Numerical Simulation of Jumping Droplet Condensation

Scaling Laws for the Influence of Gravity and Its Gradient on Dropwise Condensation: A Simulation Study

Gravity is essential for the shedding of condensed droplets on hydrophobic surfaces, whose influences on condensation parameters under unconventional gravity conditions remain unclear and are hard to probe through experiments. A simulation framework is designed here to investigate such phase-change processes. We find clear scaling laws between heat flux Q, residual volume V, gravitational acceleration g, and nucleation density N0 with Q ∼ g1/6N01/3 and V ∼ g-1/2N00. We also identify a critical gravitational acceleration determined by nucleation density, above which a counterintuitive trend emerges: the heat flux decreases with increasing gravitational acceleration. This deviation is attributed to the sharp decrease in heat flux contributed by droplets larger than the effective radius. In addition, for zero-gravity scenarios, a centrifugal strategy is proposed to simulate Earth's gravity by introducing artificial gravity with a spatial gradient. We reveal that the gradients have a significant influence on the residual volume but a minor one on the heat flux. The conclusions are informative for the estimation and design of condensation heat transfer systems for future space applications.

Single Condensation Droplet Self-Ejection from Divergent Structures with Uniform Wettability

Coalescence-induced condensation droplet jumping has been extensively studied for anti-icing, condensation heat transfer, water harvesting, and self-cleaning. Another phenomenon that is gaining attention for potential enhancements is the self-ejection of individual droplets. However, the mechanism underlying this process remains elusive due to cases in which the abrupt detachment of an interface establishes an initial Laplace pressure difference. In this study, we investigate the self-ejection of individual droplets from uniformly hydrophobic microstructures with divergent geometries. We design, fabricate, and test arrays of truncated, nanostructured, and hydrophobic microcones arranged in a square pattern. High-speed microscopy reveals the dynamics of a single condensation droplet between four cones: after cycles of growth and stopped self-propulsion, the suspended droplet self-ejects without abrupt detachments. Through analytical modeling of the droplet in a conical pore as an approximation, we describe the slow isopressure growth phases and the rapid transients driven by surface energy release once a dynamic configuration is reached. Microcones with uniform wettability, in addition to being easier to fabricate, have the potential to enable the self-ejection of all nucleated droplets with a designed size, promising significant improvements in the aforementioned applications and others.

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.

Condensation droplet sieve

Large droplets emerging during dropwise condensation impair surface properties such as anti-fogging/frosting ability and heat transfer efficiency. How to spontaneously detach massive randomly distributed droplets with controlled sizes has remained a challenge. Herein, we present a solution called condensation droplet sieve, through fabricating microscale thin-walled lattice structures coated with a superhydrophobic layer. Growing droplets were observed to jump off this surface once becoming slightly larger than the lattices. The maximum radius and residual volume of droplets were strictly confined to 16 μm and 3.2 nl/mm² respectively. We reveal that this droplet radius cut off is attributed to the large tolerance of coalescence mismatch for jumping and effective isolation of droplets between neighboring lattices. Our work brings forth a strategy for the design and fabrication of high-performance anti-dew materials.

Spontaneous droplet jumping and control of dropwise condensation are relevant for water-harvesting, heat transfer and anti-frosting applications. The authors design a superhydrophobic surface with microscale thin-walled lattice structure to achieve effective jumping of droplets with specified radius range.

Microscale Confinement and Wetting Contrast Enable Enhanced and Tunable Condensation

Dropwise condensation represents the upper limit of thermal transport efficiency for liquid-to-vapor phase transition. A century of research has focused on promoting dropwise condensation by attempting to overcome limitations associated with thermal resistance and poor surface-modifier durability. Here, we show that condensation in a microscale gap formed by surfaces having a wetting contrast can overcome these limitations. Spontaneous out-of-plane condensate transfer between the contrasting parallel surfaces decouples the nanoscale nucleation behavior, droplet growth dynamics, and shedding processes to enable minimization of thermal resistance and elimination of surface modification. Experiments on pure steam combined with theoretical analysis and numerical simulation confirm the breaking of intrinsic limits to classical condensation and demonstrate a gap-dependent heat-transfer coefficient with up to 240% enhancement compared to dropwise condensation. Our study presents a promising mechanism and technology for compact energy and water applications where high, tunable, gravity-independent, and durable phase-change heat transfer is required.

A Deep Learning Perspective on Dropwise Condensation

Condensation is ubiquitous in nature and industry. Heterogeneous condensation on surfaces is typified by the continuous cycle of droplet nucleation, growth, and departure. Central to the mechanistic understanding of the thermofluidic processes governing condensation is the rapid and high-fidelity extraction of interpretable physical descriptors from the highly transient droplet population. However, extracting quantifiable measures out of dynamic objects with conventional imaging technologies poses a challenge to researchers. Here, an intelligent vision-based framework is demonstrated that unites classical thermofluidic imaging techniques with deep learning to fundamentally address this challenge. The deep learning framework can autonomously harness physical descriptors and quantify thermal performance at extreme spatio-temporal resolutions of 300 nm and 200 ms, respectively. The data-centric analysis conclusively shows that contrary to classical understanding, the overall condensation performance is governed by a key tradeoff between heat transfer rate per individual droplet and droplet population density. The vision-based approach presents a powerful tool for the study of not only phase-change processes but also any nucleation-based process within and beyond the thermal science community through the harnessing of big data.

Dropwise condensation: From fundamentals of wetting, nucleation, and droplet mobility to performance improvement by advanced functional surfaces

As a ubiquitous vapor-liquid phase-change process, dropwise condensation has attracted tremendous research attention owing to its remarkable efficiency of energy transfer and transformative industrial potential. In recent years, advanced functional surfaces, profiting from great progress in modifying micro/nanoscale features and surface chemistry on surfaces, have led to exciting advances in both heat transfer enhancement and fundamental understanding of dropwise condensation. In this review, we discuss the development of some key components for achieving performance improvement of dropwise condensation, including surface wettability, nucleation, droplet mobility, and growth, and discuss how they can be elaborately controlled as desired using surface design. We also present an overview of dropwise condensation heat transfer enhancement on advanced functional surfaces along with the underlying mechanisms, such as jumping condensation on nanostructured superhydrophobic surfaces, and new condensation characteristics (e.g., Laplace pressure-driven droplet motion, hierarchical condensation, and sucking flow condensation) on hierarchically structured surfaces. Finally, the durability, cost, and scalability of specific functional surfaces are focused on for future industrial applications. The existing challenges, alternative strategies, as well as future perspectives, are essential in the fundamental and applied aspects for the practical implementation of dropwise condensation.

Enhancement and Guidance of Coalescence-Induced Jumping of Droplets on Superhydrophobic Surfaces with a U-Groove

Coalescence-induced droplet jumping has received considerable attention owing to its potential to enhance performance in various applications. However, the energy conversion efficiency of droplet coalescence jumping is very low and the jumping direction is uncontrollable, which vastly limits the application of droplet coalescence jumping. In this work, we used superhydrophobic surfaces with a U-groove to experimentally achieve a high dimensionless jumping velocity V_j^* ≈ 0.70, with an energy conversion efficiency η ≈ 43%, about a 900% increase in energy conversion efficiency compared to droplet coalescence jumping on flat superhydrophobic surfaces. Numerical simulation and experimental data indicated that a higher jumping velocity arises from the redirection of in-plane velocity vectors to out-of-plane velocity vectors, which is a joint effect resulting from the redirection of velocity vectors in the coalescence direction and the redirection of velocity vectors of the liquid bridge by limiting maximum deformation of the liquid bridge. Furthermore, the jumping direction of merged droplets could be easily controlled ranging from 17 to 90^° by adjusting the opening direction of the U-groove, with a jumping velocity V_j^* ≥ 0.70. When the opening direction is 60^°, the jumping direction shows a deviation as low as 17^° from the horizontal surface with a jumping velocity V_j^* ≈ 0.73 and corresponding energy conversion efficiency η ≈ 46%. This work not only improves jumping velocity and energy conversion efficiency but also demonstrates the effect of the U-groove on coalescence dynamics and demonstrates a method to further control the droplet jumping direction for enhanced performance in applications.

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.

Breaking Droplet Jumping Energy Conversion Limits with Superhydrophobic Microgrooves

Coalescence-induced droplet jumping has the potential to enhance the performance of a variety of applications including condensation heat transfer, surface self-cleaning, anti-icing, and defrosting to name a few. Here, we study droplet jumping on hierarchical microgrooved and nanostructured smooth superhydrophobic surfaces. We show that the confined microgroove structures play a key role in tailoring droplet coalescence hydrodynamics, which in turn affects the droplet jumping velocity and energy conversion efficiency. We observed self-jumping of individual deformed droplets within microgrooves having maximum surface-to-kinetic energy conversion efficiency of 8%. Furthermore, various coalescence-induced jumping modes were observed on the hierarchical microgrooved superhydrophobic surface. The microgroove structure enabled high droplet jumping velocity (≈0.74U) and energy conversion efficiency (≈46%) by enabling the coalescence of deformed droplets in microgrooves with undeformed droplets on adjacent plateaus. The jumping velocity and energy conversion efficiency enhancements are 1.93× and 6.67× higher than traditional coalescence-induced droplet jumping on smooth superhydrophobic surfaces. This work not only demonstrates high droplet jumping velocity and energy conversion efficiency but also demonstrates the key role played by macroscale structures on coalescence hydrodynamics and elucidates a method to further control droplet jumping physics for a plethora of applications.

Simulation of Drop-Size Distribution During Dropwise and Jumping Drop Condensation on a Vertical Surface: Implications for Heat Transfer Modeling

Accurate models for condensation heat transfer are necessary to improve condenser design. Drop-size distribution is an important aspect of heat transfer modeling that is difficult to measure for small drop sizes. The present work uses a numerical simulation of condensation which incorporates the possibility of coalescence and coalescence-induced jumping over a range of drop sizes. Results of the simulation are compared with previous theoretical models and the impact of the assumptions used in those models is explored. In particular, previous drop-size distribution models may predict heat transfer rates less accurately for high contact angles and for coalescence-induced jumping since coalescence occurs over a range of drop sizes and does not always result in departure. The influence of various input parameters (nucleation site distribution approach, nucleation site density, contact angle, maximum drop size, heat transfer modeling to individual drops, and minimum jumping size) on the drop-size distribution and overall heat transfer rate is explored. Assignment of the nucleation site spatial distribution and heat transfer model affect both the drop-size distribution and predicted overall heat transfer rate. Results from the simulation suggest that, when the contact angle is large (as on superhydrophobic surfaces) and no coalescence-induced jumping occurs, the heat transfer may not be as sensitive to the maximum drop-size as previously supposed. Furthermore, this work suggests that when coalescence-induced jumping occurs, reducing the maximum drop size may not always increase heat transfer since drops similar in size to those removed by coalescence-induced jumping can contribute significantly to the overall heat transfer rate.