No abstract

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.

Nanodroplets residing near wedges or edges of solid substrates exhibit a disjoining pressure induced dynamics. Our nanoscale hydrodynamic calculations reveal that non-volatile droplets are attracted or repelled from edges or wedges depending on details of the corresponding laterally varying disjoining pressure generated, e.g., by a possible surface coating.

We investigate the dynamics of nanoscale droplets in the vicinity of chemical steps which separate parts of a substrate with different wettabilities. Due to long-ranged dispersion forces, nanodroplets positioned on one side of the step perceive the different character of the other side even at a finite distance from the step, leading to a dynamic response. The direction of the ensuing motion of such droplets depends not only on the difference between the equilibrium contact angles on these two parts but in particular on the difference between the corresponding Hamaker constants. Therefore, the motion is not necessarily directed toward the more wettable side and can also be different from that of droplets which span the step.