Gradient dynamics model for drops of volatile liquid on a porous substrate

The article presents a mesoscopic hydrodynamic model for a spreading drop of volatile partially wetting liquid on a solid porous substrate. The model describes the coupled dynamics of the the three-phase system in terms of the drop height profile, the vertically averaged saturation profile in the porous layer and the vertically averaged vapor density above the substrate. Our approach is based on the gradient dynamics framework widely used for modeling thin liquid films. After developing the model, we discuss a selection of theoretical and numerical results, e.g., the resulting sorption isotherm or a simulation of coupled spreading, imbibition, and evaporation dynamics.