Gradient dynamics model for chemically driven running drops

TL;DR

This paper develops a thermodynamically consistent gradient dynamics model for chemically driven, self-propelling drops on substrates, highlighting the role of chemical reactions and wettability contrasts in sustained motion.

Contribution

It introduces a novel gradient dynamics framework for chemically driven drops, including a reduced model capturing self-propulsion due to wettability changes.

Findings

Drops can self-propel due to wettability contrast maintained by chemical reactions.

The model predicts drift-pitchfork bifurcations leading to running drops.

Numerical simulations demonstrate sustained drop motion driven by chemical potential differences.

Abstract

We present a thermodynamically consistent model for chemically driven running drops on a solid substrate with reversible substrate adsorption of a wettability-changing chemical species. We consider drops confined to a vertical gap, thereby allowing us to first obtain a gradient dynamics description of the closed system, corresponding to a set of coupled dynamical equations for the drop profile and the chemical concentration profiles of species on the substrate and in both fluids (drop, ambient medium). Chemostatting the species in the drop and the ambient medium, we then derive a reduced model for the dynamics of the drop and the adsorbate on the substrate. When the externally imposed chemical potentials are distinct, the system is driven away from thermodynamic equilibrium, allowing for sustained drop self-propulsion across the substrate due to a wettability contrast maintained by chemical reactions. We numerically study the resulting running drops and show how they emerge from drift-pitchfork bifurcations.