusion through six different inert gases: helium, nitrogen, air, argon, CO₂ and xenon. The Maxwell-Stefan (M-S) equations afford a rigorous quantification of the achievable separation. For steady-state transfer, analytic solutions to the M-S formulation were obtained in parametric form by Gilliland. For each investigated system in this study, the Gilliland approach yields three different solution sets for the transfer fluxes of alcohol and water; only one of these is physically realizable in practice. The physically realistic solution can be identified by invoking the Prigogine principle of minimum entropy production. Robust computational algorithms are essential for modeling and development of diffusion distillation technology; these are indicated. The efficacy of diffusion distillation depends on differences in alcohol-inert and water-inert friction in the vapor phase; such differences increase with increasing molar mass of the inert component. Inert gases such as CO₂ and Xe are more effective than lighter inerts such as air, nitrogen or helium. Some of the strategies in the published literature, involve interposing porous barriers between the vapor and liquid phases; the choice of the pore diameter influences the efficacy of diffusion distillation. For alcohol/water mixtures, it is preferable to choose the pore diameter such that “bulk” diffusion, rather than Knudsen diffusion regime prevails inside the pores.