Membrane technology is of significant importance in water treatment applications, and also gaining momentum in other separations due to advantages such as environmentally friendly operation, less complex and lower-cost operating conditions compared to alternative options. To provide for sustainable and efficient membrane-based applications, the selection of appropriate membranes is crucial. Such a selection is based on membrane characterization, which offers critical information on parameters such as porosity, average pore size and pore size distribution (PSD). The two main classes of characterization methods are direct and indirect, with the latter having a theoretical basis, being more affordable, and also generally being able to characterize larger membrane areas compared to the direct techniques. This study reviews the indirect membrane characterization methods, the key theoretical backgrounds of which are the Young-Laplace equation, Kelvin equation, Gibbs-Thomson equation, and spectroscopy-based equations. The mathematical details are first presented, followed by the measurement details and experimental requirements, and finally the studies on membrane characterization via indirect methods. The advantages and limitations of each method are also discussed. For a complete understanding of the membrane, indirect methods may need to be complemented with direct ones and also with appropriate retention experiments of the feeds of interest.

To comparatively assess the Evapoporometry (EP) technique vis-à-vis the Liquid-Liquid Displacement Porosimetry (LLDP) technique, the pore size distributions, mean pore diameters (d_avg) and porosities of five polymeric (namely, nylon, PES, PTFE, PET and PVDF) and one inorganic (namely, alumina) UF/tight MF membranes were quantified by both techniques. For all the membranes, the pore size ranges were generally narrower and the pore size distributions had distinctive peaks for the LLDP technique. For the nylon, PES and PTFE membranes, the d_avg values obtained from the two techniques agreed well. However, for the PET and PVDF membranes, the differences were twofold due to the higher pressure needed for the LLDP tests. Specifically, for PET, the d_avg value obtained via EP was half that via LLDP, because the higher pressure compacted the lower mechanical strength polymer, leading to pore closure. On the other hand, for PVDF, due to the rubber nature, the higher pressure caused the pores to be stretched, leading to larger pores. As for the alumina membrane, because of the more ideal cylindrical pores, the d⁴-weighting of the LLDP measurement gave a greater d_avg value than that of the d²-weighting of the EP measurement. Also, porosity measurements were erroneous for LLDP if the active layer cannot be precisely quantified. With respect to MWCO, while EP does not explicitly quantify this, the LLDP generally over-estimated the values, because of the errors associated with the measurement of the first (largest) pores at the lowest pressures.