Symmetry-Breaking in Point-Heated Droplets

TL;DR

This paper analyzes the stability of thermo-capillary convection in point-heated droplets, showing that the base state is generally stable but off-center heating induces persistent vortices, aligning with experimental observations.

Contribution

It provides a theoretical stability analysis and 3D simulations of vortex formation in point-heated droplets, extending understanding of their fluid dynamics.

Findings

Base state is stable over wide parameters.

Off-center heating induces persistent vortices.

Simulations agree with experimental results.

Abstract

We investigate theoretically the stability of thermo-capillary convection within a droplet when heated by a point source from below. To model the droplet, we use a mathematical model based on lubrication theory. We formulate a base-state droplet profile, and we examine its respect to small-amplitude perturbations in the azimuthal direction. Such linear stability analysis reveals that the base state is stable across a wide parameter space. We carry out transient simulations in three spatial dimensions: the simulations reveal that when the heating is slightly off-centered with respect to the droplet center, vortices develop within the droplet. The vortices persist when the contact line is pinned. These findings are consistent with experimental studies of point-heated sessile droplets.