Choice of DLVO approximation method for quantifying the affinity between latex particles and membranes

The Derjaguin-Landau-Verwey-Overbeek (DLVO) model, as well as the extended model (XDLVO), is popularly employed to quantify the interfacial interactions underlying membrane fouling. However, disagreements between membrane fouling extent and the interaction energies derived from DLVO or XDLVO models have been reported, which suggests gaps in the understanding. This study demonstrates that the DLVO approximation methods for predicting the interfacial foulant-membrane interaction are sensitive to the boundary condition assumptions (e.g., constant charge versus constant potential). In particular, while both the Poisson-Boltzmann (P–B) and linear superposition approximation (LSA) equations can quantify the electrostatics (EL) interaction energy component, the former assumes constant potential, while the latter additionally considers constant charge scenarios. The relative accuracy of these two equations were evaluated here. For dead-end filtration tests, flux decline trends, OCT analysis results and fouling model parameters were obtained. Regarding fouling of pristine PCTE membrane by latex particles of opposite charge signs, both the P–B and LSA equations contribute to predict relative fouling extents correctly. However, for the case of the BPEI-coated membrane, the P–B equation failed whereas the LSA equation gave good agreements. For cross-flow filtration tests in organic solvents, LSA also out-performed the P–B equation in providing more accurate predictions of membrane fouling. The results here highlight the shortcomings in the commonly used P–B equation and are expected to be potentially valuable in the development of better approximations for quantifying interfacial interaction energies.