Modeling liquid penetration into porous materials based on substrate and liquid surface energies

The widely used Lucas-Washburn (LW) equation depends on the contact angle as the driving force for liquid penetration. However, the contact angle depends on both, the liquid and the substrate. It would be desirable to predict the penetration into porous materials, without the requirement to measure the solid-liquid interaction. Here, we propose a novel modeling approach for liquid penetration from mutually independent substrate- and liquid properties. For this purpose, the contact angle in the LW-equation is replaced by polar and dispersive surface energies, utilizing the theories of Owens-Wendt-Rabel-Kaelble (OWRK), Wu, or van Oss, Good, Chaudhury (vOGC).

The proposed modelling approach is validated exhaustively by measuring penetration speed for 96 substrate-liquid pairings and comparing the results to model predictions based on literature- and measured data.

Liquid absorption is predicted very well (R² = 0.8-0.9) with all three approaches, spanning a wide range of penetration speed, substrate- and liquid surface energy, viscosity, and pore size. The models for liquid penetration without measurement of solid-liquid interaction (contact angle) performed well. Modeling calculations are entirely relying on physical data of the solid and the liquid phase (surface energies, viscosity and pore size), which can be measured or retrieved from databases.