Spreading with evaporation and condensation in one-component fluids

TL;DR

This study models the spreading dynamics of a liquid droplet on a substrate in a one-component fluid, highlighting how temperature variations influence evaporation, condensation, and film growth through a detailed hydrodynamic simulation.

Contribution

It introduces a dynamic van der Waals model to simulate the effects of inhomogeneous temperature and latent heat on droplet spreading and film formation.

Findings

Cooling promotes condensation and film growth near the edge.

Heating induces evaporation and can lead to droplet disappearance.

Latent heat creates temperature peaks near the film edge.

Abstract

We investigate the dynamics of spreading of a small liquid droplet in gas in a one-component simple fluid, where the temperature is inhomogeneous around 0.9Tc and latent heat is released or generated at the interface upon evaporation or condensation (with Tc being the critical temperature). In the scheme of the dynamic van der Waals theory, the hydrodynamic equations containing the gradient stress are solved in the axisymmetric geometry. We assume that the substrate has a finite thickness and its temperature obeys the thermal diffusion equation. A precursor film then spreads ahead of the bulk droplet itself in the complete wetting condition. Cooling the substrate enhances condensation of gas onto the advancing film, which mostly takes place near the film edge and can be the dominant mechanism of the film growth in a late stage. The generated latent heat produces a temperature peak or a hot spot in the gas region near the film edge. On the other hand, heating the substrate induces evaporation all over the interface. For weak heating, a steady-state circular thin film can be formed on the substrate. For stronger heating, evaporation dominates over condensation, leading to eventual disappearance of the liquid region.