Abstract
The theoretical description of multicomponent transport across nonporous polymeric membranes was investigated using two alternative frameworks; the phenomenological approach of irreversible thermodynamics and the mechanistic Stefan-Maxwell formulation. The transport models developed account for potential equilibrium and/or kinetic coupling of fluxes and the contribution of diffusion induced non-selective flow within the polymer. Transient measurements coupled with transient models enable a more detailed evaluation of the complex multicomponent transport phenomena occurring within the nonporous polymer. The models developed in this study were validated against transient dialysis and pervaporation data for (ethanol-water)/silicone rubber system. A critical assessment was obtained by recovering the model parameters from the dialysis data and using the same parameters to predict the transient pervaporation performance. Separate evaluation of the equilibrium and kinetic contributions requires a thermodynamic model to describe the non-ideality of the polymer solution. The uptake of small polar solutes by hydrophobic polymers is not well described by the classical Flory-Huggins model. An empirical modification was developed which retains the basic form of the Flory-Huggins model but allows the interaction parameters to be a simple function of activity. This modification provided a physically realistic description of the sorption equilibria for the {ethanol- water}/silicone rubber system over conditions ranging from a low pressure vapour to a saturated liquid. The phenomenological approach of irreversible thermodynamics was used to develop transient models of dialysis and pervaporation. The numerical solution of the model equations, which constitute a set of coupled partial differential equations, was accomplished by the application of the method of lines. Average phenomenological diffusion coefficients recovered from dialysis data can give a good qualitative prediction of pervaporation performance provided the diffusion coefficients satisfy the Onsagar reciprocal relationships. However, a quantitative prediction requires the explicit inclusion of the concentration dependence of the diffusivities, which is best achieved within the mechanistic Stefan-Maxwell formulation. A generic model of membrane transport was formulated using the mechanistic Stephan-Maxwell approach and generalised driving forces, which included the contribution from the various internal and external driving forces. Transient models of dialysis and pervaporation were developed which used exactly the same generic model to describe the transport through the membrane. A notable advantage of the generic model lies in the fact that the Stephan-Maxwell diffusivities retain their physical significance irrespective of the number of components present. This offers the opportunity of recovering many of the model parameters from relatively simple binary experiments. The results obtained indicate that the generic model is capable of describing the transient dialysis and pervaporation of the {ethanol-water}/silicone rubber system with an identical set of concentration dependent equilibrium and diffusive parameters. The generic model provides a solid framework for the theoretical description of diverse processes employing a nonporous polymer as the selective separation barrier.