Session L03: Heat Transfer, Evaporation and Buoyancy Effects II

Controlling Droplet Size Density during Dropwise Condensation on Silicone Oil Grafted Surfaces

Condensation is a critical phenomenon for various industrial applications, with dropwise condensation able to achieve higher heat transfer rates (6-8 times) than filmwise condensation. Various surface modification techniques have been explored to promote dropwise condensation via the application of low surface energy coatings, which create low contact angle hysteresis (CAH) surfaces and stimulate smaller size droplets shedding. In this work, silicone oil grafting is exploited to transform an intrinsically hydrophilic silicon substrate (CA ≈ 60^o) into a hydrophobic surface (CA ≈ 108^o). Different fabrication parameters (5, 20, and 100 cSt) enable different CAH ranging between 1° to 20°, and as such, dropwise condensation with different droplet mobilities and droplet size distributions. High viscosity oil grafted surfaces show the lowest CAH and shedding of very mobile small-sized droplets when compared to low viscosity oil, creating space for new droplets to nucleate, grow, coalesce, and shed. This technique has also been utilized to impose surface patterns for control of the droplet size distribution and mobility during condensation.   

Evaporation Behaviour of a Pair of Sessile Droplets on a Heated Substrate

The evaporation of water droplets is important for a wide range of industrial applications, including inkjet printing and DNA mapping; Here, we present an experimental investigation which addresses the evaporation characteristics of a pair of sessile droplets on a heated aluminum substrate.

Experiments were conducted to monitor the changes in contact angle and surface temperature of pairs of droplets during evaporation for different substrate temperatures. The temperature distributions over the droplet surfaces were visualized using an infrared camera. Also, it aims to study the effect of the high vapour concentration wedge area, formulated between the droplets when they come close to each other, on evaporation behaviour.

The results demonstrated a relationship between the droplet separation distance and the uniformity of temperature distribution of their surfaces. We further determined a critical separation distance beyond which the temperature distributions were relatively uniform. This threshold separating distance proves that the effect of the wedge area formulated between the droplets is less, and the droplets behave as if they are isolated single ones. In addition, the substrate's temperature significantly affects the initial contact angle of the droplets, in which increasing the substrate temperature decreases the contact angle of the droplet. The evaporation process can be optimized with the help of this knowledge, leading to higher control and consistency in industrial applications.

These findings positively enhance numerous industrial applications, resulting in improved performance in fields where evaporation is crucial.   

Leidenfrost Effect in the Flash Vaporization of Hydrogen Peroxide and Water Mixtures: Droplet Dynamics and Evaporation Efficiency

The Leidenfrost effect can significantly impact the flash vaporization of binary mixtures comprising hydrogen peroxide and water, a process widely employed to obtain sterilizing atmospheres. Through high-speed visualisations of droplets using shadowgraph imagery, the influence of varying hydrogen peroxide concentrations and surface temperatures on the dynamics of Leidenfrost droplets is explored. Our results provide insights into the complex interactions between hydrogen peroxide concentration, surface temperature, droplet dynamics, and evaporation efficiency in Leidenfrost phenomena, more specifically within the context of flash vaporization. Notably, a relationship between droplet fate, namely vaporization or ejection away from the heated plate, and evaporation efficiency is established, underscoring the importance of maintaining surface temperatures below the Leidenfrost point, and of understanding the dynamics associated with phase change in binary mixtures. We demonstrate that hydrogen peroxide concentration has minimal influence on droplet dynamics, with surface temperature being the primary driver of droplet behavior. The results show that hundreds of sub-millimetre droplets can be ejected following contact with the hot surface, with size distribution following a log-normal trend. Velocities may reach amplitudes of meters per second, magnitudes over their equivalent diameter. Most of these droplets will not evaporate due to their velocity bringing them out of bounds of the hot surface.   

Evaporation of a binary mixture droplet with a slightly non-monotonic surface tension

Evaporating droplets consisting of a mixture of water and 1,2-hexanediol can be considered as an idealized model system for commercial ink used in water-based inkjet printing.

In these droplets, water evaporates - preferentially near the contact line - leaving behind the non-volatile 1,2-hexanediol.

With decreasing water concentration, the surface tension of this mixture initially strongly declines, giving rise to an axisymmetric Marangoni flow from the hexanediol-rich contact line along the liquid-gas interface to the water-rich top of the droplet.

However, in the limit of high hexanediol concentrations, the surface tension slightly increases again. This tiny increase of less than half a mN/m triggers the emergence of a reversed Marangoni flow in the rim region of the droplet, which breaks the azimuthal symmetry of the flow and composition field. When the hexanediol concentration near the contact line exceeds the critical composition with minimum surface tension, tiny spots of enhanced hexanediol concentrations appear at the contact line. Subsequently, the Marangoni dynamics leads to a coarsening of these spots until the entire droplet is covered and the flow ceases.

By means of experiments, three-dimensional finite element simulations and numerical azimuthal stability analysis, we investigate this intriguing phenomenon. Furthermore, we predict the wavelength of this remarkable and naively unexpected instability for any locally parabolic surface tension profile by means of a Marangoni number.   

Physcis added and informed neural network for time-dependent prediction of droplet evaporation

In this paper, a deep learning approach is proposed for predicting droplet evaporation over time, using image-based analysis. The method's key feature lies in the enhancement of prediction accuracy and reduced demand for extensive training data by incorporating physical laws into the learning process. Two methods introduce biases based on the underlying physics. Firstly, the contact angle and diameter are measured from training images, and this information is used to enhance the physical plausibility of predicted images. Secondly, the time-dependent changes in the contact angle and contact diameter of output images are monitored, ensuring their alignment with known physical phenomena such as receding angles—whether they are increasing, decreasing, or remaining constant—thus guiding the learning process of the neural network. Promising results showcase improved predictive capabilities for droplet evaporation. By combining image-based learning with physical constraints, an approach that presents a step towards accurate and efficient prediction of droplet evaporation phenomena is discussed. The potential applications of this approach encompass various fields, including materials science, engineering, and environmental studies. Overall, the successful integration of deep learning and physical principles to tackle complex and time-dependent processes is showcased, paving the way for advancements in droplet evaporation prediction and beyond.   

A theoretical and experimental investigation of the simultaneous spreading and freezing of droplets

This research explores the freezing process of water droplets on solid surfaces through a validated theoretical model with experimental observations. Understanding the dynamics of frozen droplets is essential in advancing manufacturing research, such as 3D printing and freeze casting, as well as bioengineering. A very few studies have delved into the intricacies of this process, specifically the freezing dynamics while the droplet's mass and volume are increasing. To study this, a liquid needle technique was used to deposit droplets on a subcooled surface and trigger solidification. The theoretical model considers the overall energy balance, including incoming jet kinetic energy, surface energy, gravitational energy, viscous dissipation, and heat transfer on a subcooled substrate. A jet impact model, combined with heat transfer between the drop and substrate, is used for the initial condition. The current model simultaneously predicts the temporal evolution of droplet growth and solidification rate while the droplet is spreading. Non-dimensionalization of the governing equations indicates that the Bond, Reynolds, Weber, and Stefan numbers significantly influence the outcome and help us better understand the different stages of droplet freezing.   

Investigation of selective evaporation in binary mixture droplet using laser interferometry

Recently, the evaporation of multicomponent droplets on solid substrates has gained significant attention due to its practical applications in various industrial fields, such as spray cooling, inkjet printing, uniform coating, and evaporation-induced self-assembly (EISA). A crucial aspect to understand during the evaporation process of such droplets is selective evaporation, which arises from the different volatility of each component. The selective evaporation induces Marangoni stresses along the droplet surface that can generate a circulating internal flow. Kim and Stone (JFM 2018) used physicochemical effects to directly visualize the selective evaporation of the more volatile liquid components in the evaporating binary mixture droplet. However, there has been no direct observation of the selective evaporation phenomena across the gas-liquid interface of the droplet yet. In this study, using laser interferometry, we measured the time-dependent mole fraction distribution of evaporated vapors of more volatile liquid components. Additionally, we performed side-view shadowgraphy measurements simultaneously to track the change in the droplet radius and contact angle during evaporation. To ensure the accuracy of our findings regarding selective evaporation, we compared and validated the results obtained from interferometry and shadowgraphy. We expect that this direct observation of selective evaporation, i.e., its visualization across the gas-liquid interface using laser interferometry, will provide useful insights into its complex process of the evaporation of a multi-component liquid droplet. These insights can have significant implications for various industrial applications, enabling better understanding and control of evaporation processes in practical settings.   

Evaporation dynamics of airborne water-based droplets with contaminants

Accurate measurement of bioaerosol particles is crucial to assess the risks associated with the airborne transmission of pathogens. However, the size of these airborne water-based pathogen-laden particles changes rapidly due to evaporation. The presence of contaminants that affect surface tension and viscosity pose a challenge for accurate prediction of droplet fate. In this study, this phenomenon is investigated experimentally under controlled ambient conditions. Droplets 53 micrometers in diameter are produced using an inkjet printhead and injected in a concurrent flow of pressurized air, under controlled temperatures and relative humidities. The evolution of the droplet size is quantitatively assessed through phase Doppler anemometry. Oil-based droplets are used as a reference as they do not evaporate significantly. Water droplets are then considered, first pure and then contaminated with a surfactant or dissolved Polyethylene glycol, to simulate the properties of potentially contaminated droplets from humans or engineered sources. The results will quantify the discrepancies in the evaporative behavior of solid-containing droplets compared to their pure water counterparts, highlighting how the infection risk is affected by ambient conditions and emphasizing the need to consider evaporation when measuring the size of potentially contaminated droplets.   

Phase-field simulation of freezing water droplet

When a water droplet freezes on a cold plate, a pointy tip forms as the result of volume expansion. In this presentation, we will introduce a quasi-compressible phase-field model that deals with this non-isothermal three-phase system involving water, ice, and air. The water-ice phase transition and the water-air fluid interface are handled by the Allen-Cahn and the Cahn-Hilliard equations, respectively. The governing equations, including the two phase-field equations, the Navier-Stokes equations, and the energy equation, are designed such that the non-negative entropy production is guaranteed. These equations are then solved by finite-element methods using the open-source deal.ii library. Our model reproduces the Gibbs-Thomson and Clausius-Clapeyron equations, which establish the dependence of the melting temperature on interface curvature and pressure, respectively. Furthermore, the built-in quasi-compressibility accurately accounts for the volume change due to the water-ice density contrast during the phase transition. With proper parameters, our simulation captures the pointy tip of the frozen droplet with good agreement with the experiment. In the end, we will discuss the effects of the water-ice-air tri-junction conditions and other parameters on the final shape of the frozen droplet.   

Snowphobic Behavior of Needle-Like Surfaces

Numerous icing-induced hazards occur due to snow accumulation on surfaces such as electrical wires and poles in extremely cold, humid environments. Needle-like leaves of some conifer species such as the pine trees can exhibit effective snowphobic behavior to survive in such harsh winter environments by localizing snow and minimizing snow accumulation. We hypothesize that the hierarchical structure of the pine leaves and the arrangement of the leaves effectively reduce the effects of snow and partially melted snow. Experimentally, and numerically, we observe and analyze the deposition and removal mechanism of snow on real conifer leaf samples as well as on artificial samples with hierarchical structures. We further investigate various phase change of snow, leading to partially melted snow and water vapor flux diffusion associated with preventing the leaf stems from icing problems. This research will provide important insights while designing functional snowphobic surfaces by employing hierarchical features under various forced convection conditions.