Mathematical modeling of the pressure-driven performance of McMaster pore-filled membranes

The McMaster Pore-filled (MacPF) membranes are a new class of nanofiltration membranes prepared by co-polymerizing a polyelectrolyte (PEL) gel into a microporous substrate. The PEL gives unique characteristics to the MacPF membranes that make them suitable for water softening and fractionation.; The main objective of this investigation is to develop a procedure that can be used to design MacPF membranes for specific applications from theory a priori. This procedure involves the combination of two mechanistic models. The first model (gel model) predicts the physicochemical structure (i.e., membrane parameters) of the pore-filling gel (Mika and Childs, 2001). The second model (transport model) can be used in combination with the parameters predicted by the gel model to predict the pressure-driven transport of the MacPF membranes. The transport model is developed in this dissertation.; The design procedure and mathematical models outlined in here would be the first time a membrane design is attempted using only theoretical arguments.; The membrane transport model is a pseudo 2-dimensional transport model that consists of the extended Nernst-Planck equation (viscous flow and frictional model), a modified Poisson Boltzmann equation, and hydrodynamic calculations to relate the frictional and steric forces to the membrane structure. The model has three fitting parameters that describe four structural properties of the membrane: pore radius, pure water permeability, surface charge density and the ratio of effective membrane thickness to water content.; The model successfully predicts and explains the performance of the MacPF membranes as well as one commercial thin-film composite membrane tested simultaneously. The model parameters estimated here are statistically significant and are comparable to previous results (Garcia-Aleman, 1998).; A comparison of the performance of the commercial and MacPF membrane was performed using experimental data and the transport model. This analysis shows that the rejection and transport mechanisms are the same in the commercial and MacPF membranes. Convection, diffusion and electromigration are the main mechanisms of solute transport. However, their contribution is different for each type of membrane. Solute rejection in NF membranes is determined primarily by steric and electrostatic effects. For the MacPF membranes separation and selectivity are primarily determined by the latter. The contribution of steric effects to rejection is significantly smaller compared to commercial membranes.; Additionally, the membrane parameters were estimated using both the gel and transport models. At this point, the results obtained separately from the two models show similar parameter estimates and separation. However, additional work has to be done to improve the agreement between the models before the procedure outline here can be used to truly tailor-make the MacPF membranes.