Nucleation Rate Of Droplets Research Articles

Model optimization and mechanism analysis of two-stage ejector considering nonequilibrium condensation

Two-stage ejectors are widely used in multi-effect distillation and refrigeration systems owing to their vacuum and pressurization capabilities. However, most studies on two-stage ejectors are based on the dry-gas hypothesis, which neglects the universal physical phenomenon of condensation. A wet-steam model of two-stage ejectors is established and compared to the dry-gas model in this paper. Simulation results indicate that the proposed wet-steam model more accurately describes the performance and complex flow field characteristics of the two-stage ejector. Moreover, the nonequilibrium condensation mechanism of the fluid within the two-stage ejector under variable conditions is revealed. The results show that as the two-stage main nozzle pressure increases from 300 kPa to 550 kPa, the liquid mass fraction increases, and the droplet nucleation rate of the two stages decreases by 14.17 % and 13.14 %. When the first-stage actuating pressure is increased, the first-stage fluid restricts the expansion state of the second-stage main jet core and weakens the vapor condensation in the region of the shock chain. Furthermore, the experimental results demonstrate that compared with the dry-gas model, the prediction error of entrainment ratio and the secondary flow obtained by the proposed model are reduced by 26.67 % and 43.04 %, respectively.

Rational design and easy fabrication of transparent photothermal/hygroscopic composite coatings with long-lasting antifogging performance under sunlight activation.

Hygroscopic polymers are good candidates for antifogging coatings, but their long-term effectiveness is limited by the equilibrium between water absorption and expansion. As an efficient and environmentally friendly solution, photothermal materials are being introduced into the field of antifogging. However, there is a need for enhancement in the spectral characteristics of most photothermal materials within the visible light region. In addition, photothermal antifogging coatings often exhibit a delay in heating response, which hinders their ability to promptly evaporate condensed water droplets in the absence of illumination or during initial illumination. Here, a bilayer structure design of photothermal nanomaterials/hygroscopic polymers is proposed to achieve long-term antifogging under sunlight activation. Ensuring the rapid absorption of condensed water droplets on the coating surface, while simultaneously achieving efficient photothermal conversion for a swift temperature increase over the entire coating, is key to this approach, which will not only suppress early fogging but also lead to an exponential decrease of the nucleation rate of droplets. During this process, a dynamic equilibrium is gradually established between the condensation and evaporation of fog droplets, leading to long-term antifogging properties. The light transmittance of the composite coatings reaches as high as ca. 75% in the visible light region, making them well suited for a diverse range of transparent substrate and device applications. A clear field of view can be maintained for at least 6 h under 1 sun illumination above 65 °C hot steam. The antifogging/defogging performance is effectively demonstrated even under challenging non-ideal natural conditions, such as low solar irradiation during dusk or when placed indoors behind windows.

Effects of surface temperature and Weber number on the dynamic and freezing behavior of impacting water droplets on a superhydrophobic ultra-cold surface

The dynamic and freezing behavior of a water droplet impacting a superhydrophobic cold surface is worthy of investigation. In this study, experiments are conducted to examine the impact and freezing of a water droplet on a cold superhydrophobic surface whose temperature changes in a wide range between −10 °C and −60 °C. A numerical model that introduces a continuous energy balance equation is developed to investigate the process numerically. The effects of surface temperature, Weber number, and initial droplet temperature on the droplet morphology, spread factor, contact time, and rebound height are investigated. The droplet exhibits three different behaviors as the surface temperature decreases: full rebound, partial rebound, and full adhesion. For the full rebound case, the results indicate that the growth rate of the contact time with decreasing surface temperature increases as the Weber number decreases. For the full adhesion case, the variation in the surface temperature minimally affects the dynamic behavior of the droplet impacting on an ultracold superhydrophobic surface (below −40 °C). The effect of surface temperature on the maximum spread factor is more pronounced at higher Weber numbers. Additionally, the ice nucleation rate is analyzed theoretically. The results show that the nucleation rate of droplets impacting an ultracold surface remains almost constant regardless of the surface temperature and surface roughness. Moreover, a regime map showing the different droplet morphologies correlating with the surface temperature and Weber number is established. The critical surface temperatures for different droplet morphologies of supercooled and room-temperature droplets are analyzed. This study allows us to better understand the dynamic and heat transfer mechanisms involved in the impact and freezing of a water droplet on a superhydrophobic surface.

Numerical Analysis of Steam Ejector Performance with Non-Equilibrium Condensation for Refrigeration Applications

In recent years, there has been great interest in developing cooling systems with humidity- and temperature-independent control capabilities that can operate efficiently at varying temperatures. This paper proposes a bi-loop double-evaporator ejection–compression cycle, which utilizes low-grade heat and is suitable for the construction industry. The proposed cycle involves the concurrent operation of a vapor compression cycle and an ejector refrigeration cycle that enables it to handle altered pressure levels and operate with varying compression ratios all the way to a common condenser pressure. Conventional computational fluid dynamics (CFD) approaches often model steam as an ideal gas with single-phase flow. In contrast, this research employs the wet steam model to optimize ejector geometry. The wet steam model takes into account non-equilibrium water vapor condensation, thus providing a more precise assessment of spontaneous condensation behavior and its impact on ejector performance. When compared to the conventional dry gas model, the use of the wet steam model dramatically decreases the entrainment ratio error from 16.24% for single-phase steam to 3.92% when compared to experimental data. This study concentrates on four critical attributes of wet steam, including Mach number, droplet nucleation rate, average droplet radius, and liquid mass fraction, to develop a strategy for enhancing ejector performance and efficiency. The study demonstrates that optimal area and primary nozzle diameter ratios for the steam ejector are 5 and 2.4, respectively. Increasing the area ratio mitigates condensation intensity, thereby reducing the liquid mass fraction in the diffuser. Overall, this paper provides valuable insights into improving and optimizing ejector performance, thus highlighting the importance of considering the behavior of spontaneous condensation in ejector design and modeling.

Detection of Fibril Nucleation in Micrometer-Sized Protein Condensates and Suppression of Sup35NM Fibril Nucleation by Liquid-Liquid Phase Separation.

Elucidating the link between amyloid fibril formation and liquid-liquid phase separation (LLPS) is crucial in understanding the pathologies of various intractable human diseases. However, the effect of condensed protein droplets generated by LLPS on nucleation (the initial step of amyloid formation) remains unclear because of the lack of available quantitative analysis techniques. This study aimed to develop a measurement method for the amyloid droplet nucleation rate based on image analysis. We developed a method to fix micrometer-sized droplets in gel for long-term observation of protein droplets with known droplet volumes. By combining this method with image analysis, we determined the nucleation dynamics in droplets of a prion disease model protein, Sup35NM, at the single-event level. We found that the nucleation was unexpectedly suppressed by LLPS above the critical concentration (C*) and enhanced below C*. We also revealed that the lag time in the Thioflavin T assay, a semi-quantitative parameter of amyloid nucleation rate, does not necessarily reflect nucleation tendencies in droplets. Our results suggest that LLPS can suppress amyloid nucleation, contrary to the conventional hypothesis that LLPS enhances it. We believe that the proposed quantitative analytical method will provide insights into the role of LLPS from a pathological perspective.

Nucleation enhancement by energy dissipation with the collision of a supercooled water droplet

Lack of knowledge on nucleation with mechanical disturbances hinders researchers in understanding the anti-icing properties of superhydrophobic surfaces. In this research, experiments are designed to observe the freezing process of a supercooled water droplet at −14 °C with different levels of external disturbances by changing the impact velocity, and the nucleation rates are statistically analyzed. It is found that compared with the static state, the nucleation rates of droplets during the collision increase by three and five orders of magnitude on the hydrophilic epoxy resin and superhydrophobic polytetrafluoroethylene (PTFE) surfaces, respectively, which leads to a much higher instantaneous nucleation rate on the superhydrophobic surface than on the hydrophilic surface. Then, the mechanical energy dissipation during the impact is analyzed. The logarithm of the nucleation rate is approximately linear in relation to the logarithm of the average energy dissipation rate, while the nucleation rate of the rough PTFE surface increases more rapidly than that of the other smooth surface. Finally, the effect of the energy dissipation on the nucleation energy barrier is discussed theoretically and an impact-nucleation model is proposed, which drives the reconsideration of the design of a superhydrophobic anti-icing coating.

Enhanced dropwise condensation on heterogeneously hybrid patterned surfaces

Superhydrophilic and superhydrophobic hybrid (SSH) surfaces were developed to study the condensation heat transfer enhancement on copper substrates. The synergistic combination of superhydrophobic and superhydrophilic surfaces is conducive to enhancing droplet nucleation rate, well-controlled coalescence and efficient condensate removal. Three types of superhydrophilic and superhydrophobic hybrid surfaces were investigated, having pattern spacing (the distance between two superhydrophilic regions) of 300 μm, 600 μm, and 600 μm, and corresponding pattern dimensions of 600 × 600 μm2，600 × 600 μm2, and 800 × 800 μm2, named as SSH-1, SSH-2, and SSH-3, respectively. The experimental results revealed condensation heat transfer performance of hybrid surfaces outperformed than that of conventional complete superhydrophobic surface. The SSH-2 surface had the largest heat transfer coefficient under the entire range of surface subcooling. At a surface subcooling of 7.1 K, heat transfer coefficient of SSH-2 surface was 1.1 and 1.3 times than that of SSH-3 and SSH-1 surfaces, respectively. Pattern spacing could produce significant influence on the heat transfer performance of hybrid surfaces in relative to the influence of pattern dimension. Compared with complete superhydrophobic surface, the heat flux of SSH-2 surface was enhanced up to 31–73%.

Gradient mixed wettability surfaces for enhancing heat transfer in dropwise flow condensation

Steam condensation plays a pivotal role in a broad range of industrial applications. Dropwise condensation, which occurs on hydrophobic and superhydrophobic surfaces, has been proven to have a larger heat transfer coefficient than filmwise condensation because of enhanced droplet detachment. However, hydrophilic surfaces possess a better droplet nucleation rate compared to hydrophobic and superhydrophobic surfaces. These two characteristics (high droplet nucleation rate and better droplet removal) require counteracting properties. Many studies increased the nucleation rate by creating nanostructured surfaces. Wettability contrast mechanism is another approach, which could achieve both high nucleation rate and droplet removal, and have attracted much attention in enhancing a better heat transfer performance. In this study, gradient mixed wettability surfaces were developed on copper surfaces to improve heat transfer during steam flow condensation inside a minichannel. Circular hydrophobic islands were fabricated on a nanostructured superhydrophobic background surface. Various configurations of different island and pitch sizes are considered. Real-time images captured by a high-speed camera are used to examine the droplet dynamics and the influence of wettability on droplet size distribution. Thus, a parametric study is conducted to present the optimum conditions at different steam mass fluxes. According to the heat transfer analysis results, the heat transfer coefficient could be enhanced by 37% compared to a plain hydrophobic surface. A higher ratio of hydrophobic area provided better conditions for droplet nucleation and growth, while larger superhydrophobic regions in the downstream section was advantageous for droplet removal and sweeping. As a result, the role of mixed wettability in achieving the best performance was revealed for dropwise flow condensation.

Review of Hygroscopic Coating on Aluminum Fin Surface of Air Conditioning Heat Exchanger

Air conditioning energy consumption accounts for most building energy consumption, indoor dehumidification is the main cause of air conditioning energy consumption. Optimize the dehumidification methods of air conditioning systems have great significance to the development of green buildings and people’s pursuit of comfort. Improvement of fins on air conditioning heat exchangers is a hot topic of current research and has achieved considerable results in terms of indoor dehumidification and energy saving compared to traditional air conditioners. This paper reviews two kinds of heat exchangers modified by coating, including desiccant-coated heat exchangers and hydrophobic/hydrophilic coated heat exchangers. For desiccant-coated heat exchangers, the preparation methods of advanced desiccant materials and the possibilities of using this material to achieve excellent energy efficiencies were presented, and the operating parameters that affect thermal performance and dehumidification are determined, including airflow temperature, air velocity, inlet air relative humidity, and regeneration temperature. For hydrophobic/hydrophilic coated heat exchangers, different kinds of hybrid hydrophobic-hydrophilic surfaces are highlighted for they are a high water droplet nucleation rate and surface heat transfer efficiency. In addition, the challenges and future works are explained at last. This paper will provide a valuable reference for the follow-up research, which will be helpful for indoor humidity control and reducing the energy consumption of air conditioning.

Molecular dynamics simulations of homogeneous nucleation of liquid phase in highly supersaturated propylene glycol vapors

The homogeneous nucleation rate of the liquid phase from a supersaturated propylene glycol vapor is a key factor in aerosol formation from condensation aerosol generators. The droplet nucleation rate is difficult to measure experimentally at high supersaturations. This paper demonstrates the feasibility of using classical Molecular Dynamics (MD) simulations to describe the nucleation of propylene glycol from the vapor phase in air at 320 and 343 K. After an initial induction period, nucleation was observed in many of the scenarios studied here. The classical nucleation theory underestimates the nucleation rate compared to the MD simulation results at high supersaturations. However, a kinetic model that assumed no free energy barrier to nucleation had better agreement with the MD predictions at extremely high supersaturations. For systems where a quasi-steady state was reached during the simulation, it is possible to determine the nucleation free energy as a function of cluster size. From this analysis it is found that the MD simulations predict over a factor of two larger critical clusters and about 50% higher free energy barriers than the classical nucleation theory.

Effects of external particles on the liquefaction property of natural gas in a Laval nozzle

In order to study the effects of external particles on the supersonic condensation process of natural gas, an experimental system to test the supersonic condensation efficiency is set up and the models for spontaneous (homogeneous) and heterogeneous condensation of natural gas are established. Vapor and liquid flow control equations are derived based on the two-fluid Euler model, and internally consistent classical theory and Gyarmathy's model are used to calculate the droplet nucleation rate and growth rate respectively. The results show that the due to the inhomogeneous condensation caused by the external particles, the measured droplet radius is larger, but the number of droplets is smaller in the experiment. With the increase of external particle concentration, the spontaneous condensation is gradually suppressed and heterogeneous nucleation is becoming more and more obvious. The increase of external particles concentration is beneficial to the condensation and the total humidity becomes larger, but when the external particle concentration increases to a certain value, the promotion effect is limited. In addition, other parameters such as the radius of particles also have influence on the heterogeneous condensing flow of natural gas.

Nucleation rates of droplets in supersaturated steam and water vapour–carrier gas mixtures between 200 and 450 K

We compare experimental nucleation rates for water vapour in various carrier gases, estimated nucleation rates for steam, and nucleation rates obtained from molecular simulations. The data for steam are deduced from empirical adjustments of the classical nucleation theory developed by various authors to reproduce pressure and optical data for condensing steam flows in converging-diverging nozzles and turbine stages. By combining the data for nucleation in carrier gases and the data for steam nucleation, an unprecedented temperature range of 250 K is available to study the temperature dependence of nucleation rate. Original results of molecular dynamic simulations for TIP4P/2005 force field in the NVE (system constrained by number of particles, volume and energy) conditions are provided. Correction of classical nucleation theory for non-isothermal nucleation conditions is applied to experimental and simulated data. The nucleation rate data for steam follow a similar temperature trend as the nucleation rate data for water vapour in carrier gases at lower temperatures. The ratio of observed nucleation rates to classical nucleation theory predictions decreases more steeply with temperature than the empirical correlation by Wölk et al. ( J Chem Phys 2002; 117: 4954–4960). On the contrary to experimental data, the ratios of nucleation rates computed from molecular simulations to classical nucleation theory predictions do not show a significant temperature trend.

Dropwise Condensation on Soft Hydrophobic Coatings.

Promoting dropwise condensation (DWC) could improve the efficiency of many industrial systems. Consequently, a lot of effort has been dedicated to finding durable materials that could sustainably promote DWC as well as finding routes to enhance the heat transfer rate during this phase change process. Motivated by previous reports of substrate softening increasing droplet nucleation rate, here we investigated how mechanical properties of a substrate impact relevant droplet-surface interactions and DWC heat transfer rate. Specifically, we experimentally quantified the effect of hydrophobic elastomer's shear modulus on droplet nucleation density and shedding radius. To quantify the impact of substrate softening on heat transfer through individual droplets, we combined analytical solution of elastomer deformation induced by droplets with finite element modeling of the heat transfer process. By substituting these experimentally and theoretically derived values into DWC heat transfer model, we quantified the compounding effect of the substrate's mechanical properties on the overall heat transfer rate. Our results show that softening of the substrates below a shear modulus of 500 kPa results in a significant reduction in the condensation heat transfer rate. This trend is primarily driven by additional thermal resistance of the liquid posed by depression of the soft substrate.

Numerical study of non-equilibrium condensation and shock waves in transonic moist-air and steam flows

Transonic condensing/evaporating moist-air flow through converging-diverging nozzles is investigated numerically using non-equilibrium thermodynamic model. In this study, the results of moist-air and pure steam flows through nozzles are compared, in other words, carrier gas effects are investigated numerically. It is observed that, under similar operating conditions for steam, the wetness fraction and droplet nucleation rate along the nozzle in the case of moist-air flow is more than pure steam case. That is due to the internal flow of heat from steam portion towards the air that enhances the wetness fraction and droplet nucleation rate in moist-air case. In this study, the influence of the normal aerodynamic shocks is also studied. It is interestingly observed that, although the entropy of the mixture (steam+air) and steam portion increases along the shock, the entropy of the air portion can be reduced in response to evaporation of the liquid phase. Validation of the results is performed versus the experimental data for pure steam and moist-air flows, which show relatively good agreements.

Numerical Study on condensation Process of Steam Flow in Nozzles

Steam ejector is an important component in engineering applications, which require high vacuum, such as steam plant condenser. Prediction of steam ejector performance is very significant tool for the design of the ejector. The steam ejector consists of three parts; nozzle, mixing chamber and diffuser. The nozzle has the task of creating the vacuum required. In the current paper numerical treatment of wet steam flow through the nozzle of an ejector is presented. The first task of this work is to test and evaluate several turbulence models on a generic case, constructed for turbulent steam flow in a convergent-divergent nozzle. The effect of pressure ratios, that is responsible for controlling the location or absence of the generated shock wave as well as the impact of the shock wave on the condensation of steam inside the nozzle are numerically concerned. These features are clearly observed from the pressure distribution, Mach number, liquid mass fraction, droplet nucleation rate, droplet critical radius and static temperature. It is concluded from the current work that the standard k-ω model is the most appropriate turbulence model for simulating this complex flow compared to the other considered models for nozzle steam flow sumulation.

Dew condensation on desert beetle skin.

Some tenebrionind beetles inhabiting the Namib desert are known for using their body to collect water droplets from wind-blown fogs. We aim to determine whether dew water collection is also possible for desert insects. For this purpose, we investigated the infra-red emissivity, and the wetting and structural properties, of the surface of the elytra of a preserved specimen of Physasterna cribripes (Tenebrionidæ) beetle, where the macro-structure appears as a series of "bumps", with "valleys" between them. Dew formation experiments were carried out in a condensation chamber. The surface properties (infra-red emissivity, wetting properties) were dominated by the wax at the elytra surface and, to a lower extent, its micro-structure. We performed scanning electron microscope on histological sections and determined the infra-red emissivity using a scanning pyrometer. The emissivity measured (0.95±0.07 between 8-14 μm) was close to the black body value. Dew formation occurred on the insect's elytra, which can be explained by these surface properties. From the surface coverage of the condensed drops it was found that dew forms primarily in the valleys between the bumps. The difference in droplet nucleation rate between bumps and valleys can be attributed to the hexagonal microstructure on the surface of the valleys, whereas the surface of the bumps is smooth. The drops can slide when they reach a critical size, and be collected at the insect's mouth.

Use of diffusion controlled drop evaporation equations for dropwise condensation during dew formation and effect of neighboring droplets

In this study, we determined that the equations derived for the diffusion controlled drop evaporation processes can be successfully applied to the condensation rate of water droplets on polymer surfaces having a surface temperature just below the dew point. The differences between the growth rates of condensed isolated droplets on five different polyolefin surfaces, whose surface free energies were in a close range of 30–37mJ/m2, were attributed to the difference in surface roughness which alters the droplet nucleation rate, drop pinning effect and initial contact angles. The condensation rate of isolated droplets decreased with the increase of surface roughness, water contact angle and contact angle hysteresis in the order of ethylene–vinyl acetate copolymer (EVA)>low density polyethylene (LDPE)>high density polyethylene (HDPE)>polypropylene–polyethylene copolymer (PPPE)>polypropylene (PP). The drop radius of the individual isolated droplets was found to grow according a power law with exponent 1/3 except PP similar to previous reports. We also compared the volume increase of an isolated single droplet with the volume increase of another similar sized single droplet which was surrounded by neighboring droplets and found that when neighboring droplets are present in close proximity, the condensation rate was 14–40% lower than that of a single isolated droplet due to blocking of lateral water vapor diffusion. This effect was more pronounced on substrates having high surface roughness.

Shear viscosity and the nucleation of antikaon condensed matter in protoneutron stars

We study shear viscosities of different species in hot and neutrino-trapped dense matter relevant to protoneutron stars. It is found that the shear viscosities of neutrons, protons and electrons in neutrino-trapped matter are of the same orders of magnitude as the corresponding shear viscosities in neutrino-free matter. Above all, the shear viscosity owing to neutrinos is higher by several orders of magnitude than that of other species in neutrino-trapped matter. Next we investigate the effect of shear viscosity, in particular, neutrino shear viscosity, on the thermal nucleation rate of droplets of antikaon condensed matter in protoneutron stars. The first-order phase transition from hadronic matter to antikaon condensed matter is driven by the thermal nucleation process. We compute the equation of state used for the calculation of shear viscosity and thermal nucleation time within the relativistic mean-field model. Neutrino shear viscosity enhances the prefactor in the nucleation rate by several orders of magnitude compared with the ${T}^{4}$ approximation of earlier calculations. Consequently the thermal nucleation time in the ${T}^{4}$ approximation overestimates our result. Furthermore, the thermal nucleation of an antikaon droplet might be possible in neutrino-trapped matter before neutrino diffusion takes place.

Nucleation of liquid droplets in a fluid with competing interactions

Using a simple density functional theory (DFT) the height of the free energy barrier for forming a droplet of the liquid phase from the metastable gas phase is determined for a model colloidal fluid exhibiting competing interactions. The pair potential has a hard core of diameter σ, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. It is found that even a very weak long-range repulsive tail in the pair potential has a profound effect on nucleation: increasing the amplitude of the repulsive Yukawa tail reduces significantly the free energy barrier height and therefore increases the liquid droplet nucleation rate. The method introduced for calculating the droplet density profile and free energy employs a fictitious external potential to stabilize a liquid droplet of the desired size, i.e. with a given excess number of particles. For the critical droplet, corresponding to an extremum of the grand potential, this fictitious potential is everywhere zero. The decay of the droplet density profiles into the bulk gas is examined. For a range of nucleation state points the DFT predicts exponentially damped, long wavelength oscillatory decay for systems exhibiting long-range repulsion, contrasting sharply with the monotonic decay found when the pair potential has only an attractive Yukawa piece. The changes in nucleation properties found for small amplitudes of the repulsive Yukawa tail reflect the propensity of the fluid to form modulated structures such as clusters or stripes.

Effect of shear viscosity on the nucleation of antikaon condensed matter in neutron stars

We investigate a first-order phase transition from hadronic matter to antikaon condensed matter during the cooling stage of protoneutron stars. The phase transition proceeds through the thermal nucleation of antikaon condensed matter. In this connection we study the effect of shear viscosity on the thermal nucleation rate of droplets of antikaon condensed matter. Here we adopt the same equation of state for the calculation of shear viscosity and thermal nucleation time. We compute the shear viscosity of neutron star matter composed of neutrons, protons, electrons, and muons using the relativistic mean field model. The prefactor in the nucleation rate, which includes the shear viscosity, is enhanced by several orders of magnitude compared with the ${T}^{4}$ approximation of earlier calculations. Consequently the thermal nucleation time in the ${T}^{4}$ approximation overestimates our result. Further, the thermal nucleation of an antikaon droplet might be possible in our case for surface tension smaller than $20\text{ }\text{ }\mathrm{MeV}\text{ }{\mathrm{fm}}^{\ensuremath{-}2}$.