A model of wetting of partially wettable porous solids by thin liquid films

- First principles model for predicting wetting dynamics of partially wettable porous solids.
- Case of thin film spreading and retraction into single and two “bottomless” pores presented.
- Work paves the way for development of wetting correlations using a “bottom-up” approach.

Wetting of partially wettable porous solids is encountered in many and diverse applications such as imbibition of liquid reactants into pores of porous catalysts and adsorbents in reactor beds, water vapor condensation on porous substrates like leaves, and spreading of liquid condensate on fuel cell membranes. This wetting is a combination of liquid spreading/retraction on the external surface and imbibition into the pores. In this paper, we establish the basic “building block” of this problem, i.e., the dynamics of wetting and retraction of a thin film in the vicinity of a single infinite pore of a porous solid and show the way forward by discussing the case of two such adjacent pores.The coupled process described by a unified and simple model derived from equations of motion under the lubrication approximation for thin film flow on the external surface and Hagen-Poiseulle flow inside the pores. A single final evolution equation tracks the externally wetted region in time by solving for the height of the liquid surface starting from an initial liquid droplet. The wetted area initially expands as the droplet spreads and then contracts as droplet retracts due to imbibition in the pore. The liquid surface becomes increasingly liable to rupture under the influence of intermolecular forces as it thins because of imbibition. The governing equation can track the rupture and subsequent dewetting of the surface also. The liquid morphology and kinetics of wetting show good agreement with the reported experiments implying that the description of a spreading liquid as a thin film indeed manages to incorporate the most important physics governing the internal wetting of liquids on porous substrates at the micro scale. The model shows a possible way to develop wetting correlations for larger scales of flow in industrial trickle bed reactors in a bottom-up manner.