Dynamic Roughness Ratio-Based Framework for Modeling Mixed Mode of Droplet Evaporation

Abstract

The spatiotemporal evolution of an evaporating sessile droplet and its effect on lifetime is crucial to various disciplines of science and technology. Although experimental investigations suggest three distinct modes through which a droplet evaporates, namely, the constant contact radius (CCR), the constant contact angle (CCA), and the mixed, only the CCR and the CCA modes have been modeled reasonably. Here we use experiments with water droplets on flat and micropillared silicon substrates to characterize the mixed mode. We visualize that a perfect CCA mode after the initial CCR mode is an idealization on a flat silicon substrate, and the receding contact line undergoes intermittent but recurring pinning (CCR mode) as it encounters fresh contaminants on the surface. The resulting increase in roughness lowers the contact angle of the droplet during these intermittent CCR modes until the next depinning event, followed by the CCA mode of evaporation. The airborne contaminants in our experiments are mostly loosely adhered to the surface and travel along with the receding contact line. The resulting gradual increase in the apparent roughness and hence the extent of CCR mode over CCA mode forces appreciable decrease in the contact angle observed during the mixed mode of evaporation. Unlike loosely adhered airborne contaminants on flat samples, micropillars act as fixed roughness features. The apparent roughness fluctuates about the mean value as the contact line recedes between pillars. Evaporation on these surfaces exhibits stick-jump motion with a short-duration mixed mode toward the end when the droplet size becomes comparable to the pillar spacing. We incorporate this dynamic roughness into a classical evaporation model to accurately predict the droplet evolution throughout the three modes, for both flat and micropillared silicon surfaces. We believe that this framework can also be extended to model the evaporation of nanofluids and the coffee-ring effect, among others.