Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects that affect jumping behavior, including droplet size mismatch, droplet−surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius R i and surface structure length scale L. For small droplets (R i ≤ 5L), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80°. Surface structure length scale effects were shown to vanish for large droplets (R i > 5L). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction was observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping continued...

Superhydrophobicity has received significant attention over the past three decades owing to its significant potential in self-cleaning and anti-icing surfaces, drag reduction, energy harvesting devices, anti-bacterial coatings, and enhanced heat transfer applications. Superhydrophobicity can be obtained via the roughening of an intrinsically hydrophobic surface, the creation of a re-entrant geometry, or by the roughening of a hydrophilic surface followed by a conformal coating of a hydrophobic material. Intrinsically hydrophobic surfaces have poor thermophysical properties such as thermal conductivity, and thus are not suitable for heat transfer applications. Re-entrant geometries, although versatile in applications where droplets are deposited, break down during spatially random nucleation and flood the surface. Chemical functionalization of rough metallic substrates, although promising, is not utilized due to the poor durability of conformal hydrophobic coatings. Here we develop a radically different approach to achieve stable superhydrophobicity. By utilizing laser processing and thermal oxidation of copper (Cu) to create a high surface energy hierarchical copper oxide (CuO), followed by repeatable and passive atmospheric adsorption of hydrophobic volatile organic compounds (VOCs), we show that stable superhydrophobicity with apparent advancing contact angles ≈ 160° and contact angle hysteresis as low as ≈ 20° can be achieved. We exploit the structure length scale and structure geometry dependent VOC adsorption dynamics to rationally design CuO nanowires with enhanced superhydrophobicity. To gain an understanding of the VOC adsorption physics, we utilized X-Ray Photoelectron and Ion Mass Spectroscopy to identify the chemical species deposited on our surfaces in two distinct locations: Urbana, IL, USA and Beijing, China. To test the stability of the atmosphere-mediated superhydrophobic surfaces during heterogeneous nucleation, we used high-speed optical microscopy to demonstrate the occurrence of dropwise condensation and stable coalescenceinduced droplet jumping. Our work not only provides rational design guidelines for developing passively-durable superhydrophobic surfaces with excellent flooding-resistance and self-healing capability, but also sheds light on the key role played by the atmosphere in governing wetting.

The past few decades have seen substantial effort for the design and manufacturing of hydrophobic structured surfaces for enhanced steam condensation in water-based applications. Such surfaces promote dropwise condensation and easy droplet removal. However, less priority has been given to applications utilizing low-surface-tension fluids as the condensate. Lubricant-infused surfaces (LISs) or slippery liquid-infused porous surfaces (SLIPSs) have recently been developed, where the atomically smooth, defect-free slippery surface leads to reduced pinning of water droplets and omniphobic characteristics. The remarkable results of LISs and SLIPSs with a range of working fluid droplets give hope of their viability with low-surface-tension condensates. However, the presence of the additional liquid in the form of lubricant brings other issues to consider. Here, in an effort to study the dropwise condensation potential of LISs and SLIPSs, we investigate the miscibility of a range of low-surface-tension fluids with widely used lubricants in LIS and SLIPS design. We consider a wide range of condensate surface tensions (12-73 mN/m) and different categories of lubricants with varied viscosities (5-2700 cSt), namely, fluorinated Krytox oils, hydrocarbon silicone oils, mineral oil, and ionic liquids. In addition, we use both theory and pendant drop experiments to predict the cloaking behavior of the lubricants and immiscible condensate working fluid pairs. Our work not only shows that careful attention must be paid to lubricant-condensate selection to create long-lasting LISs or SLIPSs but also develops lubricant selection design guidelines for stable LISs and SLIPSs for enhanced condensation in applications utilizing low-surface-tension working fluids.

This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of realworld multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover,

Droplet transport on, and shedding from, surfaces is ubiquitous in nature and is a key phenomenon governing applications including biofluidics, self-cleaning, anti-icing, water harvesting, and electronics thermal management. Conventional methods to achieve spontaneous droplet shedding enabled by surface−droplet interactions suffer from low droplet transport velocities and energy conversion efficiencies. Here, by spatially confining the growing droplet and enabling relaxation via rationally designed grooves, we achieve single-droplet jumping of micrometer and millimeter droplets with dimensionless jumping velocities v* approaching 0.95, significantly higher than conventional passive approaches such as coalescence-induced droplet jumping (v* ≈ 0.2−0.3). The mechanisms governing single-droplet jumping are elucidated through the study of groove geometry and local pinning, providing guidelines for optimized surface design. We show that rational design of grooves enables flexible control of droplet-jumping velocity, direction, and size via tailoring of local pinning and Laplace pressure differences. We successfully exploit this previously unobserved mechanism as a means for rapid removal of droplets during steam condensation. Our study demonstrates a passive method for fast, efficient, directional, and surface-pinning-tolerant transport and shedding of droplets having micrometer to millimeter length scales.

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.

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Dropwise condensation (DWC) on non-wetting surfaces has remarkable potential to enhance heat transfer performance compared to filmwise condensation on wetting substrates. In this article, we discuss important recent developments and challenges in the field of DWC, including durability of DWC-promoting coatings, DWC of low surface tension fluids, physical mechanisms governing DWC, unconventional methods to achieve DWC, and promising metrology techniques for DWC. We end the article by providing a road map detailing where we believe the community should direct both fundamental and applied efforts in order to solve the identified century-old challenges that limit DWC implementation.