Pore wall rugosity: The role of extended wetting contact line length during spontaneous liquid imbibition in porous media

Abstract

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed as a function of the square root of time using the traditional Lucas–Washburn equation. Commonly, to account for this deviation from uniform absorption into a single equivalent hydraulic capillary, many experimentalists propose an effective contact angle change. Such an assumption, however, challenges the consistency of constant surface energy and is difficult to justify physically. In this work, we consider rather the general term of the Wilhelmy wetting force in respect to the Washburn wetting line length, and apply a proposed increase in the liquid–solid contact line length provided by the introduction of surface meso and nanoscale rugosity in respect to the pore wall roughness. The experimental characteristic wetting line length is here defined via a relation between capillary condensation area, as measured independently using nitrogen gas (BET surface area determination plus BJH hysteresis analysis), and an equivalent capillary length containing the known saturation absorbed liquid volume. This model, constructed by applying the extended wetting contact line length to the equivalent hydraulic capillary observed at the longer timescale II imbibition, is applied for the initial timescale I imbibition rate whilst keeping the imbibition volume of the equivalent capillary tube constant. The longer timescale II imbibition is then subsequently defined traditionally by the smooth-walled equivalent hydrodynamic capillary, in which the surface rugosity is prefilled via a precursor liquid film supported further by liquid vapour condensation within the pore wall surface meso/nano-roughness. This two-stage model is compared with experimental liquid absorption data from a ground calcium carbonate porous compact and shown to provide good agreement. Using this concept, it is possible to unite the process of imbibition in complex porous media with a single equivalent hydraulic radius and an experimentally justified extended wetting line length to predict the imbibition rate of porous media on both the initial and longer timescales in cases where the imbibed liquid mass is low and the nano and microcapillary pressure of fine pore media far exceeds the effect of gravity.