Effects of membrane morphology on the rejection of oil droplets: Theoretical analysis based on network modeling

Membrane-based treatment is emerging as an effective way to remove the oil and reclaim fresh water from an oil-in-water emulsion. The mechanisms underlying the complex interactions between the oil droplets and the porous membrane substructures, however, are not fully understood, which may hinder our effort to design novel membranes. The objective of this study is to establish a correlation between the rejection of oil droplets and the membrane morphology via a theoretical approach based on network modeling. The porous membrane was numerically discretized into a system of cubic unit cells, whose coordinate directions were exploited to derive a bond-node structure. Numerical algorithms based on the finite element analysis and a 'maze' solver were developed to explore the network topology in a complementary way. It was established by the network modeling that the trans-droplet pressure (TDP) should be markedly less than the trans-membrane pressure (TMP) when the porous structure is highly connected; the surface coverage could have a significant impact on the distribution of the TDPs. Instead of assuming that the membrane be composed of straight-through cylindrical pores, a critical pressure model was integrated with the network modeling to predict the initial rejection of oil droplets as the membrane morphology was topologically varied. The modeling results were then exploited to reconcile the critical pressure model with the experimental data in the literature. To conclude, the network model would offer a powerful tool that could help understand mechanisms for the rejection of oil droplets and thus enhance the performance of membrane-based oily wastewater treatment.