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

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.

Nanorough Is Not Slippery Enough: Implications on Shedding and Heat Transfer

Lowering droplet-surface interactions via the implementation of lubricant-infused surfaces (LISs) has received important attention in the past years. LISs offer enhanced droplet mobility with low sliding angles and the recently reported slippery Wenzel state, among others, empowered by the presence of the lubricant infused in between the structures, which eventually minimizes the direct interactions between liquid droplets and LISs. Current strategies to increase heat transfer during condensation phase-change relay on minimizing the thickness of the coating as well as enhancing condensate shedding. While further surface structuring may impose an additional heat transfer resistance, the presence of micro-structures eventually reduces the effective condensate-surface intimate interactions with the consequently decreased adhesion and enhanced shedding performance, which is investigated in this work. This is demonstrated by macroscopic and optical microscopy condensation experimental observations paying special attention at the liquid-lubricant and liquid-solid binary interactions at the droplet-LIS interface, which is further supported by a revisited force balance at the droplet triple contact line. Moreover, the occurrence of a condensation-coalescence-shedding regime is quantified for the first time with droplet growth rates one and two orders of magnitude greater than during condensation-coalescence and direct condensation regimes, respectively. Findings presented here are of great importance for the effective design and implementation of LISs via surface structure endowing accurate droplet mobility and control for applications such as anti-icing, self-cleaning, water harvesting, and/or liquid repellent surfaces as well as for condensation heat transfer.

Modeling Dropwise Condensation on Hydrophobic Microgrooved Surface

Dropwise condensation heat transfer on water-repellent surfaces is inherently linked to the mode of droplet departure from the surface. When a microgrooved hydrophobic surface is exposed to condensation, multiple spontaneous droplet removal pathways for surface renewal are manifested. We present numerical modeling of dropwise condensation on a microgrooved hydrophobic surface. Our model is an extension of the well-established one-dimensional modeling approach involving estimation of overall condensation heat transfer through the integration of individual droplet contributions. The model presented here accounts for all the surface renewal mechanisms observed on the microgrooved hydrophobic surface: growth and coalescence of condensate droplets within the microgroove and on the ridges, imbibition of the microgrooves with condensate, bulge formation, spontaneous dewetting of the microgrooves, and shedding of large drops through gravity. The modeling results show that the microgrooves trigger condensate shedding from the surface much earlier compared to a planar hydrophobic surface. As a result, the microgrooved hydrophobic surface maintains a much lower area coverage and attains a significantly higher condensation heat flux compared to a planar surface. The model also enables isolation of the relative contributions of the four mechanisms, wherein it is observed that the spontaneous dewetting transition of microgrooves dominates the other mechanisms in terms of the overall surface renewal rate. This is in contrast to the planar hydrophobic surface where droplet shedding under gravity is the main surface renewal mechanism. Finally, we also evaluate the effect of microgroove geometry on the condensation heat transfer performance. The model predicts that hydrophobic microgrooves with depth of ∼200 μm and narrow widths below ∼100 μm can yield enhanced thermal performance.

Interplay of Drop Shedding Mechanisms on High Wettability Contrast Biphilic Stripe-Patterned Surfaces

To improve the rate of DWC, numerous studies have adjusted the distribution of drops through biphilic surface patterning and wettability gradients to control the nucleation and drop shedding rates on the condensing surface, yet the connection between drop shedding mechanisms and surface wettability patterning remains unclear. Moreover, wettability patterning places geometric bounds on the governing forces (i.e., gravity, capillary, and inertia), which drive the droplet shedding mechanisms. Thus, the subsequent influence of droplet distribution along the DWC regions on the shedding mechanisms may not be known a priori. In this study, the area fraction, ADWC, of the DWC and also the DWC region width, LN, were varied between 10 and 50% and 0.5-1.5 mm, respectively, to probe the dominant droplet shedding mechanisms on a high wettability contrast surface (i.e., the contact angle on the DWC was 159 ± 3.4° and the hysteresis 9 ± 3.6°, whereas the FWC was nearly perfectly wetting). Humid air was introduced inside a custom-built chamber with the upright steady-state condensation imaged by both real-time and high-speed imaging techniques. We found that the droplet shedding mechanisms changed with increasing LN where the sliding drop radii are reduced with LN while the jumping drop radii remained unchanged with LN. The maximum drop size for shedding also decreased by 13%, which we attribute to the secondary droplet inertia, which helps gravity overcome the capillary retention force. Lastly, although many studies have probed DWC enhancements via surface wettability patterning, an optimal combination of ADWC and LN provided in this study significantly aids in the improvement of future DWC-based condensers and water collector applications.

Retention Forces for Drops on Microstructured Superhydrophobic Surfaces

Accurate models of retention forces between drops and superhydrophobic (SH) surfaces are required to predict drop dynamics on the surface. This retention force is, in turn, useful in modeling heat transfer rates for dropwise condensation on a SH surface. Drop contact angle distribution and base area on SH surfaces are essential factors for predicting retention forces. The present work measures the contact angle distribution and base area shapes of various drop sizes over a wide range of solid fraction for inclined microstructured SH surfaces at the point of drop departure. Base area shape was found to be well approximated using two ellipses with different aspect ratios, and the contact angle distribution was found to be best fit by a sigmoid function. At an incline near the roll-off angle, drop base area for surfaces with solid fraction close to 1 and close to 0 were found to be nearly circular, whereas the base area of drops on surfaces with an intermediate solid fraction deviated from circular behavior. In this work, maximum advancing and minimum receding contact angles were found as a function of solid fraction and used to calculate retention forces. Contact angle distribution and base area shapes are then used to calculate retention forces between drops and SH surfaces. These calculations are compared with the component of measured drop weight acting parallel to the plane on a tilted surface for validation. Previous retention force studies that investigate base area shape and contact angle distribution for smooth surfaces are not applicable for microstructured SH surfaces. The work shows that using a sigmoid contact angle distribution and modified base area shape yields retention forces that are on average 50% better than previously reported methods. Retention forces for smooth and SH surfaces calculated in this study were used to suggest retention force factor values for varying solid fraction surfaces.

Enhanced Moisture Condensation on Hierarchical Structured Superhydrophobic-Hydrophilic Patterned Surfaces

Patterned surfaces combining hydrophobic and hydrophilic properties show great promise in moisture condensation; however, a comprehensive understanding of the multiscale interfacial behavior and the further controlling method is still lacking. In this paper, we studied the moisture condensation on a hybrid superhydrophobic-hydrophilic surface with hierarchical structures from micro- to nanoscale. For the first time, we demonstrated the effects of wettability difference and microstructure size on the final condensation efficiency. By optimizing the wettability difference, sub-millimeter pattern width, and microstructure size, maximum 90% enhancement of the condensation rate was achieved as compared with the superhydrophobic surface at a subcooling of 13 K. We also demonstrated the enhanced condensation mechanism by a detailed analysis of the condensation process. Our work proposed effective and systematical methods for controlling and optimizing moisture condensation on the patterned surfaces and shed light on application integration of such promising functional surfaces.

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.

Condensation Behavior of Hierarchical Nano/Microstructured Surfaces Inspired by Euphorbia myrsinites

In nature, many extant species exhibit functionalized surface structures during evolution. In particular, wettability affects the functionalization of the surface, and nano/microstructures have been found to enable functions, such as droplet jumping, thereby making self-cleaning, antifog, antibacterial, and antireflection surfaces. Important efforts are underway to understand the surface structure of plant leaves and establish rational design tools for the development of new engineering materials. In this study, we focused on the hierarchical nano/microstructure of the leaves of Euphorbia myrsinites (hereinafter, E. myrsinites), which has a hierarchical shape with microsized papillae, covered with nanosized protruding wax, and observed the condensation behavior on the leaf surface. Si is vertically etched via reactive ion etching (RIE) to artificially mimic the hierarchical nano/microstructures on the leaves of E. myrsinites. We made four types of artificial hierarchical structures, with micropillars having pillar diameters of 5.6 and 16 μm (pillar spacing of 20 and 40 μm, respectively) and heights of 6.5 and 19.5 μm, and nanopillars formed on the surface. The optical observation with a microscope revealed a very high density of condensed droplets on the artificial surface and a stable jumping behavior of droplets of 10 μm or more. Furthermore, in the samples with a micropillar diameter of 5.6 μm and a micropillar height of 19.5 μm, the droplets that had jumped and fallen thereupon bounced off, thereby preventing reattachment. As a result, no droplets of 35 μm or more could exist even after 10 min. In addition, it was clear that a small underlying droplet of less than 10 μm was generated at the bottom of the relatively large secondary droplet existing on the large micropillar of 16 μm, and a frequent coalescence of the droplets occurred. This study revealed the phenomenon of condensation on the surface of plants as well as made it possible to improve the heat exchange process by significantly promoting the heat transfer of condensation using artificial surfaces.

About the Role of Falling Droplets' Sweeping in Surface Renewal during Dropwise Condensation

To determine the heat transfer coefficient during dropwise condensation, two models are necessary: a heat transfer model through a single drop and a model of drop-size distribution. To model the distribution of the drop size, most studies dissociate the drop population into two distinct parts. A semiempirical model is then used to evaluate the drop-size distribution of "large" drops (i.e., typically greater than few micrometers), while the drop-size distribution of "small" drops is modeled using a statistical approach based on population balance. Currently, no accurate data are available to validate this latter distribution. In the present study, the statistical approach is compared to an individual-based numerical approach. This numerical approach takes into account the entire lifecycle of a drop: nucleation, growth, coalescence, and disappearance by sweeping of moving drops (jumping droplets are not considered in this paper). The drop-size distributions of large drops obtained thanks to this model are very similar to those obtained from the classical law in all configurations studied. Nevertheless, the distributions of "small" drops are notably different between the two types of modeling. In the configurations considered in the present study, an analysis of the main hypotheses used in the statistical approach (in particular, the assumption of a constant removal characteristic time τ irrespective of the range of drop size) revealed that the main mechanism for surface renewal is not the sweeping of the surface by moving drops. From these results, a modification of the statistical model is proposed and discussed.