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

TL;DR

This paper introduces a mesoscopic gradient dynamics model for volatile liquid drops spreading on porous substrates, capturing coupled vapor, saturation, and height profiles with detailed free energy considerations.

Contribution

It presents a novel coupled hydrodynamic model for volatile drops on porous media, including saturation-dependent wettability and entropy effects.

Findings

Model predicts saturation halo formation

Illustrates drop spreading and imbibition behaviors

Analyzes sorption isotherm characteristics

Abstract

We present a mesoscopic hydrodynamic model for a spreading drop of volatile partially wetting liquid on a solid porous layer of small thickness. Thereby, evaporation takes place under strong confinement, i.e., we consider a drop that spreads on one of two parallel plates that form a narrow gap. Our gradient dynamics model describes the coupled dynamics of the vertically averaged vapor density profile, the drop height profile, and the vertically averaged saturation profile in the porous layer. The underlying free energy incorporates saturation-dependent wettability, capillarity of the drop and within the porous layer, air and vapor entropy, and an entropic contribution relevant close to complete filling of the porous layer. After developing the model we discuss the resulting sorption isotherm and illustrate typical drop spreading and imbibition behavior including the formation of a saturation halo within the porous substrate.