Evaporation kinetics of sessile droplets morphed by substrate curvature

Abstract

In this article, we report the experimental evidence and an analytical model for the first time to predict the evaporation kinetics of sessile droplets seated on generic curved surfaces, either concave or convex. We appeal to the steady state, isothermal vapor diffusion theory, and incorporate conditions suitable to the geometry of curved substrates in a toroidal coordinate system, which is inherently different and more complicated than flat surfaces. We portray the mannerism in which the nature and magnitude of the curvature may dictate the evaporation behavior compared to a flat substrate. To validate the analytical model, we experimentally delineate the droplet evaporation phenomenon under the influence of substrate curvature. Convex cylinders and concave grooves of different radii have been employed for this purpose, and optical diagnostics of the droplet profile has been carried out to monitor evolution of the evaporation progress. Our model predicts that substrate convexity leads to substantial increase in evaporation rates due to augmented vapor diffusion domain over the liquid–vapor interface, whereas on a concave surface there is a decrease in evaporation rates due to droplet confinement phenomenon. The present model also addresses the fact that on the concave surface, the evaporation rate is not directly governed by substrate curvature, as discussed in the literature. The predictions from the model are found to be in good agreement with our detailed experimental observations.