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

Simon Hartmann* and Uwe Thiele†

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Phys. Rev. Fluids 10, 014003 – Published 27 January, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.014003

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 the 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.

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Phys. Rev. Fluids 10, 014003– Published 27 January, 2025
  • Received 31 July 2024
  • Accepted 3 December 2024
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