Nondestructive high-throughput screening of nanopore geometry in porous membranes by imbibition

A fluid dynamic model for imbibition into closed-end, axisymmetric pores having diameters that change as a function of the pore depth is presented. Despite the fact that liquid invasion into nonbranched closed-end pores is characterized by a wealth of different transient and/or metastable nonequilibrium stages related to precursor film formation, we show that a simple hydraulic model accounting for geometry- and air compression-induced deviations from classical Lucas-Washburn dynamics precisely describes the imbibition dynamics except at the late stage. The model was validated by laser interferometry experiments with submillisecond temporal resolution. Imbibition of three simple liquids (isopropanol, ethanol, and hexane) into self-ordered anodic alumina membranes containing arrays of parallel closed-end nanopores characterized by slight conicity was studied. The model provides an improved description of nanoscale fluid dynamics and allows geometric characterization of nanoporous membranes by their imbibition kinetics accounting for the back pressure of the compressed gas. Thus, a precise calibration of porous membranes with simple liquids becomes possible, and changes in the mean pore diameter as a function of the pore depth can be assessed.