Competing Bifurcations\nDetermine Symmetry Breaking\nDuring Droplet Snaps on Smooth Patterned Surfaces

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