The control of droplet transport on solid surfaces and associated wetting phenomena is important for a wide range of technological applications. Quite often the volume of the droplets is subject to external, time-dependent variations, such as e.g. when there is a mass exchange through the droplet interface (evaporation/condensation phenomena), or when droplets sit on porous materials so that liquid is absorbed through the pores. Under these conditions, an important issue is to understand how the properties of the solid substrate may affect the dynamics and shape of the droplet.
We consider droplets with a time-dependent volume on solid surfaces that have simple, macroscopic, and smooth (pinning-free) variations. We show that the droplet exhibits complex dynamics characterised by a series of sudden and fast lateral movements that occur at some specific values of the droplet size. These fast moves (snaps) are not a consequence of pinning but rather are triggered by a series of underlying bifurcations that obey a hierarchy dictated by properties of the solid surface. Because the evolution of the droplet as its volume changes is controlled by smooth (well-defined) variations of the solid, and not by surface roughness, these ideas can be used to achieve better control of droplet localisation and transport.