Abstract:
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.
