Water vapor condensation on superhydrophobic surfaces has received much attention in recent years because of its ability to shed water droplets at length scales 3 decades smaller than the capillary length (∼1 mm) via coalescence-induced droplet jumping. Jumping-droplet condensation has been demonstrated to enhance heat transfer, anti-icing, and self-cleaning efficiency and is governed by the theoretical inertial-capillary scaled jumping speed (U). When two droplets coalesce, the experimentally measured jumping speed (Uexp) is fundamentally limited by the internal fluid dynamics during the coalescence process (Uexp < 0.23U). Here, we theoretically and experimentally demonstrate multidroplet (>2) coalescence as an avenue to break the two-droplet speed limit. Using side-view and top-view high-speed imaging to study more than 1000 jumping events on a copper oxide nanostructured superhydrophobic surface, we verify that droplet jumping occurs as a result of three fundamentally different mechanisms: (1) coalescence between two droplets, (2) coalescence among more than two droplets (multidroplet), and (3) coalescence between one or more droplets on the surface and a returning droplet that has already departed (multihop). We measured droplet-jumping speeds for a wide range of droplet radii (5-50 μm) and demonstrated that while the two-droplet capillary-to-inertial energy conversion mechanism is not identical to that of multidroplet jumping, speeds above the theoretical two-droplet limit (>0.23U) can be achieved. However, we discovered that multihop coalescence resulted in drastically reduced jumping speeds (≪0.23U) due to adverse momentum contributions from returning droplets. To quantify the impact of enhanced jumping speed on heat-transfer performance, we developed a condensation critical heat flux model to show that modest jumping speed enhancements of 50% using multidroplet jumping can enhance performance by up to 40%. Our results provide a starting point for the design of enhanced-performance jumping-droplet surfaces for industrial applications.

Droplet nucleation and condensation are ubiquitous phenomena in nature and industry. Over the past century, research has shown dropwise condensation heat transfer on nonwetting surfaces to be an order of magnitude higher than filmwise condensation heat transfer on wetting substrates. However, the necessity for nonwetting to achieve dropwise condensation is unclear. This article reports stable dropwise condensation on a smooth, solid, hydrophilic surface ( a = 38°) having low contact angle hysteresis (<3°). We show that the distribution of nano-to micro-to macroscale droplet sizes (about 100 nm to 1 mm) for coalescing droplets agrees well with the classical distribution on hydrophobic surfaces and elucidate that the wettability-governed dropwise-to-filmwise transition is mediated by the departing droplet Bond number. Our findings demonstrate that achieving stable dropwise condensation is not governed by surface intrinsic wettability, as assumed for the past eight decades, but rather, it is dictated by contact angle hysteresis.

With the recent advances in surface fabrication technologies, condensation heat transfer has seen a renaissance. Hydrophobic and superhydrophobic surfaces have all been employed as a means to enhance condensate shedding, enabling micrometric droplet departure length scales. One of the main bottlenecks for achieving higher condensation efficiencies is the difficulty of shedding sub-10 μm droplets due to the increasing role played by surface adhesion and viscous limitations at nanometric length scales. To enable ultraefficient droplet shedding, we demonstrate hierarchical condensation on rationally designed copper oxide microhill structures covered with nanoscale features that enable large (∼100 μm) condensate droplets on top of the microstructures to coexist with smaller (<1 μm) droplets beneath. We use high-speed optical microscopy and focal plane shift imaging to show that hierarchical condensation is capable of efficiently removing sub-10-μm condensate droplets via both coalescence and divergent-track-assisted droplet self-transport toward the large suspended Cassie−Baxter (CB) state droplets, which eventually shed via classical gravitational shedding and thereby avoid vapor side limitations encountered with droplet jumping. Interestingly, experimental growth rate analysis showed that the presence of large CB droplets accelerates individual underlying droplet growth by ∼21% when compared to identically sized droplets not residing beneath CB droplets. Furthermore, the steady droplet shedding mechanism shifted the droplet size distribution toward smaller sizes, with ∼70% of observable underlying droplets having radii of ≤5 μm compared to ∼30% for droplets growing without shading. To elucidate the overall heat transfer performance, an analytical model was developed to show hierarchical condensation has the potential to break the limits of minimum droplet departure size governed by finite surface adhesion and viscous effects through the tailoring of structure length scale, coalescence, and self-transport. More importantly, abrasive wear tests showed that hierarchical condensation has good durability against mechanical damage to the surface. Our study not only demonstrates the potential of hierarchical condensation as a means to break the limitations of droplet jumping, it develops rational design guidelines for micro/nanostructured surfaces to enable excellent heat transfer performance as well as extended durability.

Understanding the fundamental mechanisms governing vapor condensation on nonwetting surfaces is crucial to a wide range of energy and water applications. In this paper, we reconcile classical droplet growth modeling barriers by utilizing two-dimensional axisymmetric numerical simulations to study individual droplet heat transfer on nonwetting surfaces (90° < θa < 170°). Incorporation of an appropriate convective boundary condition at the liquid-vapor interface reveals that the majority of heat transfer occurs at the three phase contact line, where the local heat flux can be up to 4 orders of magnitude higher than at the droplet top. Droplet distribution theory is incorporated to show that previous modeling approaches underpredict the overall heat transfer by as much as 300% for dropwise and jumping-droplet condensation. To verify our simulation results, we study condensed water droplet growth using optical and environmental scanning electron microscopy on biphilic samples consisting of hydrophobic and nanostructured superhydrophobic regions, showing excellent agreement with the simulations for both constant base area and constant contact angle growth regimes. Our results demonstrate the importance of resolving local heat transfer effects for the fundamental understanding and high fidelity modeling of phase change heat transfer on nonwetting surfaces.

Frost spreads on nonwetting surfaces during condensation frosting via an interdroplet frost wave. When a supercooled condensate water droplet freezes on a hydrophobic or superhydrophobic surface, neighboring droplets still in the liquid phase begin to evaporate. Two possible mechanisms govern the evaporation of neighboring water droplets: (1) The difference in saturation pressure of the water vapor surrounding the liquid and frozen droplets induces a vapor pressure gradient, and (2) the latent heat released by freezing droplets locally heats the substrate, leading to evaporation of nearby droplets. The relative significance of these two mechanisms is still not understood. Here, we study the significance of the latent heat released into the substrate by freezing droplets, and its effect on adjacent droplet evaporation, by studying the dynamics of individual water droplet freezing on aluminum-, copper-, and glass-based hydrophobic and superhydrophobic surfaces. The latent heat flux released into the substrate was calculated from the measured droplet sizes and the respective freezing times ( t), defined as the time from initial ice nucleation within the droplet to complete droplet freezing. To probe the effect of latent heat release, we performed three-dimensional transient finite element simulations showing that the transfer of latent heat to neighboring droplets is insignificant and accounts for a negligible fraction of evaporation during microscale frost wave propagation. Furthermore, we studied the effect of substrate thermal conductivity on the transfer of latent heat transfer to neighboring droplets by investigating the velocity of ice bridge formation. The velocity of the ice bridge was independent of the substrate thermal conductivity, indicating that adjacent droplet evaporation during condensation frosting is governed solely by vapor pressure gradients. This study not only provides key insights into the individual droplet freezing process but also elucidates the negligible role of latent heat released into the substrate during frost wave propagation.