A Theory of Shape-Shifting Droplets

TL;DR

This paper develops a theoretical model to explain the shape transformations of cooled oil emulsion droplets, capturing the observed polygonal shapes and their evolution, including protrusions and topological changes.

Contribution

It introduces a geometric competition model between phase transition and surface tension, extending to three-dimensional structures and topological transitions.

Findings

Sequence of polygonal shapes matches experimental observations

Model predicts protrusion formation from vertices

Topological transitions in droplet structures are explained

Abstract

Recent studies of cooled oil emulsion droplets uncovered transformations into a host of flattened shapes with straight edges and sharp corners, driven by a partial phase transition of the bulk liquid phase. Here, we explore theoretically the simplest geometric competition between this phase transition and surface tension in planar polygons, and recover the observed sequence of shapes and their statistics in qualitative agreement with experiments. Extending the model to capture some of the three-dimensional structure of the droplets, we analyze the evolution of protrusions sprouting from the vertices of the platelets and the topological transition of a puncturing planar polygon.