Coalescence-Induced Droplet Jumping for Electro-Thermal Sensing.

Jumping droplet condensation, whereby microdroplets (ca. 1-100 µm) coalescing on suitably designed superhydrophobic surfaces jump away from the surface, has recently been shown to have a 10× heat transfer enhancement compared to filmwise condensing surfaces. However, accurate measurements of the condensation heat flux remain a challenge due to the need for low supersaturations (<1.1) to avoid flooding. The low corresponding heat fluxes (<5 W/cm2) can result in temperature noise that exceeds the resolution of the measurement devices. Furthermore, difficulties in electro-thermal measurements such as droplet and surface electrostatic charge arise in applications where direct access to the condensing surface, such as in isolated chambers and small integrated devices, is not possible. Here, we present an optical technique that can determine the experimental electro-thermal parameters of the jumping droplet condensation process with high fidelity through the analysis of jumping droplet trajectories. To measure the heat flux, we observed the experimental trajectories of condensate droplets on superhydrophobic nanostructures and simultaneously matched them in space and time with simulated trajectories using the droplet dynamic equations of motion. Two independent approaches yielded mean heat fluxes of approximately 0.13 W/cm2 with standard deviations ranging from 0.047 to 0.095 W/cm2, a 79% reduction in error when compared with classical energy balance-based heat flux measurements. In addition, we analyzed the trajectories of electrostatically interacting droplets during flight and fitted the simulated and experimental results to achieve spatial and temporal agreement. The effect of image charges on a jumping droplet as it approaches the surface was analyzed, and the observed acceleration has been numerically quantified. Our work presents a sensing methodology of electro-thermal parameters governing jumping droplet condensation.

Nanostructured jumping-droplet thermal rectifier.

Analogous to an electrical rectifier, a thermal rectifier (TR) can ensure that heat flows in a preferential direction. In this paper, thermal transport nonlinearity is achieved through the development of a phase-change based TR comprising an enclosed vapor chamber having separated nanostructured copper oxide superhydrophobic and superhydrophilic functional surfaces. In the forward direction, heat transfer is facilitated through evaporation on the superhydrophilic surface and self-propelled jumping-droplet condensation on the superhydrophobic surface. In the reverse direction, heat transfer is minimized due to condensate film formation within the superhydrophilic condenser and inability to return the condensed liquid to the superhydrophobic evaporator. We examine the coupled effects of gap size, coolant mass, heat transfer rate, and applied electric field on the thermal performance of the TR. A maximum thermal diodicity, defined as the ratio of forward to reverse heat transfer, of 39 is achieved.

Numerical Simulation of Jumping Droplet Condensation.

Jumping droplet condensation has been shown to enhance heat transfer performance (≈100%) when compared to dropwise condensation by reducing the time-averaged droplet size (≈10 µm) on the condensing surface. Here, we develop a rigorous, three-dimensional numerical simulation of jumping droplet condensation to compute the steady-state time-averaged droplet size distribution. To characterize the criteria for achieving steady state, we use maximum radii (Rmax) tracking on the surface, showing that Rmax settles to an average in time once steady state is reached. The effects of the minimum jumping radius (0.1-10 µm), maximum jumping radius, apparent advancing contact angle (150-175°), and droplet growth rate were investigated. We provide a numerical fit for the droplet size distribution with an overall correlation coefficient greater than 0.995. The heat transfer performance was evaluated as a function of apparent contact angle and hydrophobic coating thickness, showing excellent agreement with prior experimentally measured values. Our simulations uncovered that droplet size mismatch during coalescence has the potential to impede the achievement of steady state and describe a new flooding mechanism for jumping droplet condensation. Our work not only develops a unified numerical model for jumping droplet condensation that is extendable to a plethora of other conditions but also demonstrates design criteria for nonwetting surface manufacture for enhanced jumping droplet condensation heat transfer.

Enhanced Jumping-Droplet Departure.

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.

A Comprehensive Model of Electric-Field-Enhanced Jumping-Droplet Condensation on Superhydrophobic Surfaces.

Superhydrophobic micro/nanostructured surfaces for dropwise condensation have recently received significant attention due to their potential to enhance heat transfer performance by shedding positively charged water droplets via coalescence-induced droplet jumping at length scales below the capillary length and allowing the use of external electric fields to enhance droplet removal and heat transfer, in what has been termed electric-field-enhanced (EFE) jumping-droplet condensation. However, achieving optimal EFE conditions for enhanced heat transfer requires capturing the details of transport processes that is currently lacking. While a comprehensive model has been developed for condensation on micro/nanostructured surfaces, it cannot be applied for EFE condensation due to the dynamic droplet-vapor-electric field interactions. In this work, we developed a comprehensive physical model for EFE condensation on superhydrophobic surfaces by incorporating individual droplet motion, electrode geometry, jumping frequency, field strength, and condensate vapor-flow dynamics. As a first step toward our model, we simulated jumping droplet motion with no external electric field and validated our theoretical droplet trajectories to experimentally obtained trajectories, showing excellent temporal and spatial agreement. We then incorporated the external electric field into our model and considered the effects of jumping droplet size, electrode size and geometry, condensation heat flux, and droplet jumping direction. Our model suggests that smaller jumping droplet sizes and condensation heat fluxes require less work input to be removed by the external fields. Furthermore, the results suggest that EFE electrodes can be optimized such that the work input is minimized depending on the condensation heat flux. To analyze overall efficiency, we defined an incremental coefficient of performance and showed that it is very high (∼10(6)) for EFE condensation. We finally proposed mechanisms for condensate collection which would ensure continuous operation of the EFE system and which can scalably be applied to industrial condensers. This work provides a comprehensive physical model of the EFE condensation process and offers guidelines for the design of EFE systems to maximize heat transfer.