Modeling the abnormally slow infiltration rate in mesoporous films

Mesoporous films have been shown to exhibit striking behaviors in capillary-driven infiltration experiments. The process has been shown to follow classical Lucas-Washburn dynamics, but the effective pore radius has been calculated from hydrodynamic resistance considerations to be orders of magnitude lower than measured pore dimensions. In addition, the infiltration rate has been observed to decrease with increasing pore diameter, in contrast to the expected trend for capillary-like pores. Here, we present a simple model accounting for the mechanism behind these anomalous effects. We found the infiltration rate to be inversely proportional to the cubed ratio of pore to neck size. This physical scaling correctly modeled both the magnitude of the infiltration rate and its variation with pore diameters, for a wide range of experimental data. The model established a connection between capillary filling dynamics and nanoscale pore structure, which is of practical interest for the design and characterization of mesoporous films.