Droplet Growth Dynamics Research Articles

Numerical Investigation of Heat Transfer and Development in Spherical Condensation Droplets.

This study establishes thermodynamic assumptions regarding the growth of condensation droplets and a mathematical formulation of droplet energy functionals. A model of the gas-liquid interface condensation rate based on kinetic theory is derived to clarify the relationship between condensation conditions and intermediate variables. The energy functional of a droplet, derived using the principle of least action, partially elucidates the inherent self-organizing growth laws of condensed droplets, enabling predictive modeling of the droplet's growth. Considering the effects of the condensation environment and droplet heat transfer mechanisms on droplet growth dynamics, we divide the process into three distinct stages, marked by critical thresholds of 105 nm3 and 1010 nm3. Our model effectively explains why the observed contact angle fails to reach the expected Wenzel contact angle. This research presents a detailed analysis of the factors affecting surface condensation and heat transfer. The predictions of our model have an error rate of less than 3% error compared to baseline experiments. Consequently, these insights can significantly contribute to and improve the design of condensation heat transfer surfaces for the phase-change heat sinks in microprocessor chips.

Effect of water droplet growth dynamics on electrode current in fuel-cell catalyst layers

Fuel cells are a promising next-generation energy-conversion technology designed to replace internal combustion engines in transportation applications. However, much work remains to optimize them. Operation at high humidities causes liquid water droplet formation on Pt catalyst particles during oxygen reduction, potentially impeding reactant arrival to the reactive electrode. In this work, four different cases of water droplet growth in fuel-cell catalyst layers are considered: pinned or advancing droplets on a bare Pt surface, advancing droplets on a Nafion film, and water-layer growth in carbon nanopores. Transient drop growth is captured with a combination of mass, species mass, and momentum balances, and the subsequent limiting current is determined via oxygen diffusion and Tafel kinetics. Water droplets are found not to be mass-transfer limiting due to the relatively large liquid-gas area compared to the Pt nanoparticle. Mass-transfer-limited behavior is calculated in carbon nanopores.

Microscale Confinement and Wetting Contrast Enable Enhanced and Tunable Condensation.

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

Numerical simulations of growth dynamics of breath figures on phase change materials: The effect of accelerated coalescence due to droplet motion

We present the growth dynamics of breath figures on phase change materials using numerical simulations. We propose a numerical model which accounts for both growth due to condensation and random motion of droplets on the substrate. We call this model as growth and random motion (GRM) model. Our analysis shows that for dynamics of droplet growth without droplet motion, simulation results are in good agreement with well-established theories of growth laws and self-similarity in surface coverage. We report the emergence of a growth law in the coalescence-dominated regime for the droplets growing simultaneously by condensation and droplet motion. The overall growth of breath figures (BF) exhibits four growth regions, namely, initial , intermediate or crossover , coalescence-dominated regime , and no coalescence regime in late time , where and t are the average droplet radius and time, respectively. The power law exponents are , , , and . Moreover, the surface coverage reaches a maximum value where the third growth regime starts. We also demonstrate that during the growth dynamics of BF, the random motion amplitude δ and its probability p(R) linked to the power exponent γ of droplet radius R have a specific limiting range within which its effect is more predominant.

Numerical investigation of multiple droplet growth dynamics on a solid surface using three-dimensional lattice Boltzmann simulations

We present an investigation of multiple droplet growth dynamics on homogeneous and patterned surfaces during dropwise condensation. Our analysis is based on three-dimensional thermal lattice Boltzmann simulations. First, we investigate the growth dynamics on homogeneous surfaces. The analysis of growth dynamics of droplets on a homogeneous surface shows that the lower the static contact angle of the surface, the higher the condensed volume of liquid. After that, we discuss the growth dynamics of droplets on patterned surfaces (a surface with hydrophilic and hydrophobic regions). We show that the pattern formed by the condensed droplets on the patterned surfaces is completely different from the homogeneous surface. This is due to the pinning effect at the interface of the hydrophilic–hydrophobic region. Moreover, the shape of the droplets is not spherical, as we observe in the case of homogeneous surfaces. We also demonstrate that the condensed volume V for all patterned surfaces is higher than that for the homogeneous surface. However, the condensed volume decreases with an increase in the contact angle of the hydrophilic region. We then present the effect of size of the hydrophilic spot. We find that the condensed volume increases with an increase in radius of the hydrophilic spot.

Chromatin Mechanics Dictates Subdiffusion and Coarsening Dynamics of Embedded Condensates

DNA is organized into chromatin, a complex polymeric material which stores information and controls gene expression. An emerging mechanism for biological organization, particularly within the crowded nucleus, is biomolecular phase separation into condensed droplets of protein and nucleic acids. However, the way in which chromatin impacts the dynamics of phase separation and condensate formation is poorly understood. Here, we utilize a powerful optogenetic strategy to examine the interplay of droplet coarsening with the surrounding viscoelastic chromatin network. We demonstrate that droplet growth dynamics are directly inhibited by the chromatin-dense environment, which gives rise to an anomalously slow coarsening exponent, beta∼0.12, contrasting with the classical prediction of beta=1/3. Using scaling arguments and simulations, we show how this arrested growth can arise due to subdiffusion of individual condensates, predicting beta∼alpha/3, where alpha is the diffusive exponent. Tracking the fluctuating motion of condensates within chromatin reveals a subdiffusive exponent, alpha∼0.5, which explains the anomalous coarsening behavior and is also consistent with Rouse-like dynamics arising from the entangled chromatin. Our findings have implications for the biophysical regulation of the size and shape of biomolecular condensates and suggest that condensate emulsions can be used to probe the viscoelastic mechanical environment within living cells.

Chromatin mechanics dictates subdiffusion and coarsening dynamics of embedded condensates

DNA is organized into chromatin, a complex polymeric material that stores information and controls gene expression. An emerging mechanism for biological organization, particularly within the crowded nucleus, is biomolecular phase separation into condensed droplets of protein and nucleic acids. However, the way in which chromatin impacts the dynamics of phase separation and condensate formation is poorly understood. Here we utilize a powerful optogenetic strategy to examine the interplay of droplet coarsening with the surrounding viscoelastic chromatin network. We demonstrate that droplet growth dynamics are directly inhibited by the chromatin-dense environment, which gives rise to an anomalously slow coarsening exponent, β ≈ 0.12, contrasting with the classical prediction of β = 1/3. Using scaling arguments and simulations, we show how this arrested growth can arise due to subdiffusion of individual condensates, predicting β ≈ α/3, where α is the diffusive exponent. Tracking the fluctuating motion of condensates within chromatin reveals a subdiffusive exponent, α ≈ 0.5, which explains the anomalous coarsening behaviour and is also consistent with Rouse-like dynamics arising from the entangled chromatin. Our findings have implications for the biophysical regulation of the size and shape of biomolecular condensates and suggest that condensate emulsions can be used to probe the viscoelastic mechanical environment within living cells. Biomolecules in the cell nucleus form condensates at a rate slower than that predicted by the theory of droplet growth. Experiments on living cells attribute this anomalous coarsening behaviour to subdiffusive dynamics in the crowded nucleus.

Accelerated Ripening in Chemically Fueled Emulsions**

AbstractChemically fueled emulsions are solutions with droplets made of phase‐separated molecules that are activated and deactivated by a chemical reaction cycle. These emulsions play a crucial role in biology as a class of membrane‐less organelles. Moreover, theoretical studies show that droplets in these emulsions can evolve to the same size or spontaneously self‐divide when fuel is abundant. All of these exciting properties, i. e., emergence, decay, collective behavior, and self‐division, are pivotal to the functioning of life. However, these theoretical predictions lack experimental systems to test them quantitively. Here, we describe the synthesis of synthetic emulsions formed by a fuel‐driven chemical cycle, and we find a surprising new behavior, i. e., the dynamics of droplet growth is regulated by the kinetics of the fuel‐driven reaction cycle. Consequently, the average volume of these droplets grows orders of magnitude faster compared to Ostwald ripening. Combining experiments and theory, we elucidate the underlying mechanism.

Phase separation and nucleation in mixtures of particles with different temperatures

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase separation kinetics and propose a theory of phase separation of colloidal mixtures in the diffusive limit. Our model considers a mixture of diffusing particles coupled to different thermostats, it thus has a non-equilibrium nature due to the temperature differences. However, we show that indeed the system recovers an effective equilibrium thermodynamics in the dilute limit. We obtain phase diagrams showing the asymmetry in concentrations due to activity differences. By using a more general approach, we show the equivalence of phase separation kinetics with the well known Cahn-Hilliard theory. On the other hand, higher order expansions in concentration indicate the emergence of non-equilibrium effects leading to a breakdown of the equilibrium analogy. We lay out the general theory in terms of accessible parameters which we demonstrate by several applications. In this simple formalism, we capture a positive surface tension for hard spheres}, and interesting scaling laws for interfacial properties, droplet growth dynamics, and phase segregation conditions. \rev{Several of our results are in agreement with existing numerical simulations while we also propose testable predictions.

ANALYSIS OF GEOMETRIC CHARACTERISTICS OF TWO-PHASE POLYMER-SOLVENT SYSTEMS DURING THE SEPARATION OF SOLUTIONS ACCORDING TO THE INTENSITY OF THE IMAGE OF MICROGRAPHS

This paper discusses the study of the shapes and sizes of polymer droplets formed during the phase separation of their solutions with increasing temperature, as well as the parameters of the transitional layers of polymer condensing on the droplet surface formed during this process. For the study, a copolymer of polyethylene oxide and polypropylene oxide was chosen, whose behavior in aqueous solutions and the change in hydrophilic-hydrophobic balance depends on temperature. It has been established that the application of the method of digital image processing allows the introduction of the quantitative criterion – image intensity of a photo. For a more detailed study of the behavior of polymer molecules at the phase boundary, depending on the temperature, the studies of the temperature-dependent behavior of a number of polymers of different composition and structure have been carried out. The use of the digital image processing method for polymer droplets makes it possible to determine the parameters of droplets and their transition layers, to determine the dynamics of nucleation and droplet growth and density changes in the transition layer by the image intensity parameter. The paper has found out that embryos of pluronic are unevenly distributed by volume of solution with the presence of zones with a maximum number of molecules and a zone with a minimum of assembly of molecules. The practical value of the work is in the fact that the results of the study can be used to assess the dynamics of the separation of polymer solutions without involving the time-consuming and expensive instrumental methods of physical and chemical analysis.

Electrowetting-based enhancement of droplet growth dynamics and heat transfer during humid air condensation

Condensation heat transfer can be significantly enhanced by condensing vapor as droplets (instead of a film), which rapidly roll-off. This work studies the use of electrowetting to enhance coalescence, growth and roll-off dynamics of condensed droplets, thereby enhancing the condensation rate and associated heat transfer. This enhancement depends on the nature of fluid motion (translation of droplets, oscillations of the three phase line), which in turn depends on the magnitude and frequency of the applied electrical actuation waveform. Experiments are conducted to study early-stage droplet growth dynamics, as well as steady state condensation under the influence of an electric field. It is seen that droplet growth is enhanced as the voltage and frequency of AC electric fields is increased, with AC electric fields seen to be more effective than DC electric fields. Roll-off dynamics also depends on the frequency of the AC field. Overall, electric fields alter the droplet size distribution and move the condensate to more favorable states for removal from the surface. The condensation rate depends on the roll-off diameter of the droplet, frequency of roll-off events, and on the interactions of the rolled-off droplets with the remainder of the droplets. An analytical heat transfer model is utilized to relate the measured condensation rate with condensation heat transfer. It is noted that this study deals with condensation of humid air, and not pure steam. Overall, this study reports more than 30% enhancement in condensation rate resulting from the applied electric field, which highlights the attractiveness of electrowetting for condensation heat transfer enhancement.

Study of Microdroplet Growth on Homogeneous and Patterned Surfaces Using Lattice Boltzmann Modeling

We present droplet growth dynamics on homogeneous and patterned surfaces (surface with hydrophilic and hydrophobic region) using two-dimensional thermal lattice Boltzmann method (LBM). In the first part, we performed 2D simulations on homogeneous hydrophobic surfaces. The result shows that the droplet grows at higher rate on a surface with higher wettability which is attributed to low conduction resistance and high solid–liquid contact area. In the later part, we performed simulations on patterned surface and observed that droplet preferentially nucleates on the hydrophilic region due to lower energy barrier and grows in constant contact line (CCL) mode because of contact line pinning at the interface of hydrophilic–hydrophobic region. As the contact angle reaches the maximum value of hydrophobic surface, contact line depins and droplet shows constant contact angle (CCA) growth mode. We also discuss the effect of characteristic width of hydrophilic region on growth of droplet. We show that contact angle of the droplet increases rapidly and reaches the contact angle of hydrophobic region on a surface with a lower width of the hydrophilic surface.

Characterizing droplet breakup rates of shear-thinning dispersed phase in microreactors

A two-phase flow predictive model with the integration of conservative level-set method (LSM) and Carreau-Yasuda constitutive equation was developed herein. The LSM was chosen as a potential interface capturing scheme for elucidating the interfacial phenomena including insight into the mechanism of shear-thinning droplets. In present paper, the dynamics of shear-dependent droplet emergence, growth, detachment and translocation in a Newtonian microsystem were examined via computational fluid dynamics (CFD) analysis. Dilute sodium carboxymethylcellulose (Na-CMC) solution was treated as dispersed phase (70 mPa.s < ηo < 10.2644 Pa.s) whereas the olive oil (68 mPa.s) was designated as continuous phase. Visualisation experiments were carried out and these laboratory data were used to validate the simulation results. Detailed 2D simulations were presented to examine systematically the impact of fluid properties on the droplet breakup rate at predefined flow rate ratio, Q of 0.05. The results yielded an inflection point in the dependence of droplet breakup rate on Na-CMC concentration was found in between the dilute and semi-dilute concentration regimes. This inflection point displays a non-monotonic profile which is mainly caused by the considerable viscosity effect of Na-CMC polymer when its concentration increases above a critical value (C > C*˜0.40 wt%). This striking behaviour highlights the importance of rheological effects in flows with a shear-dependent fluid under various flow conditions. The viscous effect of Na-CMC fluids substantially affects the manipulation over the droplet pinch-off time and production rate. Thus, it necessitate the control of the shear rate by adjusting the flow conditions and aspect ratio of microchannels.

Droplet Growth Dynamics during Atmospheric Condensation on Nanopillar Surfaces

ABSTRACTThe Gibbs free energy barrier for heterogeneous nucleation of a condensed droplet on a rough surface changes significantly with changes of humidity content in the condensing environment. The influence of environmental factors (ambient temperature and relative humidity) and substrate characteristics (topology, surface chemistry, and substrate temperature) on atmospheric condensation phenomenon is very important to elucidate the condensed droplet wetting state and condensate harvesting applications. Condensation from the humid air has been reported for plain silicon and fabricated nanopillar surfaces to facilitate condensate harvesting. Droplet growth and size distributions were recorded for 90 min. Spherical droplets condensed on the silicon surfaces and irregular-shaped droplets were observed on the nanopillar surfaces due to the pinning effect of the pillars. The effect of droplet pinning on coalescence events has been described based on the energy balance for the condensed droplets. A mathematical model reveals that certain dimensional combinations (pillar pitch, pillar diameter, and pillar height) of the nanopillar geometry are required to exhibit the pinning mechanism for condensed droplets. Regeneration of droplets was observed at void spaces generated from coalescence events. The growth of individual droplets was tracked over multiple time and length scales, starting from nucleation to get further insight into the direct growth and coalescence mechanisms.Abbreviation: ESEM: Environmental Scanning Electron Microscope; HCP: Hexagonal Closed-Packed; MPL: Microsphere Photolithography; RH: Relative Humidity

Synthesizing Pickering Nanoemulsions by Vapor Condensation.

Nanoparticle-stabilized (Pickering) emulsions are widely used in applications such as cosmetics, drug delivery, membranes, and material synthesis. However, formulating Pickering nanoemulsions remains a significant challenge. Herein, we show that Pickering nanoemulsions can be obtained in a single step even at very low nanoparticle loadings (0.2 wt %) by condensing water vapor on a nanoparticle-infused subcooled oil that spreads on water. Droplet nuclei spontaneously submerge within the oil after nucleating at the oil-air interface, resulting in the suppression of droplet growth by diffusion, and subsequently coalesce to larger sizes until their growth is curtailed by nanoparticle adsorption. The average nanoemulsion size is governed by the competition between nanoparticle adsorption kinetics and droplet growth dynamics, which are in turn a function of nanoparticle size, concentration, and condensation time. Controlling such factors can lead to the formation of highly monodisperse nanoemulsions. Emulsion formation via condensation is a fast, scalable, energy-efficient process that can be adapted for a wide variety of emulsion-based applications in biology, chemistry, and materials science.

Dropwise Condensation on Superhydrophobic Microporous Wick Structures

Previous research in dropwise condensation (DWC) on rough microtextured superhydrophobic surfaces has demonstrated evidence of high heat transfer enhancement compared to smooth hydrophobic surfaces. In this study, we experimentally investigate the use of microporous sintered copper powder on copper substrates coated with a thiol-based self-assembled monolayer to attain enhanced DWC for steam in a custom condensation chamber. Although microtextured superhydrophobic surfaces have shown advantageous droplet growth dynamics, precise heat transfer measurements are underdeveloped at high heat flux. Sintered copper powder diameters from 4 μm to 119 μm were used to investigate particle size effects on heat transfer. As powder diameter decreased, competing physical factors led to improved thermal performance. At consistent operating conditions, we experimentally demonstrated a 23% improvement in the local condensation heat transfer coefficient for a superhydrophobic 4 μm diameter microporous copper powder surface compared to a smooth hydrophobic copper surface. For the smallest powders observed, this improvement is primarily attributed to the reduction in contact angle hysteresis as evidenced by the decrease in departing droplet size. Interestingly, the contact angle hysteresis of sessile water droplets measured in air is in contradiction with the departing droplet size observations made during condensation of saturated steam. It is evident that the specific design of textured superhydrophobic surfaces has profound implications for enhanced condensation in high heat flux applications.

Growth Rates and Spontaneous Navigation of Condensate Droplets Through Randomly Structured Textures.

Dropwise condensation is a phenomenon of common occurrence in everyday life, the understanding and controlling of which is of great interest to applications ranging from technology to nature. Scalable superhydrophobic textures on metals are of direct relevance in improving phase change heat transport in realistic industrial applications. Here we reveal important facets of individual droplet growth rate and droplet departure during dropwise condensation on randomly structured hierarchical superhydrophobic aluminum textures, that is, surfaces with a microstructure consisting of irregular re-entrant microcavities and an overlaying nanostructure. We demonstrate that precoalescence droplet growth on such a surface can span a broad range of rates even when the condensation conditions are held constant. The fastest growth rates are observed to be more than 4 times faster as compared to the slowest growing droplets. We show that this variation in droplet growth on the hierarchical texture is primarily controlled by droplet growth dynamics on the nanostructure overlaying the microstructure and is caused by condensation-induced localized wetting nonuniformity on the nanostructure. We also show that the droplets nucleating and growing within the microcavities are able to spontaneously navigate the irregular microcavity geometry, climb the microtexture, and finally depart from the surface by coalescence-induced jumping. This self-navigation is realized by a synergistic combination of self-orienting Laplace pressure gradients induced within the droplet as it dislodges itself and moves through the texture, as well as multidroplet coalescence.

Highly Ordered Arrays of Femtoliter Surface Droplets

Highly ordered arrays of attoliter to femtoliter droplets are created on substrates pre-patterned with smooth circular microdomains. The morphology and volume of the droplets are governed by the droplet growth dynamics during the solvent exchange. These tunable droplet arrays can be potentially exploited for the fabrication of nanolens arrays for photon manipulation, among other applications.

Hierarchical Superhydrophobic Copper for Sustained Dropwise Condensation

Engineering surfaces that sustain continuous dropwise condensation, and are composed of materials commonly employed in heat transfer applications, are of great interest for scaled-up industrial systems. We fabricate hierarchical micro/nano-structured superhydrophobic surfaces on copper substrates. Condensate droplet growth dynamics on the as-fabricated samples were investigated using an environmental scanning electron microscope (ESEM; FEI Quanta 3D, ~6 torr, ~3 °C stage). Time-lapse ESEM images show that the condensate droplets preferentially nucleate at the bases of the hill-shaped microstructures (40 s). The droplets at the microstructure bases coalesce; merged droplets rise and appear to be suspended atop adjacent microstructures (180-220 s). These droplets, when triggered by coalescence, can gain sufficient kinetic energy by a reduction in droplet surface area/energy to spontaneously depart from the substrate. This droplet motion sweeps additional droplets in the trajectory and exposes fresh space for formation of new droplets (220-250 s). These droplet growth and departure dynamics are facilitated by the combination of microscale and nanoscale roughness features on the surface, and the behavior provides important insight into surface design requirements for sustaining dropwise condensation in thermal management applications.

The effect of relative humidity on dropwise condensation dynamics

Abstract Dropwise condensation of atmospheric water vapor is important in multiple practical engineering applications. The roles of environmental factors and surface morphology/chemistry on the condensation dynamics need to be better understood to enable efficient water-harvesting, dehumidification, and other psychrometric processes. Systems and surfaces that may promote faster condensation rates and self-shedding of condensate droplets could lead to improved mass transfer rates and higher water yields in harvesting applications. In the present study, experiments are performed in a facility that allows visualization of the condensation process on a vertically oriented, hydrophobic surface at a controlled relative humidity and surface subcooling temperature. The distribution and growth of water droplets are monitored across the surface at different relative humidities (45%, 50%, 55%, and 70%) at a constant surface subcooling temperature of 15 °C below the ambient temperature (20 °C). The droplet growth dynamics exhibits a strong dependency on relative humidity in the early stages during which there is a large population of small droplets on the surface and single droplet growth dominates over coalescence effects. At later stages, the dynamics of droplet growth is insensitive to relative humidity due to the dominance of coalescence effects. The overall volumetric rate of condensation on the surface is also assessed as a function of time and ambient relative humidity. Low relative humidity conditions not only slow the absolute rate of condensation, but also prolong an initial transient regime over which the condensation rate remains significantly below the steady-state value.