It was recently discovered that condensation growing on a nanostructured superhydrophobic surface can spontaneously jump off the surface, triggered by naturally occurring coalescence events. Many reports have observed that droplets must grow to a size of order 10 μm before jumping is enabled upon coalescence; however, it remains unknown how the critical jumping size relates to the topography of the underlying nanostructure. Here, we characterize the dynamic behavior of condensation growing on six different superhydrophobic nanostructures, where the topography of the nanopillars was systematically varied. The critical jumping diameter was observed to be highly dependent upon the height, diameter, and pitch of the nanopillars: tall and slender nanopillars promoted 2 μm jumping droplets, whereas short and stout nanopillars increased the critical size to over 20 μm. The topology of each surface is successfully correlated to the critical jumping diameter by constructing an energetic model that predicts how large a nucleating embryo needs to grow before it can inflate into the air with an apparent contact angle large enough for jumping. By extending our model to consider any possible surface, it is revealed that properly designed nanostructures should enable nanometric jumping droplets, which would further enhance jumping-droplet condensers for heat transfer, antifogging, and antifrosting applications.

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Tuning Superhydrophobic Nanostructures to Enhance Jumping-Droplet Condensation

Liquid-Vapor Phase-Change Heat Transfer on Functionalized Nanowired Surfaces and Beyond

It was recently discovered that condensation growing on a nanostructured superhydrophobic surface can spontaneously jump off the surface, triggered by naturally occurring coalescence events. Many reports have observed that droplets must grow to a size of order 10 μm before jumping is enabled upon coalescence; however, it remains unknown how the critical jumping size relates to the topography of the underlying nanostructure. Here, we characterize the dynamic behavior of condensation growing on six different superhydrophobic nanostructures, where the topography of the nanopillars was systematically varied. The critical jumping diameter was observed to be highly dependent upon the height, diameter, and pitch of the nanopillars: tall and slender nanopillars promoted 2 μm jumping droplets, whereas short and stout nanopillars increased the critical size to over 20 μm. The topology of each surface is successfully correlated to the critical jumping diameter by constructing an energetic model that predicts how lar...

Tuning Superhydrophobic Nanostructures To Enhance Jumping-Droplet Condensation.

Hotspot cooling is critical to the performance and reliability of electronic devices, but existing techniques are not very effective in managing mobile hotspots. We report a hotspot cooling technique based on a jumping-drop vapor chamber consisting of parallel plates of a superhydrophilic evaporator and a superhydrophobic condenser, where the working fluid is returned via the spontaneous out-of-plane jumping of condensate drops. While retaining the passive nature of traditional vapor-chamber heat spreaders (flat-plate heat pipes), the jumping-drop technique offers a mechanism to address mobile hotspots with a pathway toward effective thermal transport in the out-of-plane direction.

Hotspot cooling with jumping-drop vapor chambers

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 Ri and surface structure length scale L. For small droplets ( Ri ≤ 5 L), 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 ( Ri > 5 L). 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 direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions but provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.

Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties

Solid heat spreaders, particularly those made of copper or graphite, are often benchmark solutions for hotspot thermal management In this paper, we present exact and approximate analytical solutions of steady-state hotspot cooling with a planar heat spreader, which is subjected to adiabatic conditions except for a hotspot centered at the top surface and a constant temperature at the bottom surface The approximate solution bridges exact solutions at two limits of hotspot size: infinitesimal hotspot at the center and uniform heat flux across the spreader The approximate solution accounts for variable hotspot size and anisotropic thermal conductivity in a compact form, which is useful for estimating thermal parameters such as conduction shape factor and effective thermal conductivity

Kris F. Wiedenheft

Papers

Hotspot cooling with jumping-drop vapor chambers

Hotspot Size Effect on Conductive Heat Spreading