Interface-dominated sliding compound drops

TL;DR

This study models and analyzes the behavior of sliding compound drops of immiscible liquids on inclined surfaces, focusing on their configurations, velocities, and dynamic angles using a mesoscopic hydrodynamic two-layer approach.

Contribution

It provides a detailed investigation of the static and dynamic properties of compound drops, including their bifurcation behavior and dependence on physical parameters.

Findings

Drop velocity depends on inclination and interface profiles.

Stationary configurations are influenced by volume and viscosity ratios.

Time-periodic behaviors occur outside the stationary existence range.

Abstract

We investigate compound drops composed of two immiscible nonvolatile partially wetting liquids that slide down an inclined homogeneous smooth solid substrate based on a mesoscopic hydrodynamic two-layer model in full-curvature formulation. First, drops of one liquid stationarily sliding on a layer of the other liquid are briefly investigated with a focus on the dependence of drop velocity and interface profiles on inclination and mean thickness of the adaptive substrate. Then, stationary sliding compound drops are studied with a focus on the dependence of their configuration, velocity, dynamic Young and Neumann angles on three control parameters, namely, the inclination, the volume ratio and the viscosity ratio. The reasons for the encountered dependence of the velocity on configuration are clarified based on a discussion of the lateral dissipation profile. Finally, we briefly consider the time-periodic fusion-overtaking-splitting behavior found outside the existence range of the stationary sliding compound drops as determined by saddle-node bifurcations.