Shrinking instability of toroidal droplets

Abstract

Significance Liquid doughnuts or tori exhibit an inherent instability consisting in the shrinking of their “hole.” For sufficiently thick tori, this behavior is the only route for the torus to become spherical and thus minimize the area for a given volume. Of note, this shrinking instability is not completely understood. In this work, we experimentally determine the flow field of toroidal droplets as they shrink and account for our observations by solving the relevant equations of motion in toroidal coordinates. We find that four modes, out of the many possible ones, are needed to successfully account for all of the relevant features in the experiment. These results highlight the rich fluid mechanics that results in the presence of interfaces with nonconstant mean curvature.