Variational approach to droplet motion on uneven solid surfaces, including contact line dynamics and evaporation

TL;DR

This paper develops a variational framework for modeling droplet motion on uneven surfaces, incorporating contact line dynamics and evaporation, grounded in Onsager's principle, applicable to overdamped isothermal conditions.

Contribution

It introduces a variational formulation for droplet dynamics on complex surfaces, unifying contact line behavior and evaporation effects within a thermodynamically consistent approach.

Findings

Reproduces known contact line dynamics results.

Analyzes droplet pinning and sliding on inclined corrugated surfaces.

Framework naturally incorporates equilibrium properties.

Abstract

We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle. The theory applies in the isothermal overdamped-dynamics limit. We apply this general approach to obtain several well-known results on contact line dynamics and to study drops pinning and sliding on inclined corrugated surfaces. This approach constructs the dynamical equations starting from the free energy of the system and therefore has the advantage that it naturally incorporates the correct equilibrium properties.