Superhydrophobic Surface Curvature Dependence of Internal Advection Dynamics within Sessile Droplets

Sessile droplets seated on superhydrophobic surfaces are known to exhibit internal circulation patterns. The present article experimentally demonstrates and theoretically confirms, for the very first time, that the nature and velocity of the internal circulation in sessile droplets seated on superhydrophobic surfaces are strongly governed by the curvature of the surface and its directionality. Sessile droplets were rested on concave and convex superhydrophobic surfaces, and both with one curvature (cylindrical) and two curvatures (spherical) and varying droplet diameter to curve diameters were studied. Particle image velocimetry (PIV) was employed for flow visualization and quantification. It was observed that increasing convexity of the surface leads to deterioration in the velocity of advection within the droplet, whereas increasing concavity of the surface augments the velocity of circulation. A scaling model based on the effective curvature-modulated change in wettability has been put forward to predict the phenomenon, but it was found to be weak in deducing the circulation velocities. Consequently, potential flow theory is employed and the curvatures are approximated as equivalent wedges, with the rested droplet engulfing the wedge partly. Based on the curvature of the surface, the equivalent included wedge angle is deduced. Flow theory over wedged structures is employed to deduce the changes in the internal velocity in the presence of curved surfaces. The spatiotemporally averaged experimental velocities are found to conform to predictions from the proposed model, and good agreement between the theoretical predictions and experimental observations is achieved. The present findings may have strong implications in thermofluidic transport phenomena or multiphase transport processes at the interfacial and/or microscale.