Competing Bifurcations Determine Symmetry Breaking During Droplet Snaps on Smooth Patterned Surfaces

The shape and stability of a droplet in contact with a solid surface is affected by the chemical composition and topography of the solid, and crucially, by the droplet's size. During a variation in size, most often observed during evaporation, droplets on smooth patterned surfaces can undergo sudden shape and position changes. Such changes, called snaps, are prompted by the surface pattern and arise from fold and pitchfork bifurcations which respectively cause symmetric and asymmetric motions. Yet, which type of snap is likely to be observed is an open fundamental question that has relevance in the rational design of surfaces for managing droplets. Here we show that the likelihood of observing symmetric or asymmetric snaps depends on the distance between fold and pitchfork bifurcation points and on how this distance varies for droplets that grow or shrink in size on surfaces patterned with a smooth topography. Our results can help develop strategies to control droplets by exploiting smooth surface patterns but also have broader relevance in situations where different types of bifurcations compete in determining the stability of a system, for instance in snap-through instabilities observed in elastic media.