Dynamics of droplets passing through bifurcation points

We study the problem of droplet dynamics on patterned surfaces. We focus on droplets subjected to an external driving process that slowly changes the droplet's volume, such as e.g., evaporation, and consider solid surfaces with smooth chemical variations. In our previous works, we reported the emergence of a hierarchy of bifurcation points arising when a droplet evaporates on smooth patterns. Building upon these results, here we use a combination of theory and simulations to study the dynamics of droplets passing through such bifurcation points, and how it depends on the physical properties of the system quantified in terms of the Ohnesorge and Bond numbers. We show that at each bifurcation point the droplet exhibits a rapid change in its position that we quantify in terms of its instantaneous velocity. We find that the maximum droplet's speed follows scaling relationships with the droplet's size, wetting strength, and Ohnesorge number. Our results indicate that the interplay between a phase change and surface wettability can be exploited to control the motion of droplets on patterned solids.