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.
Highlights
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
A promising exemplar of such systems, revealed in recent work by Denkov et al [3], is small, micron-sized oil droplets suspended in an aqueous surfactant solution: as the temperature of the solution is slowly lowered towards the bulk freezing point of the oil, the initially spherical droplets undergo remarkable shape transformations
The picture that emerges from this analysis is that the initial deformations of the spherical droplets to polyhedral shapes may be driven by the topological defects and the associated elastic scalings [9,10] resulting from the freezing of a planar, multi- or monomolecular layer, before the formation of tubules of rotator phase stretches and flattens the droplets
Summary
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. 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.
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