Freezing Of Water Droplets Research Articles

Thermodynamic method for establishment of relationship between icephobicity/superhydrophobicity and microstructure–Based on computing for adhesion work

Superhydrophobic surfaces (SHS) have potential in solving the icing of aircraft, high-voltage overhead transmission lines, and other power network devices exposed to the air. For this reason, we wish to establish the relationship between microstructure and the adhesion work by thermodynamic method, also for analysis of the relationship between the hydrophobicity and icephobicity (or anti-icing). Therefore, respectively considering Cassie-Baxter and Wenzel states, such relationship was theoretically established based on one/two-step surface model, enlightened by natural and artificial SHS. Among it, how to obtain the adhesion work of icing per unit ice-solid interface is the key to this study. Followed by it, hydrothermal experiment, chemical deposition, and etching methods were performed to verify our theoretical results.•How to model for the SHS based on the natural and artificial SHS;•Computation for adhesion work (waw) per unit area of a water droplet–SHS interface;•Computation for adhesion work (wai) per unit area of a frozen water droplet–SHS interface;•Computation for reduced adhesion work (wa2) after icing;•Hydrothermal experiment, chemical deposition and etching methods were used for validation of modeling.

Compare study between icephobicity and superhydrophobicity

Although surface microstructures is the key to superhydrophobicity, and possibly leads to significant icephobicity when a water droplet freezes on superhydrophobic surfaces (SHS), thermodynamic mechanisms responsible for the icephobicity and anti–icing still need to be further studied. For this reason, we established the relationships between some quantities, i.e., contact angle (CA) together hysteresis (CAH), adhesion work and the microstructures by a three–dimension (3–D) surface model, and theoretically explained the anti–icing and icephobicity from the SHS. Our theoretical and experimental study indicate, the adhesion work (Wai) of a frozen water droplet to the SHS in composite wetting state (CWS) is apparently less than that in the non–composite wetting state (NCWS). Therefore it is necessary to create such CWS by designing surface micro/nanostructure. Further study also shows, the adhesion work (Waw) of a water droplet to the SHS is larger than that (Wai) of their frozen, thus implying decrease of the adhesion work after icing. This will improve on the understanding of the SHS for anti–icing and icephobicity.

Study of the Dynamics of Water Droplet Freezing on the Surface of Nanocomposites in the Long-Wavelength Infrared Range

A technique is developed to determine the freezing time, thermal resistance, heat transfer coefficient, and cooling power of water droplet on the surface of studied materials by means of video recording in the long-wavelength infrared range. These parameters are found for water droplets on a hydrophobic coating based on organosilicon polymer filled with carbon nanotubes as well as on polyethylene terephthalate film. On hydrophobic coatings the water droplets froze 1.5–4 times slower than on polyethylene terephthalate film, which is explained by an increase in the contact angle and thermal resistance between the droplet and surface of the coating. Correlation between the freezing time and thermal resistance reveals that the heat flux from the droplet towards the material surface is crucial for the freezing time. In tests, partial adiabatic droplet freezing with the following complete isothermal freezing were observed during a single freezing process. The studied hydrophobic coatings may potentially be used as anti-icing coatings.

A comprehensive model for predicting droplet freezing features on a cold substrate

Water droplet freezing affects many aspects of our daily lives, although there is no comprehensive model which retrieves all of the experimentally observed features when a liquid water droplet deposited on a cold substrate turns to ice. In this paper, we present general governing equations to describe water droplet freezing on a solid substrate by accounting for the physical properties of each phase present, namely the liquid and ice, in addition to the solid substrate. The approach, which takes advantage of the full mean curvature expression of both the droplet–air and liquid–ice interfaces, disjoining pressure, the Gibbs–Thomson effect, natural convection and the substrate thermal and physico-chemical properties, enables us to model a more realistic frozen droplet shape, without a prior assumption for the freezing growth angle. In addition to correctly predicting the freezing time, we capture both qualitatively and quantitatively the key experimentally observed features during water droplet freezing such as volume expansion, concave ice front and the cusp singularity. Furthermore, the proposed equation for the tip angle seems to explain its experimentally observed variability.

Stability of frozen water droplets on highly hydrophobic porous surfaces: Temperature effects

We report on an experimental study of water droplets freezing on highly hydrophobic surfaces decorated by a random distribution of nanometric pores. We particularly analyze the influence of the substrate temperature ranging between 23 °C and 80 °C on the freezing phenomenon and the temporal stability of the resulting frozen droplets. The cooling and the subsequent spontaneous freeze of droplets were obtained by quickly reducing the pressure inside the cell from 101 kPa to 2 kPa. In all experiments the humidity rate was maintained very low (4%), allowing us to minimize its influence on the freezing process. The experimental results show that: (i) the freezing process is initiated by homogeneous nucleation near the gas-liquid interface, and is delayed by a factor between 2 and 3 on the substrates at the highest temperature. (ii) three different mechanisms, influenced by the substrate’s temperature, lead to the disappearance of the frozen droplets. Fragmentation and sublimation of frozen droplets are observed for all substrates’ temperatures. A melting of the ice shell is observed for droplets on substrate at 80 °C. This temperature appears as a minimal value from which we can expect to better control the water freezing and the frost formation on heated hydrophobic surfaces.

Suppression of droplets freezing on glass surfaces on which antifreeze polypeptides are adhered by a silane coupling agent.

The development of ice-phobic, glass-substrate surfaces is important for many reasons such as poor visibility through the ice-covered windshields of vehicles. The present authors have developed new glass surfaces coated with a silane coupling agent and polypeptides whose amino-acid sequence is identical to a partial sequence of winter flounder antifreeze protein. We have conducted experiments on the freezing of sessile water droplets on the glass surfaces, and measured the droplet temperature, contact angle, contact area and surface roughness. The results show that the supercooling temperature decreased noticeably in the case where a higher concentration solution of polypeptide was used for the coating. The adhesion strength of frozen droplets was lowest in the same case. In addition, we observed many nanoscale humps on the coated surface, which were formed by polypeptide aggregates in the solution. We argue that the combination of the hydrophilic humps and the hydrophobic base surfaces causes water molecules adjacent to the surfaces to have a variety of orientations in that plane, even after the ice layer started to grow. This then induces a misfit of water-molecule spacing in the ice layers and consequent formation of fragile polycrystalline structure. This explains the lower values of ice adhesion strength and supercooling enhancement in the cases of the polypeptide-coated glass plates.

Freezing of mineralized water droplets in winter sprinkling

Drip congelation is an effective method of desalination of salt water. The results of mathematical modelling of freezing of fresh and salt water droplets in conditions of free fall at negative air temperatures are presented. Different options of salt rejection from the frost boundary and mineralization growth in the unfrozen part of the drop are considered.

Optonumerical technique for mapping freezing droplet interactions on substrates

A visualization technique was developed to accurately resolve the locations and phases of liquid and frozen water droplets naturally evolving on a subfreezing surface exposed to a humid air stream. The technique utilized the lens-like properties of unfrozen condensate droplets to focus reflected light in a manner that made it possible to reliably distinguish the unfrozen from frozen droplets. By inducing this lensing effect in all visible droplets on the surface prior to freezing, a small, high contrast region within each liquid droplet was produced. When freezing occurred, the higher opacity of the ice phase caused the frozen droplets to suddenly take on a darker appearance than the unfrozen droplets. A reflected light microscope and digital camera apparatus were used to feed data into an image analysis algorithm capable of mapping the time-evolution of the freezing water droplets on the surface. The algorithm processed raw image sequences into binary image stacks from which the light foci associated with the droplets could be reliably isolated into high contrast white pixel clusters on an otherwise black background. An edge detection method was employed within each binary image to locate the coordinates of the pixels residing along the periphery of each droplet’s focal cone. Those data were subsequently used to compute the centroidal coordinates and state of each droplet over time. Compared with more laborious, frame-by-frame analyses with various commercially available software tools, this technique correctly identified the locations and states of the droplets through the entire growth and freezing processes with accuracies in excess of 99%. This technical approach also allowed for simultaneous tracking of all droplets and freezing events present within the region of interest—typically numbering in the hundreds or thousands—over time, paving the way for interdroplet coalescence and freezing interactions to be studied in detail.

Duelling dry zones around hygroscopic droplets

In the 1480s, da Vinci invented the first hygrometer using cellulose fibres to attract moisture from the atmosphere. Five hundred years later, Williams and Blanc showed that the depressed vapour pressure of a hygroscopic sessile droplet can inhibit condensation within an annular dry zone on the surface. What remains unresolved to this day is whether these regions of suppressed condensation around hygroscopic agents are due to inhibited nucleation versus inhibited growth of the condensate. We elucidate the competition between these two mechanisms by generating steady-state dry zones about frozen water droplets. The choice of ice as the hygroscopic material was motivated by its unique ability to remain undiluted as it attracts moisture from the air. Experiments, scaling models, and simulations where the ice droplet size, ambient humidity and surface temperature are systematically varied reveal that over the vast majority of the parameter space, the inhibited growth dry zone wins the duel over the nucleation dry zone.

Experimental investigation and statistical analysis of icing nucleation characteristics of sessile water droplets

Nucleation and freezing of water droplet are very common in aerospace, power, meteorology and refrigeration. This study experimentally investigates the nucleation temperatures of sessile water droplets with volumes of 1, 5 and 10 μL on a cold horizontal aluminum plate which greatly influence the droplet freezing process. Analyses are made on the droplet nucleation sequence and nucleation temperature series as well as their correlations to estimate the systematic errors in the nucleation data, and the results support that such errors are negligibly small. The nucleation temperatures are further analyzed statistically to obtain their average value, standard deviation, frequency distribution and cumulative distribution. The nucleation results for different droplet volumes indicate that a smaller droplet has a lower average nucleation temperature and a larger standard deviation (wider frequency distribution). The nucleation rates are fitted using the classical nucleation theory. The results show that the nucleation rate increases as the temperature decreases and the droplet volume increases. The nucleation time, which involves transient nucleation and is often used to evaluate the surface anti-icing/frosting characteristics, is measured experimentally at a constant plate temperature. The nucleation rate for transient nucleation is found to increase with time. A higher temperature yields larger minimum, average, and maximum nucleation times but a lower nucleation rate. These results provide guidance for predicting ice/frost accretion on surfaces and for designing anti-icing/frosting surfaces.

Modelling the dynamics of the flow within freezing water droplets

The flow within freezing water droplets is here numerically modelled assuming fixed shape throughout freezing. Three droplets are studied with equal volume but different contact angles and two cases are considered, one including internal natural convection and one where it is excluded, i.e. a case where the effects of density differences is not considered. The shape of the freezing front is similar to experimental observations in the literature and the freezing time is well predicted for colder substrate temperatures. The latter is found to be clearly dependent on the plate temperature and contact angle. Including density differences has only a minor influence on the freezing time, but it has a considerable effect on the dynamics of the internal flow. To exemplify, in the vicinity of the density maximum for water (4 ∘C) the velocities are about 100 times higher when internal natural convection is considered for as compared to when it is not.

Freezing delay, frost accumulation and droplets condensation properties of micro- or hierarchically-structured silicon surfaces

The processes of single droplet freezing, frost accumulation and droplets flooding during condensation were analyzed and compared for surfaces of different morphologies. Four samples were first fabricated – a micro-cubes silicon, a micro-cylinders silicon, a hierarchically-structured silicon and a smooth silicon. After measuring the static contact angles and roll angles, the sessile water droplet freezing and frost accumulation under a series of surface temperature were studied. The droplets condensation processes were for the first time compared through environmental scanning electron microscopy (ESEM). The results showed that the droplet freezing time on hierarchically-structured silicon was 4 times longer than that of uncoated silicon. Micro-pillared and hierarchically-structured silicons could minimize the frost thickness only in the initial stage of frost formation and had quite different frost growth patterns. The ESEM images can facilitate explain the different patterns of freezing and frosting on micro-pillared and hierarchically-structured samples.

Mixed ice accretion on aircraft wings

Ice accretion is a problematic natural phenomenon that affects a wide range of engineering applications including power cables, radio masts, and wind turbines. Accretion on aircraft wings occurs when supercooled water droplets freeze instantaneously on impact to form rime ice or runback as water along the wing to form glaze ice. Most models to date have ignored the accretion of mixed ice, which is a combination of rime and glaze. A parameter we term the “freezing fraction” is defined as the fraction of a supercooled droplet that freezes on impact with the top surface of the accretion ice to explore the concept of mixed ice accretion. Additionally we consider different “packing densities” of rime ice, mimicking the different bulk rime densities observed in nature. Ice accretion is considered in four stages: rime, primary mixed, secondary mixed, and glaze ice. Predictions match with existing models and experimental data in the limiting rime and glaze cases. The mixed ice formulation however provides additional insight into the composition of the overall ice structure, which ultimately influences adhesion and ice thickness, and shows that for similar atmospheric parameter ranges, this simple mixed ice description leads to very different accretion rates. A simple one-dimensional energy balance was solved to show how this freezing fraction parameter increases with decrease in atmospheric temperature, with lower freezing fraction promoting glaze ice accretion.

Frozen‐Droplets Aggregation at Temperature Below −40°C

AbstractThe onset of the aggregation process of frozen droplets was investigated in laboratory settings. The experiments were conducted in a cloud chamber controlled at temperatures cooler than −40°C, where pure water droplets freeze spontaneously without the need for ice nucleating particles. We present laboratory evidence supporting that the aggregation process can occur for frozen droplet sizes around 10 μm in diameter and at concentrations observed in the cloud chamber of 70 ± 20 cm−3, which can be found in some regions of anvil cirrus. The characteristics and morphology of the aggregates were examined in detail. Additional experiments performed with electrically charged droplets show that the aggregation processes can be significantly accelerated, suggesting that the mechanism of collision and adhesion could be related to electrical forces generated by different charge distributions or dipole interactions between the interacting ice surfaces. The current work aims at advancing our fundamental understanding of the aggregation process of frozen droplets, which is necessary for understanding the cloud microphysical processes.

Experiments on Freezing Water Droplets on Glass Surfaces Coated with Antifreeze Polypeptide Using a Polymer

Experiments on Freezing Water Droplets on Glass Surfaces Coated with Antifreeze Polypeptide Using a Polymer

Molecular dynamics simulation of freezing process of water droplets impinging on cold surface

The freezing of water droplet is a ubiquitous phenomenon in nature. Although the freezing process of water droplet impacting on cold surfaces is widely observed on a macroscopic scale, the study of freezing process on a micro-scale is still deficient, and it is definitely difficult to study micro-droplets and nano-droplets using experimental methods due to the obstacles in both generation and observation. For these reasons, simulation methods using molecular dynamics (MD) have been proposed to study micro-droplets and nano-droplets, as molecular dynamics can trace each atom, count up the collective behavior of a group of atoms and describe the detail interaction between atoms. In this paper, a three-dimensional model is established by molecular dynamics simulation to study the freezing process of water droplets impinging on a cold solid surface on a nanoscale. We select the micro-canonical ensemble (NVE) as a statistical system and the TIP4P/ice model as a potential energy function to simulate oxygen atoms, hydrogen atoms and water molecules. The LJ/126 model is used to simulate the interaction between water molecules and solid atoms. Different wettability walls are simulated by adjusting the potential energy parameters. For all the simulations, the velocity-rescale method is used to keep the temperature constant and the Verlet algorithm is adopted to solve the Newton equations. In the velocity-rescale method, the temperature is calculated by using the profile-unbiased thermostat. The freezing process inside the water droplet is determined by the temperature distribution of water molecules along the vertical direction, which is more concise than by the location coordinates of the microscopic atoms. Through the numerical experimentations, we find that when the surface temperature decreases, the completely freezing time of drops is reduced; meanwhile, the time required for water temperature to drop down to the wall temperature is increased. Moreover, the heat transfer inside the water droplet slows down with the decreasing of wall hydrophilicity while the total freezing time is prolonged.

Spontaneous self-dislodging of freezing water droplets and the role of wettability

Spontaneous removal of liquid, solidifying liquid and solid forms of matter from surfaces, is of significant importance in nature and technology, where it finds applications ranging from self-cleaning to icephobicity and to condensation systems. However, it is a great challenge to understand fundamentally the complex interaction of rapidly solidifying, typically supercooled, droplets with surfaces, and to harvest benefit from it for the design of intrinsically icephobic materials. Here we report and explain an ice removal mechanism that manifests itself simultaneously with freezing, driving gradual self-dislodging of droplets cooled via evaporation and sublimation (low environmental pressure) or convection (atmospheric pressure) from substrates. The key to successful self-dislodging is that the freezing at the droplet free surface and the droplet contact area with the substrate do not occur simultaneously: The frozen phase boundary moves inward from the droplet free surface toward the droplet-substrate interface, which remains liquid throughout most of the process and freezes last. We observe experimentally, and validate theoretically, that the inward motion of the phase boundary near the substrate drives a gradual reduction in droplet-substrate contact. Concurrently, the droplet lifts from the substrate due to its incompressibility, density differences, and the asymmetric freezing dynamics with inward solidification causing not fully frozen mass to be displaced toward the unsolidified droplet-substrate interface. Depending on surface topography and wetting conditions, we find that this can lead to full dislodging of the ice droplet from a variety of engineered substrates, rendering the latter ice-free.

Self-Consistent Determination of the Ice–Air Interfacial Tension and Ice–Water–Air Line Tension from Experiments on the Freezing of Water Droplets

We propose an indirect experimental method to self-consistently determine the line tension of a solid–liquid–vapor contact region and the interfacial tension of the solid–vapor interface via experiments on the homogeneous crystallization of droplets. The crucial idea of our method is that, even in the surface-stimulated mode, when a crystal nucleus forms with one of its facets at the droplet surface it initially emerges (as a subcritical cluster) homogeneously in the subsurface layer, not “pseudo-heterogeneously” at the surface. This mode is negligible for large droplets but becomes increasingly important with decreasing droplet size and is dominant in small droplets. The proposed method requires experimental data on the rate of homogeneous crystal nucleation as a function of droplet size. Using this method to examine experimental data on homogeneous crystal nucleation in droplets of 1.0, 1.7, and 2.9 μm radii in the temperature range from 234.8 to 236.2 K, we evaluated the line tension τ of ice–water–air...

Freezing and melting of a sessile water droplet on a horizontal cold plate

Water droplet freezing phenomena widely exist in the fields of aerospace, power, meteorology and refrigeration. In this research, the freezing and melting processes of a sessile water droplet on a horizontal cold plate are studied experimentally. The nucleation temperature of a supercooled droplet is determined and analyzed statistically. The freezing behaviors of a water droplet, which are characterized by the freezing front and the droplet profile, volume and height, are obtained through the photographic approach. Experiments are done on water droplets having four different volumes including 1, 5, 10 and 20μL. The experimental results show that the ice nucleation is stochastic, and its occurrence needs a large degree of supercooling. The nucleation temperature approximately satisfies the normal distribution, it scatters over a wide range, with the average nucleation temperature decreasing with reducing droplet volume. The droplet volume and height increase suddenly at the nucleation and recalescence stages, as time passes the volume expansion rate diminishes while the height increment rate increases. A colder plate yields a higher freezing rate and consequently a shorter freezing time. In contrast, a frozen droplet begins to melt at an almost fixed temperature of about 0.5°C, and the larger the droplet, the longer the melting time.

Ion Migration in the Process of Water Freezing under Alternating Electric Field and Its Impact on Insulator Flashover

Ice flashover threatens the security and reliability of power transmission. However, the ice flashover mechanism of insulators remains poorly understood. This study analyses water droplet freezing and ion distribution in ice layer under alternating electric field. It also investigates ion migration during icing process of insulator string under alternating electric field and its effects on insulator flashover. Results showed that the average freezing time of water droplets was related to electric field strength. The extent of ion migration during freezing decreased with increasing electric field strength. The maximal melting water conductivity of the ice layer and icicle of the insulator formed under energized condition was higher than the corresponding freezing water conductivity but lower than that under non-energized condition. Furthermore, the hanging location of each insulator significantly affected the melting water conductivity of the ice layer. The surface conductivity of the ice layer increased because of the conductive ion migration in freezing water during freezing, which was an important factor that decreased the flashover voltage of the ice-covered insulator. The existence of alternating electric field would impact the extent of ion migration. This study may serve as a reference for updating prediction flashover model of ice-covered insulators during the melting period.