On Localized Vapor Pressure Gradients Governing Condensation and Frost Phenomena

Micro- and Nanoengineered Metal Additively Manufactured Surfaces for Enhanced Anti-Frosting Applications

The greater geometrical design freedom offered by additive manufacturing (AM) as compared to the conventional manufacturing method has attracted increasing interest in AM to develop innovative and complex designs for enhanced performance. However, the difference in material composition and surface properties from conventional alloys has made surface micro-/nanostructuring of AM metals challenging. Frost accretion is a safety hazard in numerous engineering applications. To expand the application of AM, this study experimentally investigates the antifrosting performance of superhydrophobic and slippery lubricant-infused porous surfaces (SLIPSs) generated on AM alloy, AlSi10Mg. By strategically utilizing the subgrain structure in the metallography of the AM alloy, the functionalized superhydrophobic AM surface featuring hierarchical structures was shown to greatly reduce frost formation as compared to functionalized single-tier structured surfaces, hierarchical structures formed on conventional aluminum alloy surfaces, and SLIPSs. Optical observation of frost propagation demonstrated that the mechanism of frost delay is governed by the inhibition of spontaneous droplet freezing through exceptional Cassie state stability during condensation frosting. The Cassie stability results from the unique AM structure morphology, which creates a higher structural energy barrier to prevent condensate from infiltrating the cavities. This phenomenon also enables the formation of a high surface-to-droplet thermal resistance, which eliminates spontaneous droplet freezing down to a -15 °C surface temperature. Our work demonstrates a scalable structuring method for AM metals, which can result in delayed frost formation, and it also provides guidelines for the development of engineered surfaces requiring the antifrosting function for several industries.

Role of Molecular Water Layer State on Freezing Front Propagation Rate and Mode Studied with Thermal Imaging

In this work, we study the relationship between the molecular water layer (MWL) and frost freezing onset and propagation. The progression of frost has been reported to be governed by various localized icing phenomena, including interdroplet ice bridging, dry zones, and frost halos. Reports studying the state of water on surfaces have revealed the presence of a thin nanometer water layer on a range of surfaces. Regardless of further investigations that show environmental humidity, temperature, and surface energy to affect the thickness of the MWL on surfaces, the influence of the MWL on frost nucleation and propagation has not yet been previously addressed in the literature. To study the effect of the MWL on surface freezing events, a range of surface-functionalized glass substrates were prepared. In situ monitoring of freezing events with thermal imaging allowed studying the effect of surface chemistry and environmental relative humidity (RH) on the thickness and continuity of the MWL. We argue that the observed icing nucleation and propagation kinetics are directly related to the presence and continuity of the MWL, which can be manipulated by controlling the environmental humidity and surface chemistry.

Condensation or Desublimation: Nanolevel Structural Look on Two Frost Formation Pathways on Surfaces with Different Wettabilities

Processes of water condensation and desublimation on solid surfaces are ubiquitous in nature and essential for various industrial applications, which are crucial for their performance. Despite their significance, these processes are not well understood due to the lack of methods that can provide insight at the nanolevel into the very first stages of phase transitions. Taking advantage of synchrotron grazing-incidence wide-angle X-ray scattering (GIWAXS) and environmental scanning electron microscopy (ESEM), two pathways of the frosting process from supersaturated vapors were studied in real time for substrates with different wettabilities ranging from highly hydrophilic to superhydrophobic. Within GIWAXS, a fully quantitative structural and orientational characterization of the undergoing phase transition reveals the information on degree of crystallinity of the new phase and determines the ordering at the surfaces and inside the films at the initial stages of water/ice nucleation from vapor onto the substrates. The diversity of frosting scenarios, including direct desublimation from the vapor and two-stage condensation-freezing processes, was observed by both GIWAXS and ESEM for different combinations of substrate wettability and vapor supersaturations. The classical nucleation theory straightforwardly predicts the pathway of the phase transition for hydrophobic and superhydrophobic substrates. The case of hydrophilic substrates is more intricate because the barriers in Gibbs free energy for nucleating both liquid and solid embryos are close to each other and comparable to thermal energy kBT. At that end, classical nucleation theory allows concluding a relation between contact angles for ice and water embryos on the basis of the observed frosting pathway.

Fundamentals and Applications of Surface Wetting

In an era defined by an insatiable thirst for sustainable energy solutions, responsible water management, and cutting-edge lab-on-a-chip diagnostics, surface wettability plays a pivotal role in these fields. The seamless integration of fundamental research and the following demonstration of applications on these groundbreaking technologies hinges on manipulating fluid through surface wettability, significantly optimizing performance, enhancing efficiency, and advancing overall sustainability. This Review explores the behavior of liquids when they engage with engineered surfaces, delving into the far-reaching implications of these interactions in various applications. Specifically, we explore surface wetting, dissecting it into three distinctive facets. First, we delve into the fundamental principles that underpin surface wetting. Next, we navigate the intricate liquid-surface interactions, unraveling the complex interplay of various fluid dynamics, as well as heat- and mass-transport mechanisms. Finally, we report on the practical realm, where we scrutinize the myriad applications of these principles in everyday processes and real-world scenarios.

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.

Icephobic Gradient Polymer Coatings Deposited via iCVD: A Novel Approach for Icing Control and Mitigation

Materials against ice formation and accretion are highly desirable for different industrial applications and daily activities affected by icing. Although several concepts have been proposed, no material has so far shown wide-ranging icephobic features, enabling durability and manufacturing on large scales. Herein, we present gradient polymers made of 1,3,5,7-tetravinyl-1,3,5,7-tetramethylcyclotetrasiloxane (V4D4) and 1H,1H,2H,2H-perfluorodecyl acrylate (PFDA) deposited in one step via initiated chemical vapor deposition (iCVD) as an effective coating to mitigate ice accretion and reduce ice adhesion. The gradient structures easily overcome adhesion, stability, and durability issues of traditional fluorinated coatings. The coatings show promising icephobic performance by reducing ice adhesion, depressing the freezing point, delaying drop freezing, and inhibiting ice nucleation and frost propagation. Icephobicity correlates with surface energy discontinuities at the surface plane resulting from the random orientation of the fluorinated groups of PFDA, as confirmed by grazing-incidence X-ray diffraction measurements. The icephobicity could be further improved by tuning the surface crystallinity rather than surface wetting, as samples with random crystal orientation show the lowest ice adhesion despite high contact angle hysteresis. The iCVD-manufactured coatings show promising results, indicating the potential for ice control on larger scales and various applications.

Unraveling the role of vaporization momentum in self-jumping dynamics of freezing supercooled droplets at reduced pressures

Supercooling of water complicates phase change dynamics, the understanding of which remains limited yet vital to energy-related and aerospace processes. Here, we investigate the freezing and jumping dynamics of supercooled water droplets on superhydrophobic surfaces, induced by a remarkable vaporization momentum, in a low-pressure environment. The vaporization momentum arises from the vaporization at droplet's free surface, progressed and intensified by recalescence, subsequently inducing droplet compression and finally self-jumping. By incorporating liquid-gas-solid phase changes involving vaporization, freezing recalescence, and liquid-solid interactions, we resolve the vaporization momentum and droplet dynamics, revealing a size-scaled jumping velocity and a nucleation-governed jumping direction. A droplet-size-defined regime map is established, distinguishing the vaporization-momentum-dominated self-jumping from evaporative drying and overpressure-initiated levitation, all induced by depressurization and vaporization. Our findings illuminate the role of supercooling and low-pressure mediated phase change in shaping fluid transport dynamics, with implications for passive anti-icing, advanced cooling, and climate physics.

Recent progress in understanding the anti-icing behavior of materials

Despite the significant progress in fundamental research in the physics of atmospheric icing or the revolutionary changes in modern materials and coatings achieved due to the recent development of nanotechnology and synthetic chemistry, the problem of reliable protection against atmospheric icing remains a hot topic of surface science. In this paper, we present a brief analysis of the mechanisms of anti-icing behavior that attracted the greatest interest of the scientific community and approaches which realize these mechanisms. We also note the strengths and weaknesses of such approaches and discuss future studies and prospects for the practical application of developed coatings.

Icephobic/anti-icing properties of superhydrophobic surfaces

In the winter, icing on solid surfaces is a typical occurrence that may create a slew of hassles and even tragedies. Anti-icing surfaces are one of the effective solutions for this kind of problem. The roughness of a superhydrophobic surface traps air and weakens the contact between the solid surface and liquid water, allowing water droplets to be removed before freezing. At present, the conventional anti-icing methods including mechanical or thermal technology are not only surface structure unfriendly but also have the obsessions of low efficiency, high energy consumption and high manufacturing costs. Hence, developing a way to remove ice by just modifying the surface shape or chemical composition with a low surface energy is extremely desirable. Numerous attempts have been made to investigate the evolution of ice nucleation and icing on superhydrophobic surfaces under the direction of the ice nucleation hypothesis. In this paper, the research progress of ice nucleation in recent years is reviewed from theoretical and application. The icephobic surfaces are described using the wettability and classical nucleation theories. The benefits and drawbacks of anti-icing superhydrophobic surface are summarized, as well as deicing methods. Finally, several applications of ice phobic materials are illustrated, and some problems and challenges in the research field are discussed. We believed that this review will be useful in guiding future water freezing initiatives.

Frost Delay of a Water-Absorbing Surface with Engineered Wettability via Nonfreezing Water

Frost is common when a solid surface is subjected to a humid and cold environment. It can cause various inconveniences, complications, or fatal accidents. Water-repellent surfaces have demonstrated an antifreezing capability by enabling the water droplets to roll or bounce off before they freeze. However, these surfaces are often limited by their inability to shed the small water condensates, which can eventually grow and freeze. Recently, surfaces that can rapidly absorb and hydrogen bond with these water condensates have demonstrated significant delay in frost formation and growth. This is attributed to a lower freezing temperature of the absorbed water which makes it stay in a nonfreezing state. Herein, we report a surface with preferential wettability of water over oil (i.e., superhydrophilic and oleophobic wettability) that can significantly delay frost formation. The surface is fabricated by copolymerizing poly(ethylene glycol) diacrylate (PEGDA) and perfluorinated acrylate (1H,1H,2H,2H-heptadecafluorodecyl acrylate, HDF-acrylate) applied to a silane-grafted glass substrate (HDF-PEGDA). An HDF-PEGDA surface can quickly absorb condensed water which enables it to delay frost formation and growth for up to 20 min at a surface temperature of -35 °C. Also, the surface demonstrates that its frost-resistant capability remains almost unaffected even after being submerged in an oil bath due to its in-air oil repellency. Differential scanning calorimetry (DSC) measurements reveal that the significant quantity of absorbed water in an HDF-PEGDA surface remains in a nonfreezing state with a T_m value as low as -33 °C. A mathematical model that can predict the time at which the surface begins to be covered with frost is developed. Finally, an HDF-PEGDA is layered with a PEGDA copolymerized with sodium acrylate (Na-acrylate) that enables the continuous release of the absorbed water by posing forward osmotic pressure and regeneration of an HDF-PEGDA surface.

Dynamics of Frost Propagation on Breath Figures

We investigate the process of condensation frosting on flat surfaces using thermal imaging microscopy. This method is particularly well-suited to characterize the frosting of polydisperse assemblies of dew droplets, also called breath figures, that transform into ice droplets by the propagation of frost fronts. The front propagation speed is found to be a nonmonotonous function of the characteristic droplet size of the breath figure. In our experimental conditions, the propagation speed is maximum around 70 μm s^-1 for a characteristic droplet radius of around 300 μm. We mainly show that the frost propagation speed is governed by the competition between two characteristic time scales. The first one is the freezing time of individual droplets, and the other one is the formation time of interdroplet ice bridges that grow from frozen to liquid droplets. In addition, the experiments reveal that the mean ice bridge speed is constant regardless of the characteristic radius of the liquid droplets in the breath figure. A theoretical mean-field analysis without any adjustable parameters recovers all of the features of the front propagation observed in experiments.

Gels as emerging anti-icing materials: a mini review

Gel materials have drawn great attention recently in the anti-icing research community due to their remarkable potential for reducing ice adhesion, inhibiting ice nucleation, and restricting ice propagation. Although the current anti-icing gels are in their infancy and far from practical applications due to poor durability, their outstanding prospect of icephobicity has already shed light on a new group of emerging anti-icing materials. There is a need for a timely review to consolidate the new trends and foster the development towards dedicated applications. Starting from the stage of icing, we first survey the relevant anti-icing strategies. The latest anti-icing gels are then categorized by their liquid phases into organogels, hydrogels, and ionogels. At the same time, the current research focuses, anti-icing mechanisms and shortcomings affiliated with each category are carefully analysed. Based upon the reported state-of-the-art anti-icing research and our own experience in polymer-based anti-icing materials, suggestions for the future development of the anti-icing gels are presented, including pathways to enhance durability, the need to build up the missing fundamentals, and the possibility to enable stimuli-responsive properties. The primary aim of this review is to motivate researchers in both the anti-icing and gel research communities to perform a synchronized effort to rapidly advance the understanding and making of gel-based next generation anti-icing materials.

Enhanced Water Nucleation and Growth Based on Microdroplet Mobility on Lubricant-Infused Surfaces

Lubricant-infused surfaces (LISs) can promote stable dropwise condensation and improve heat transfer rates due to a low nucleation free-energy barrier and high droplet mobility. Recent studies showed that oil menisci surrounding condensate microdroplets form distinct oil-rich and oil-poor regions. These topographical differences in the oil surface cause water microdroplets to rigorously self-propel long distances, continuously redistributing the oil film and potentially refreshing the surface for re-nucleation. However, the dynamic interplay between oil film redistribution, microdroplet self-propulsion, and droplet nucleation and growth is not yet understood. Using high-speed microscopy, we reveal that during water condensation on LISs, the smallest visible droplets (diameter: ∼1 μm, qualitatively representing nucleation) predominantly emerge in oil-poor regions due to a lower nucleation free-energy barrier. Considering the significant heat transfer performance of microdroplets (<10 μm) and transient characteristic of microdroplet movement, we compare the apparent nucleation rate density and water collection rate for LISs with oils of different viscosities and a solid hydrophobic surface at a wide range of subcooling temperatures. Generally, the lowest lubricant viscosity leads to the highest nucleation rate density. We characterize the length and frequency of microdroplet movement and attribute the nucleation enhancement primarily to higher droplet mobility and surface refreshing frequency. Interestingly and unexpectedly, hydrophobic surfaces outperform high-viscosity LISs at high subcooling temperatures but are generally inferior to any of the tested LISs at low temperature differences. To explain the observed nonlinearity between LISs and the solid hydrophobic surface, we introduce two dominant regimes that influence the condensation efficiency: mobility-limited and coalescence-limited. We compare these regimes based on droplet growth rates and water collection rates on the different surfaces. Our findings advance the understanding of dynamic water-lubricant interactions and provide new design rationales for choosing surfaces for enhanced dropwise condensation and water collection efficiencies.

Hydrophilic Slippery Surface Promotes Efficient Defrosting

Frost accretion occurs ubiquitously in various industrial applications and causes tremendous energy and economic loss, as manifested by the Texas power crisis that impacted millions of people over a vast area in 2021. To date, extensive efforts have been made on frost removal by micro-engineering surfaces with superhydrophobicity or lubricity. On such surfaces, air or oil cushions are introduced to suspend the frost layer and promote the rapid frost sliding off, which, although promising, faces the instability of the cushions under extreme frosting conditions. Most existing hydrophilic surfaces, characterized by large interfacial adhesion, have long been deemed unfavorable for frost shedding. Here, we demonstrated that a hydrophilic and slippery surface can achieve efficient defrosting. On such a surface, the hydrophilicity gave rise to a highly interconnected basal frost layer that boosted the substrate-to-frost heat transfer; then, the resulting melted frost readily slid off the surface due to the superb slipperiness. Notably, on our surface, the retained meltwater coverage after frost sliding off was only 2%. In comparison to two control surfaces, for example, surfaces lacking either hydrophilicity or slipperiness, the defrosting efficiency was 13 and 19 times higher and the energy consumption was 2.3 and 6.2 times lower, respectively. Our study highlights the use of a hydrophilic surface for the pronounced defrosting in a broad range of industrial applications.

Frost spreading and pattern formation on microstructured surfaces

Frost is found in nature as a symphony of nucleation and heat and mass transport, cascading from angstroms to several meters. Here, we use laser-induced fluorescence microscopy to investigate the pattern formation of frost growth in experiments which tune the mesoscopic length scale by using microstructured pillar arrays as a frost condenser surface. By controlling the degree of surface supercooling and the amount of condensate, different modes of frost patterning are uncovered, ranging from complete surface coverage to fractal-looking and limited-coverage structures of spiky appearance.

How Frost Forms and Grows on Lubricated Micro- and Nanostructured Surfaces

Frost is ubiquitously observed in nature whenever warmer and more humid air encounters colder than melting point surfaces (e.g., morning dew frosting). However, frost formation is problematic as it damages infrastructure, roads, crops, and the efficient operation of industrial equipment (i.e., heat exchangers, cooling fins). While lubricant-infused surfaces offer promising antifrosting properties, underlying mechanisms of frost formation and its consequential effect on frost-to-surface dynamics remain elusive. Here, we monitor the dynamics of condensation frosting on micro- and hierarchically structured surfaces (the latter combines micro- with nano- features) infused with lubricant, temporally and spatially resolved using laser scanning confocal microscopy. The growth dynamics of water droplets differs for micro- and hierarchically structured surfaces, by hindered drop coalescence on the hierarchical ones. However, the growth and propagation of frost dendrites follow the same scaling on both surface types. Frost propagation is accompanied by a reorganization of the lubricant thin film. We numerically quantify the experimentally observed flow profile using an asymptotic long-wave model. Our results reveal that lubricant reorganization is governed by two distinct driving mechanisms, namely: (1) frost propagation speed and (2) frost dendrite morphology. These in-depth insights into the coupling between lubricant flow and frost formation/propagation enable an improved control over frosting by adjusting the design and features of the surface.

Suppressing Condensation Frosting Using an Out-of-Plane Dry Zone

The vapor pressure above ice is lower than that above supercooled water at the same temperature. This inherent hygroscopic quality of ice has recently been exploited to suppress frost growth by patterning microscopic ice stripes along a surface. These vapor-attracting ice stripes prevented condensation frosting from occurring in the intermediate regions; however, the required presence of the sacrificial ice stripes made it impossible to achieve the ideal case of a completely dry surface. Here, we decouple the sacrificial ice from the antifrosting surface by holding an uncoated aluminum surface in parallel with a prefrosted surface. By replacing the overlapping in-plane dry zones with a uniform out-of-plane dry zone, we show that even an uncoated aluminum surface can stay almost completely dry in chilled and supersaturated conditions. Using a blend of experiments and numerical simulations, we show that the critical separation required to keep the surface dry is a function of the ambient supersaturation.

Condensation Frosting on Micropillar Surfaces - Effect of Microscale Roughness on Ice Propagation

Microscale surface structures have been widely explored as a promising tool for antifreezing or frost avoidance on heat transfer surfaces. Despite studies of many surface feature designs, the mechanisms associated with condensation freezing and ice propagation on microstructured surfaces have yet to be thoroughly elucidated, espectially when it comes to quantitative understanding. In this work, condensation freezing on circular micropillar surfaces is investigated, with varying pillar spacing and height (layout/microscale roughness) but a constant pillar diameter. The pillar layout is found to have significant effects on both liquid nucleation and neighboring droplet interactions, as reflected by the condensation droplet distribution prior to soilidification and eventually the freezing front propagation area velocity. In general, nucleation is preferred on the pillar top rather than the bottom of the pillared surface unless there is a large distance between the pillars. Interactions between neighboring droplets solely on pillar tops (or bottom surfaces) can induce heterogeneity in the droplet distribution and slow freezing front propagation. Based on the roles the pillars play in nucleation, droplet coalescence, and ice bridging, four different condensation states are identified and related to the layout of the pillars, and the freezing front area propagation velocity is found to be different in each state. The findings provide a quantitative basis for designing antifreezing surfaces, applicable to a wide range of thermal systems.

Delayed Frost Growth on Nanoporous Microstructured Surfaces Utilizing Jumping and Sweeping Condensates

Self-propelled jumping of condensate droplets (dew) enables their easy and efficient removal from surfaces and is essential for enhancing the condensation heat transfer coefficient and for delaying the frost growth rate on supercooled surfaces. Here, we report the droplet-jumping phenomenon using nanoporous vertically aligned carbon nanotube (VA-CNT) microstructures grown on smooth silicon substrates and coated with poly-(1H, 1H, 2H, 2H-perfluorodecylacrylate) (pPFDA). We also report droplet-sweeping phenomenon on horizontally mounted surfaces, concluding that the frost surface coverage area and the frost growth rates observed with the droplet-sweeping phenomenon are much lower than those that are observed with the droplet-jumping phenomenon alone. We also investigate the fundamentals of droplet-jumping and the frost growth phenomena using line-shaped, hollow-cylindrical, and cylindrical microstructures, comparing the frost surface coverage area and the ice-bridging times during condensation-frosting, prolonged condensation-frosting, and direct-frosting. We find that the closely spaced thin line-shaped microstructures and hollow-cylindrical microstructures are optimal for frost coverage reduction because of their ability to exhibit droplet-jumping and droplet-sweeping phenomena. We observe that adding nonuniform roughness on top of the microstructures leads to jumping-associated droplet-sweeping on supercooled surfaces. Here, we report the evaporation of an already frozen droplet because of freezing of a supercooled condensate droplet in its close vicinity, enabling the Cassie-Baxter state frost growth and enhancing defrosting efficiency. Finally, we discuss the dynamic defrosting behavior of the pPFDA-coated VA-CNT microstructures, concluding that the small gaps (spacings) between the microstructures not only enable dewetting transitions of droplets but also promote the Cassie-Baxter state frost formation.

Rationally designed surface microstructural features for enhanced droplet jumping and anti-frosting performance

The accretion of frost on heat exchanging surfaces through the freezing of condensed water in cold and humid environments significantly reduces the operating efficiency of air-source heat pumps, refrigerators and other cryogenic equipment. The construction of hierarchical micro-nanostructured SHSs, with the ability to timely remove condensed water before freezing via self-propelled droplet jumping, serves as a promising anti-frosting strategy. However, the actual relationship between microstructural features and water removal capability through droplet jumping is still not clear, hindering the further optimization of anti-frosting SHSs. Herein, a series of aluminum SHSs with different micro-cone arrays is designed and fabricated via ultrafast laser processing and chemical etching. The effect of microstructural features on water removal capability is elucidated by statistically analyzing the condensation process. As compared to nanostructured SHSs with the micro-cone size ranging from 10 to 40 μm, the water removal through droplet jumping is remarkably enhanced from 3.42 g m-2 to as much as 13.91 g m-2 over 10 minutes of condensation experiments due to the effective transition of condensed microdroplets from the initial high-adhesion partial wetting (PW) state to low-adhesion Cassie state, leading to significantly reduced water accumulation and improved anti-frosting performance. However, a further increase in the micro-cone size decreased the water removal amount due to greater droplet adhesion to the surface, which results in higher chances for immobile coalescence and the formation of large droplets. Herein, by rationally tuning the size scale of the structured micro-cones, the optimal SHSs display the least water accumulation and render excellent frosting delay of over 90 minutes under simulated harsh operating conditions.

Mechanisms of ice formation and propagation on superhydrophobic surfaces: A review

Icephobic surfaces, used as passive anti-icing materials, are in high demand due to the costs, damage, and loss of equipment and lives related to ice formation on outdoor surfaces. The proper design of icephobic surfaces is intertwined with the need for a profound understanding of ice formation processes and how ice propagates over a surface. Ice formation (ice nucleation) and interdroplet freezing propagation are processes that determine the onset of freezing and complete ice coverage on a surface, respectively. Evaluating the nature of these phenomena, along with their interactions with substrate and environmental factors, can offer a step toward designing surfaces having an improved icephobic performance. This review paper is organized to discuss ice nucleation and rate, preferable locations of nucleation, and favorable pathways of freezing (desublimation and condensation-freezing) on superhydrophobic surfaces. Furthermore, as the propagation of ice over a substrate plays a more deterministic role for the complete freezing coverage of a surface than that of ice formation, this review also elucidates possible mechanisms of ice propagation, theoretical backgrounds, and strategies to control this propagation using surface characteristics.

Frost-free zone on macrotextured surfaces

Numerous studies have focused on designing functional surfaces that delay frost formation or reduce ice adhesion. However, solutions to the scientific challenges of developing antiicing surfaces remain elusive because of degradation such as mechanical wearing. Inspired by the discontinuous frost pattern on natural leaves, here we report findings on the condensation frosting process on surfaces with serrated structures on the millimeter scale, which is distinct from that on a conventional planar surface with microscale/nanoscale textures. Dropwise condensation, during the first stage of frosting, is enhanced on the peaks and suppressed in the valleys, causing frost to initiate from the peaks, regardless of surface chemistry. The condensed droplets in the valley are then evaporated due to the lower vapor pressure of ice compared with water, resulting in a frost-free zone in the valley, which resists frost propagation even on superhydrophilic surfaces. The dependence of the frost-free areal fraction on the geometric parameters and the ambient conditions is elucidated by both numerical simulations based on steady-state diffusion and an analytical method with an understanding of boundary conditions independent of surface chemistry. We envision that this study would provide a unified framework to design surfaces that can spatially control frost formation, crystal growth, diffusion-controlled growth of biominerals, and material deposition over a broad range of applications.

Competing Effects between Condensation and Self-Removal of Water Droplets Determine Antifrosting Performance of Superhydrophobic Surfaces

Preventing condensation frosting is crucial for air conditioning units, refrigeration systems, and other cryogenic equipment. Coalescence-induced self-propelled jumping of condensed microdroplets on superhydrophobic surfaces serves as a favorable strategy against condensation frosting. In previous reports, efforts were dedicated to enhance the efficiency of self-propelled jumping by constructing appropriate surface structures on superhydrophobic surfaces. However, the incorporation of surface structures results in larger area available for condensation to occur, leading to an increase in total amount of condensed water on the surface and partially counteracts the effect of promoted jumping on removing condensed water from the surface. In this paper, we focus on the competing effects between condensing and self-propelled jumping on promoting and preventing water accumulation, respectively. A series of micro- and nanostructured superhydrophobic surfaces are designed and prepared. The condensation process and self-propelled jumping behavior of microdroplets on the surfaces are investigated. Thousands of jumping events are statistically analyzed to acquire a comprehensive understanding of antifrosting potential of superhydrophobic surfaces with self-propelled jumping of condensed microdroplets. Further frosting experiments shows that the surface with the lowest amount of accumulated water exhibits the best antifrosting performance, which validates our design strategy. This work offers new insights into the rational design and fabrication of antifrosting materials.

How ice bridges the gap

When supercooled dew droplets form on a chilled surface, the subsequent freezing process is driven by a fascinating phenomenon of propagating inter-droplet ice bridges. Here, we explore the range of conditions under which an individual ice dendrite can successfully bridge the gap from a frozen droplet to its nearest liquid neighbor. Ranging the droplet sizes from 1 μm-10 mm, we find that the criterion for ice bridging is purely geometric and independent of temperature, ambient humidity, and surface wettability. We model the growth of individual ice bridges as well as the global speed of percolating fronts sweeping across large droplet populations. We also give a dynamical law for dry zone formation when ice fails to bridge the gap.

From Extremely Water-Repellent Coatings to Passive Icing Protection—Principles, Limitations and Innovative Application Aspects

The severe environmental conditions in winter seasons and/or cold climate regions cause many inconveniences in our routine daily-life, related to blocked road infrastructure, interrupted overhead telecommunication, internet and high-voltage power lines or cancelled flights due to excessive ice and snow accumulation. With the tremendous and nature-inspired development of physical, chemical and engineering sciences in the last few decades, novel strategies for passively combating the atmospheric and condensation icing have been put forward. The primary objective of this review is to reveal comprehensively the major physical mechanisms regulating the ice accretion on solid surfaces and summarize the most important scientific breakthroughs in the field of functional icephobic coatings. Following this framework, the present article introduces the most relevant concepts used to understand the incipiency of ice nuclei at solid surfaces and the pathways of water freezing, considers the criteria that a given material has to meet in order to be labelled as icephobic and clarifies the modus operandi of superhydrophobic (extremely water-repellent) coatings for passive icing protection. Finally, the limitations of existing superhydrophobic/icephobic materials, various possibilities for their unconventional practical applicability in cryobiology and some novel hybrid anti-icing systems are discussed in detail.

Icephobic surfaces: Definition and figures of merit

Icephobic surfaces have a critical footprint on human daily lives ranging from aviation systems and infrastructures to energy systems, but creation of these surfaces for low-temperature applications remains elusive. Non-wetting, liquid-infused and hydrated surfaces have inspired routes for development of icephobic surfaces. However, high freezing temperature, high ice adhesion strength and subsequent ice accretion, low mechanical durability, and high production cost have restricted their practical applications. In this review, we provide a comprehensive definition for icephobicity through thermodynamics, heat transfer and mechanics of ice/water-material interface and elucidate physic-based routes through which nano-scale could help to achieve exceptional icephobic surfaces. Based on conservation laws, mathematical models are developed that accurately predict ice growth rate on various substrates and wind conditions. Through physics of fracture at ice-icephobic material interface, we cast a standard method for ice adhesion measurement that has the potential to eliminate discrepancies between reported ice adhesion from different laboratories. To assure long-time performance of icephobic surfaces, durability metrics need to be defined. We provide standard methods to examine mechanical, chemical, and environmental durability of icephobic surfaces. In the developed comprehensive framework on icephobicity in this review, performance of state-of-the-art icephobic surfaces are compared and main deficiencies in this field are highlighted.

Modus Operandi of Protective and Anti-icing Mechanisms Underlying the Design of Longstanding Outdoor Icephobic Coatings

Atmospheric icing has become a global concern due to hazardous consequences of ice accretion on air, land, and sea transport and infrastructure. Icephobic surfaces due to their physicochemical properties facilitate a decrease in ice and snow accumulation under outdoor conditions. However, a serious problem of most superhydrophobic surfaces described in the literature is poor operational durability under harsh corrosive and abrasive loads characteristic of atmospheric operation. Here, we elucidate main surface phenomena determining the anti-icing behavior and show experimentally how different mechanisms contribute to long-term durability. For comprehensive exploitation of those mechanisms, we have applied a recently proposed strategy based on fine-tuning of both laser processing and protocols of deposition of the fluorooxysilanes onto the nanotextured surface. Prolonged outdoor tests evidence that a developed strategy for modification of materials on the nanolevel allows overcoming the main drawbacks of icephobic coatings reported so far and results in resistance to destroying atmospheric impacts.

Desublimation Frosting on Nanoengineered Surfaces

Ice nucleation from vapor presents a variety of challenges across a wide range of industries and applications including refrigeration, transportation, and energy generation. However, a rational comprehensive approach to fabricating intrinsically icephobic surfaces for frost formation-both from water condensation (followed by freezing) and in particular from desublimation (direct growth of ice crystals from vapor)-remains elusive. Here, guided by nucleation physics, we investigate the effect of material composition and surface texturing (atomically smooth to nanorough) on the nucleation and growth mechanism of frost for a range of conditions within the sublimation domain (0 °C to -55 °C; partial water vapor pressures 6 to 0.02 mbar). Surprisingly, we observe that on silicon at very cold temperatures-below the homogeneous ice solidification nucleation limit (<-46 °C)-desublimation does not become the favorable pathway to frosting. Furthermore, we show that surface nanoroughness makes frost formation on silicon more probable. We experimentally demonstrate at temperatures between -48 °C and -55 °C that nanotexture with radii of curvature within 1 order of magnitude of the critical radius of nucleation favors frost growth, facilitated by capillary condensation, consistent with Kelvin's equation. Our findings show that such nanoscale surface morphology imposed by design to impart desired functionalities-such as superhydrophobicity-or from defects can be highly detrimental for frost icephobicity at low temperatures and water vapor partial pressures (<0.05 mbar). Our work contributes to the fundamental understanding of phase transitions well within the equilibrium sublimation domain and has implications for applications such as travel, power generation, and refrigeration.

Effect of Latent Heat Released by Freezing Droplets during Frost Wave Propagation

Frost spreads on nonwetting surfaces during condensation frosting via an interdroplet frost wave. When a supercooled condensate water droplet freezes on a hydrophobic or superhydrophobic surface, neighboring droplets still in the liquid phase begin to evaporate. Two possible mechanisms govern the evaporation of neighboring water droplets: (1) The difference in saturation pressure of the water vapor surrounding the liquid and frozen droplets induces a vapor pressure gradient, and (2) the latent heat released by freezing droplets locally heats the substrate, leading to evaporation of nearby droplets. The relative significance of these two mechanisms is still not understood. Here, we study the significance of the latent heat released into the substrate by freezing droplets, and its effect on adjacent droplet evaporation, by studying the dynamics of individual water droplet freezing on aluminum-, copper-, and glass-based hydrophobic and superhydrophobic surfaces. The latent heat flux released into the substrate was calculated from the measured droplet sizes and the respective freezing times ( t_f), defined as the time from initial ice nucleation within the droplet to complete droplet freezing. To probe the effect of latent heat release, we performed three-dimensional transient finite element simulations showing that the transfer of latent heat to neighboring droplets is insignificant and accounts for a negligible fraction of evaporation during microscale frost wave propagation. Furthermore, we studied the effect of substrate thermal conductivity on the transfer of latent heat transfer to neighboring droplets by investigating the velocity of ice bridge formation. The velocity of the ice bridge was independent of the substrate thermal conductivity, indicating that adjacent droplet evaporation during condensation frosting is governed solely by vapor pressure gradients. This study not only provides key insights into the individual droplet freezing process but also elucidates the negligible role of latent heat released into the substrate during frost wave propagation.

Tuning Superhydrophobic Nanostructures To Enhance Jumping-Droplet Condensation

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.

Dynamic Defrosting on Scalable Superhydrophobic Surfaces

Recent studies have shown that frost can grow in a suspended Cassie state on nanostructured superhydrophobic surfaces. During defrosting, the melting sheet of Cassie frost spontaneously dewets into quasi-spherical slush droplets that are highly mobile. Promoting Cassie frost would therefore seem advantageous from a defrosting standpoint; however, nobody has systematically compared the efficiency of defrosting Cassie ice versus defrosting conventional surfaces. Here, we characterize the defrosting of an aluminum plate, one-half of which exhibits a superhydrophobic nanostructure while the other half is smooth and hydrophobic. For thick frost sheets (>1 mm), the superhydrophobic surface was able to dynamically shed the meltwater, even at very low tilt angles. In contrast, the hydrophobic surface was unable to shed any appreciable meltwater even at a 90° tilt angle. For thin frost layers (≲1 mm), not even the superhydrophobic surface could mobilize the meltwater. We attribute this to the large apparent contact angle of the meltwater, which for small amounts of frost serves to minimize coalescence events and prevent droplets from approaching the capillary length. Finally, we demonstrate a new mode of dynamic defrosting using an upside-down surface orientation, where the melting frost was able to uniformly detach from the superhydrophobic side and subsequently pull the frost from the hydrophobic side in a chain reaction. Treating surfaces to enable Cassie frost is therefore very desirable for enabling rapid and low-energy thermal defrosting, but only for frost sheets that are sufficiently thick.

Spatial Control of Condensation on Chemically Homogeneous Pillar-Built Surfaces

The random nature of dropwise condensation impedes spatial control hereof and its use for creating microdroplet arrays, yet here we demonstrate the spatial control of dropwise condensation on a chemically homogeneous pillar array surface, yielding ∼8000 droplets/mm² under normal atmospheric pressure conditions. The studied pillar array surface is defined by photolithography and etched in silicon by deep reactive ion etching. Subsequently, the surface is covered with a self-assembled monolayer of perfluorodecyltrichlorosilane (FDTS) to render the surface hydrophobic. To obtain a perfect droplet array, with one droplet per pillar, we exploit a phenomenon where the water vapor flux is focused on the apexes of surface asperities by diffusion while matching the nucleation point density to the array dimensions. Matching is here achieved through the variation of interpillar distance and vapor flow conditions.

Suppression of Frost Nucleation Achieved Using the Nanoengineered Integral Humidity Sink Effect

Inhibition of frost formation is important for increasing efficiency of refrigeration systems and heat exchangers, as well as for preventing the rapid icing over of water-repellant coatings that are designed to prevent accumulation of rime and glaze. From a thermodynamic point of view, this task can be achieved by either increasing hydrophobicity of the surface or decreasing the concentration of water vapor above it. The first approach has been studied in depth, but so far has not yielded a robust solution to the problem of frost formation. In this work, we systematically explore how frost growth can be inhibited by controlling water vapor concentration using bilayer coatings with a porous exterior covering a hygroscopic liquid-infused layer. We lay the theoretical foundation and provide experimental validation of the mass transport mechanism that governs the integral humidity sink effect based on this coating platform as well as reveal intriguing sizing effects about this system. We show that the concentration profile above periodically spaced pores is governed by the sink and source concentrations and two geometrical parameters: the nondimensional pore size and the ratio of the pore spacing to the boundary layer thickness. We demonstrate that when the ratio of the pore spacing to the boundary layer thickness vanishes, as for the nanoporous bilayer coatings, the entire surface concentration becomes uniform and equal to the concentration set by the hygroscopic liquid. In other words, the surface concentration becomes completely independent of the nanopore size. We identified the threshold geometrical parameters for this condition and show that it can lead to a 65 K decrease in the nucleation onset surface temperature below the dew point. With this fundamental insight, we use bilayer coatings to nanoengineer the integral humidity sink effect to provide extreme antifrosting performance with up to a 2 h delay in nucleation onset at 263 K. The nanoporous bilayer coatings can be designed to combine optimal antifrosting functionality with a superhydrophobic water repelling exterior to provide coatings that can robustly prevent frost, rime, and glaze accumulation. By minimizing the required amount of antifreeze, this anti-icing method can have minimal operational cost and environmental impact.