Search

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.

The design of paper-based assays that integrate passive pumping requires a precise programming of the fluid transport, which has to be encoded in the geometrical shape of the substrate. This requirement becomes critical in multiple-step processes, where fluid handling must be accurate and reproducible for each operation. The present work theoretically investigates the capillary imbibition in paper-like substrates to better understand fluid transport in terms of the macroscopic geometry of the flow domain. A fluid dynamic model was derived for homogeneous porous substrates with arbitrary cross-sectional shapes, which allows one to determine the cross-sectional profile required for a prescribed fluid velocity or mass transport rate. An extension of the model to slit microchannels is also demonstrated. Calculations were validated by experiments with prototypes fabricated in our lab. The proposed method constitutes a valuable tool for the rational design of paper-based assays.