Superior mobility of droplets on lubricant-infused surfaces (LIS) has recently attracted significant attention for designing liquid-repellent surfaces. Unlike sessile droplets on flat surfaces wherein the contact line is easily visible in experiments, the contact line on LIS is masked by the lubricant meniscus, and special imaging techniques are required to visualize the hidden droplet−lubricant interface. Moreover, the overall shape deviates significantly from the spherical cap geometry even at very low droplet volumes. These difficulties necessitate the need to model interfaces in order to assess the effect of surface and fluid properties on LIS. In this work, we first numerically simulate the droplet shapes to show that at very small volumes, droplet−air and droplet−lubricant interfaces are constant mean curvature (CMC) interfaces. Moreover, we elucidate that these mean curvatures are related by the ratio of interfacial tensions of the droplet−air and the droplet−lubricant interfaces. These insights reduce the modeling of LIS interfacial profiles to a simplified geometric problem, which is solved using the parametric equations of CMC surfaces along with the angles of the Neumann triangle as the boundary conditions. Predicted profiles of the droplet−air interface as a spherical cap, the droplet−lubricant interface as a nodoid, and the lubricant−air interface as a catenoid/ nodoid show good agreement with experimental results in the literature. Importantly, we for the first time provide a framework, which accurately predicts the true contact angle at the hidden solid contact line by just using the information of the top spherical cap portion visible in experiments.
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.
It has been recently shown that small-volume droplets on lubricant-infused surfaces (LISs) can be analytically modeled using rotationally symmetric constant mean curvature (CMC) surfaces. While such an approach is available for noncloaked droplets, a similar approach is missing for cloaked droplets that are ubiquitous in a number of LIS-related applications. The presence of a thin cloaking film on the top spherical cap portion and its gradual transition to a bulk meniscus remain unaddressed for its implications on the interfacial profile of cloaked droplets. Here, we take into account the cloaking film tension and the disjoining pressure to present a mean curvature-based framework for modeling cloaked droplets on LISs. The transition of the bulk meniscus to a thin film is formulated as a transition regime, which is then modeled as a single imaginary point akin to the Neumann point of noncloaked droplets. We next show that the shape of a small droplet on a LIS essentially obeys a simple fundamental mean curvature relation that changes forms depending on the regimes of lubrication and whether the droplet is cloaked or noncloaked. We validate our framework with the droplet profiles recorded during the evaporation of cloaked droplets in our experiments, as well as those published in the literature. In addition, we also demonstrate the ability to model the shapes of floating droplets on LISs reported in the literature. In addition to quantifying the effect of disjoining pressure on interfacial profiles, we importantly unmask the behavior of the contact line, which is optically covered by the lubricant meniscus around the droplets on LISs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.