Theory Of Droplet Growth Research Articles

Spontaneous condensation of carbon dioxide in flue gas at supersonic state

A cleaning method of removing CO2 from flue gas by supersonic flow is investigated. A condensation flow model is developed based on the classical droplet nucleation and growth theory. The non-equilibrium phase transition in supersonic flow is predicted by adding transport equations. The effects of converging-diverging nozzle, inlet subcooling and gas composition on CO2 spontaneous condensation in flue gas are studied. The results show that the nozzle with Witoszynski curve is the first to nucleate, at x = 0.121 m. Without considering the backpressure, the shrinkage ratio and diverging angle only affect the flow behavior behind the throat. With the increase of shrinkage ratio or diverging angle, the liquid mass fraction increases from 0.062 to 0.085 and 0.056 to 0.089 respectively, but there are hazards such as increased pressure loss and reduced nozzle flow rate. The diverging length has no significant effect on the flow behavior but the increase of length can prolong the droplet growth time. The higher inlet subcooling not only makes the supersonic flow reach the critical state in advance, from x = 0.121 m to x = 0.111 m, but also significantly improves the droplet growth rate, from 0.649 m/s to 0.854 m/s. The increase of CO2 concentration greatly enhances the mass and heat transfer process.

A Study of Moist Air Condensation Characteristics in a Transonic Flow System

When water vapor in moist air reaches supersaturation in a transonic flow system, non-equilibrium condensation forms a large number of droplets which may adversely affect the operation of some thermal-hydraulic equipment. For a better understanding of this non-equilibrium condensing phenomenon, a numerical model is applied to analyze moist air condensation in a transonic flow system by using the theory of nucleation and droplet growth. The Benson model is adopted to correct the liquid-plane surface tension equation for realistic results. The results show that the distributions of pressure, temperature and Mach number in moist air are significantly different from those in dry air. The dry air model exaggerates the Mach number by 19% and reduces both the pressure and the temperature by 34% at the nozzle exit as compared with the moist air model. At a Laval nozzle, for example, the nucleation rate, droplet number and condensation rate increase significantly with increasing relative humidity. The results also reveal the fact that the number of condensate droplets increases rapidly when moist air reaches 60% relative humidity. These findings provide a fundamental approach to account for the effect of condensate droplet formation on moist gas in a transonic flow system.

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.

Near-sonic pure steam flow with real-gas effects and non-equilibrium and homogeneous condensation around thin airfoils

A small-disturbance asymptotic model is derived to describe the complex nature of a pure water vapour flow with non-equilibrium and homogeneous condensation around a thin airfoil operating at transonic speed and small angle of attack. The van der Waals equation of state provides real-gas relationships among the thermodynamic properties of water vapour. Classical nucleation and droplet growth theory is used to model the condensation process. The similarity parameters which determine the flow and condensation physics are identified. The flow may be described by a nonlinear and non-homogeneous partial differential equation coupled with a set of four ordinary differential equations to model the condensation process. The model problem is used to study the effects of independent variation of the upstream flow and thermodynamic conditions, airfoil geometry and angle of attack on the pressure and condensate mass fraction distributions along the airfoil surfaces and the consequent effect on the wave drag and lift coefficients. Increasing the upstream temperature at fixed values of upstream supersaturation ratio and Mach number results in increased condensation and higher wave drag coefficient. Increasing the upstream supersaturation ratio at fixed values of upstream temperature and Mach number also results in increased condensation and the wave drag coefficient increases nonlinearly. In addition, the effects of varying airfoil geometry with a fixed thickness ratio and chord on flow properties and condensation region are studied. The computed results confirm the similarity law of Zierep & Lin (Forsch. Ing. Wes. A, vol. 33 (6), 1967, pp. 169–172), relating the onset condensation Mach number to upstream stagnation relative humidity, when an effective specific heat ratio is used. The small-disturbance model is a useful tool to analyse the physics of high-speed condensing steam flows around airfoils operating at high pressures and temperatures.

Numerical investigation of PM2.5 size enlargement by heterogeneous condensation for particulate abatement

Vapor heterogeneous condensation with PM2.5 as nuclei is a promising approach to enlarge the particle sizes and thus facilitate subsequent particulate abatement by the existing inertial separators. However, the investigation on PM2.5 size enlargement by vapor heterogeneous condensation, which is important to optimize the particulate abatement process, has been largely lacking. In this study, the evolution of particle size distribution due to vapor heterogeneous condensation on the surfaces of polydisperse insoluble PM2.5 was modelled based on the classical heterogeneous nucleation theory and the condensation droplet growth theory. Using this model, the effects of operational parameters on the particle size distribution after heterogeneous condensation were numerically investigated. The results show that the polydisperse fine particles shift to monodisperse coarse particles at a small contact angle, whereas bimodal particle size distribution after heterogeneous condensation is generated at a large contact angle. Higher vapor saturation ratio, higher gas temperature, longer residence time, and greater geometric mean particle size are beneficial to PM2.5 size enlargement and subsequent particulate abatement. Moreover, the geometric standard deviation of particle sizes has little effect on the PM2.5 size enlargement. The model predictions of the particle size distribution after vapor heterogeneous condensation match well with the experimental data.

Effect of melt superheating treatment on solidification behavior of uniform Al10Bi54Sn36 monotectic alloy

The uniform ternary Al10Bi54Sn36 monotectic alloy samples were prepared by stirring casting and rapid solidification in the copper mold. The thermodynamics and phase transition behavior of Al10Bi54Sn36 monotectic alloy were investigated by resistivity and DSC. The phase separation kinetics and the second phase droplet growth theory of alloy melt under solidification conditions were also studied. The phase composition of the alloy was analyzed by EDS in combination with XRD. The effects of melt superheating treatment on the solidification morphology of Al10Bi54Sn36 monotectic alloy were discussed. When the Al10Bi54Sn36 melts was superheated at 1000 °C, a relatively uniform microstructure that the spherical Al-rich phase distributed uniformly on the Sn-Bi-rich matrix was obtained, which is expected to provide a beneficial guidance for the preparation and application of homogeneous Al-Bi-Sn monotectic alloy in the field of lead-free solder and electronic packaging.

A Small Disturbance Model for Transonic Flow of Pure Steam With Condensation

A small-disturbance model to study transonic steady condensing flow of pure steam around a thin airfoil is developed. Water vapor thermodynamics is described by the perfect gas model and its dynamics by the compressible inviscid flow equations. Classical nucleation and droplet growth theory for homogeneous and nonequilibrium condensation is used to compute the condensate mass fraction. The model is derived from an asymptotic analysis of the flow and condensation equations in terms of the proximity of upstream flow Mach number to 1, the small thickness ratio of airfoil, the small quantity of condensate, and the small angle-of-attack. The flow field may be described by a nonhomogeneous and nonlinear partial differential equation along with a set of four ordinary differential equations for calculating condensate mass fraction. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme, which is composed of Murman and Cole's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction, is applied. The model is used to analyze the effects of heat release due to condensation on the aerodynamic performance of airfoils operating in steam at high temperatures and pressures near the vapor–liquid saturation dome.

CFD modeling of condensation process of water vapor in supersonic flows

The condensation phenomenon of vapor plays an important role in various industries, such as the steam flow in turbines and refrigeration system. A mathematical model is developed to predict the spontaneous condensing phenomenon in the supersonic flows using the nucleation and droplet growth theories. The numerical approach is validated with the experimental data, which shows a good agreement between them. The condensation characteristics of water vapor in the Laval nozzle are described in detail. The results show that the condensation process is a rapid variation of the vapor-liquid phase change both in the space and in time. The spontaneous condensation of water vapor will not appear immediately when the steam reaches the saturation state. Instead, it occurs further downstream the nozzle throat, where the steam is in the state of supersaturation.

Correlation between Surface Tension and the Bulk Dynamics in Salty Atmospheric Aquatic Droplets

The properties of the liquid–gas interface in the presence of surface-active organic matter, and the bulk response to changes of the resulting surface tension are key factors in assessing cloud microphysics or condensation/evaporation dynamics for atmospheric particles. A fundamental question rises on how we can induce changes in the bulk of an aquatic droplet by varying its surface-activity. The challenging aspect of answering such a question rises from the fact that water exerts complexity in its interactions giving rise to many anomalous properties. Here, we employ molecular dynamics simulations on salty aquatic droplets, associated with new particle formation in the atmosphere. We present a correlation between surface tension and a bulk property like the static dielectric constant, which is closely related to the water activity in Kohler theory of droplet formation and growth. We thus correlate surface to bulk properties. The particles we probe consist of water, salt (ammonium bisulfate), and surface-...

411 非平衡凝縮過程におけるエネルギ損失に関する一考察(GS6 熱工学(2),研究討論セッション)

Supersonic steam flow in nozzles has been considered in the viewpoint of release of latent heat and entropy of droplet formation during water vapor condensation. Total pressure losses were calculated by using conservation equations related to continuity, momentum and energy with both calorimetric and thermal state equations. Furthermore, the theory of nucleation and droplet growth was combined with the thermofluid dynamics equations. When the condensation rate becomes higher and non-equilibrium becomes stronger, consideration of kinetic theory and statistical mechanics have an increase need for treating the problems in that case.

Simultaneous Measurement of Condensation and Thermal Accommodation Coefficients for Cloud Droplet Growth in Due Consideration of a New Moving Surface-Boundary Effect

Abstract A droplet growth theory that describes a new effect of vapor and temperature field shift due to the growth-based movement of droplet surface boundary (moving boundary effect) was derived and found to enhance the growth rate as a function of supersaturation (S − 1) and droplet radius (a) in second order. The theory plays the role of a missing link and resolves the gap that exists among the measured data; the high (S − 1) used was found to overestimate thermal accommodation and condensation coefficients, α and β. The theory provided the basis for bettering the measurement and correction for data analyzed without the moving boundary effect, and suggested the broadening effect in the droplet size spectrum by accelerating the growth on the larger end together with the growth slowdown effect of α, β on the smaller. Measurements employing a horizontal-flow thermal diffusion chamber and the Mie scattering method using a He–Ne laser for droplet size estimation at temperature T = 277 K, (S − 1) = 0.32%, a ≈ 2 μm under two pressures of modulation, p = 100 and 860 hPa, with correction of the moving boundary effect for nuclei of NaCl and (NH4)2SO4, resulted in the simultaneous determination of α = 0.81 ± 0.07 and β = 0.043 ± 0.016 on average. For paper smoke, α = 0.68 and β = 0.022. Comparison with other data of the low moving boundary effect suggests a slight β increase with temperature lowering. Based on the result of the present measurement and other theoretical and experimental works, the mechanism of β being much smaller than α was suggested mostly as a kinetic process controlled by the removal rate of the released latent heat at the moment of molecular impact on the surface and vice versa for evaporation.

Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations

The paper discusses the classical theory of the homogeneous nucleation of water droplets from supersaturated vapour and its application in predicting condensation in steam nozzles. The first part consists of a review of classical nucleation theory, focusing on the many modifications made to the original Becker-Döring theory and providing some new insights into recent developments. It is concluded that the predictive accuracy required for engineering calculations is not yet attainable with a theory derived from first principles. The areas that require most attention relate to the properties of small molecular clusters and the energy transfer processes in the non-isothermal theory. Experiments in converging-diverging nozzles provide the best means for validation at the very high nucleation rates of interest, but measurements of pressure distribution and the Sauter mean droplet radius are insufficient to provide independent checks on the separate theories of nucleation and droplet growth. Nevertheless, a judicious choice for the nucleation rate equation, in combination with a standard droplet growth model and a suitable equation of state for steam, can provide accurate predictions over a wide range of conditions. The exception is at very low pressures where there is evidence that the droplet growth rate in the nucleation zone is underestimated.

Viscous and unsteady flow calculations of condensing steam in nozzles

The paper presents two-dimensional calculations for spontaneously nucleating flows of steam in converging–diverging nozzles. The Reynolds-averaged Navier–Stokes equations are solved for the two-phase mixture, using a Jameson-style finite volume method on an unstructured and adaptive triangular mesh. Results are first presented for steady, viscous flow, showing the influence of boundary layer growth on streamwise pressure distributions and droplet sizes. These results have implications for the interpretation of some of the experimental data used for validating the theories of nucleation and droplet growth. The numerical scheme has also been applied to compute unsteady flows in a variety of nozzle geometries, covering a range of inlet conditions in each case. Asymmetric oscillation modes, previously observed in moist air, have been predicted for one of the geometries, indicating for the first time that such oscillations are possible in pure steam.

Retrieval of microphysical, geometrical, and radiative properties of marine stratocumulus from remote sensing

Radiative transfer calculations in boundary layer stratocumulus are performed and used to retrieve cloud properties from remotely measured reflected radiances in the visible and near‐infrared. Calculations based on the vertically uniform plane‐parallel cloud model have been currently used for the retrieval of cloud optical thickness and droplet effective radius. They were extended in a previous work to the retrieval of cloud droplet number concentration and cloud geometrical thickness, by assuming a vertically stratified cloud model, with prescribed droplet spectrum. The retrieved values of cloud droplet number concentration though were substantially underestimated. Improvements are presented here with a more realistic parameterization of the droplet size distribution, based on the theory of droplet growth by vapor diffusion. The retrieval technique is applied to eight case studies of the second Aerosol Characterization Experiment and the retrieved values are compared to estimates derived from in situ cloud microphysical measurements. The technique provides accurate retrievals of cloud droplet number concentration, with no bias. The retrieval of cloud geometrical thickness though is systematically overestimated compared to that directly measured. This bias partly reflects the difference of cloud sampling between the two strategies. Remote sensing measurements, which are continuous, are capable of detecting the thickest cells of the cloud layer within the field of view of the radiometer, while discontinuous in situ vertical profiles provide a statistical average of the geometrical thickness. Part of the bias could also reflect three‐dimensional effects of the radiative transfer in spatially heterogeneous clouds, which are not accounted for by the plane‐parallel models. The data are then processed for deriving statistics of the retrieved values of cloud droplet number concentration, optical thickness, and liquid water path, for validation of large‐scale parameterizations of the aerosol indirect effect.

Experimental determination of droplet size and density field in condensing flows

We report a detailed experimental characterization of the process of homogeneous condensation in supersonic expanding flow. In our experiments, the supersaturated mixture expands in a Laval nozzle, where, depending on the initial conditions, a steady or periodically oscillating flow may evolve due to the non-linear interaction of nucleation and droplet growth rate with the flow field. Two experimental techniques are utilized: holographic interferometry for the determination of the density field and a time-resolved white-light extinction method. The latter is employed to derive the evolution in time of the droplet cloud (i.e., modal radius, number density, and relative width) and to measure the frequency of oscillations. In combination with the wide-field density data, droplet size measurements provide additional physical insights in the mechanism of interaction in condensing flows and serve as an excellent test case for the critical assessment of nucleation and droplet growth theories. To this purpose, the accuracy of the measurements is carefully reviewed due to the difficulties of characterizing dense sub-micron droplet clouds by means of light-scattering techniques. An important byproduct of this analysis is an evaluation of the applicability of single-scattering approximations, i.e., Lambert-Beer law, for a variety of experimental configurations.

Kinetics of Capillary Condensation in a Nanoscale Pore

The rate of growth of capillary condensates in a model wedgelike pore has been studied using the surface force apparatus. The method described allows the direct measurement of the diffusion-limited growth of liquid condensates with interface radii of curvature as small as 20 nm. The observed rates of condensation of vapors of $n$-pentane, $n$-hexane, cyclohexane, and water are close to, but consistently lower than, values calculated from a model based on Langmuir's theory of droplet growth.

Numerical simulation of nonequilibrium condensation in a hypersonic wind tunnel

A computational method for calculating supersonic two-dimensional nozzle flows with nonequilibrium phase change is developed. The code uses a fully implicit, finite volume formulation with Steger-Warming flux vector splitting and Jacobi point relaxation. Source terms for finite rate condensation and evaporation are constructed from the classical theories of nucleation and droplet growth. Calculations of the NASA Langley Research Center 8-ft High Temperature Tunnel nozzle are performed and compared with previously reported quasi-one-dimensional calculations and experimental data.

Condensational droplet growth as a preconditioning technique for the separation of submicron particles from gases

Droplet growth by heterogeneous condensation of water vapour as a preconditioning technique for the separation of submicron particles from gases has been investigated both theoretically and experimentally. The fundamentals of droplet growth theory including the growth of soluble particles are presented. From the results of numerical calculations, the influence of supersaturation, particle concentration, temperature and initial size distribution on the activation and growth rate of the particles is demonstrated. Furthermore, experimental results are reported and compared with the numerical results. Both theoretical and experimental results show that with a mass of condensable water vapour of ca. 5.5 gm −3, submicron particles can be enlarged with high growth rates to droplets with mean diameters of ca. 3 μm. Hence heterogeneous condensation in combination with a standard inertial separator, e.g. a cyclone, is a highly efficient technique for separating submicron particles. Additionally, some results for the growth of soluble particles, in this case NaCl particles, are presented.

Mathematical model for laser ablation to generate nanoscale and submicrometer-size particles.

Nanosize particles have several interesting features for synthesizing new materials with improved properties compared to the coarser-grained conventional materials, but the rate of production of such particles in various processes is usually very low. However, laser ablation is expected to give a higher yield. In this paper, a gas-dynamical model is developed for analyzing the plasma formation, and the velocity and particle-size distributions in the plasma during laser ablation. The melting and evaporation rates are determined by using the heat-conduction equation and the Stefan condition. To account for the discontinuity of various state variables across the Knudsen layer, jump conditions are used; the gas-dynamics equations are solved to study the convective flow of the metal particles in the region above the Knudsen layer. The plasma physics is used to model the formation of plasma and to compute the laser-beam attenuation coefficient and ion concentration in the plasma. The particle-size distribution in the plasma is determined by using a droplet-growth theory. Nanosize particles are found to exist near the vaporization front, and the particle size increases as one moves towards the plasma boundary. Similarly, the velocity of the particles is found to be higher at the plasma boundary than that inside the plasma.

Water supersaturation in convective clouds

The microphysics-dynamics interaction of clouds was theoretically studied in the zone after maximum supersaturation ( S−1) mc where the droplet number concentration remains nearly constant. The analytic solution obtained, employing the Maxwellian droplet growth theory, describes (S−1) mc =Iw u 3 4 n − 1 2 , where I is the proportionality constant, w u the updraft velocity and n the number concentration of the droplets. This solution agrees well with previous studies. Factor I increases with altitude in the adiabatic atmosphere, decreases with temperature under constant pressure and increases with pressure under constant temperature. For the zone sufficiently after ( S−1) mc, an approximate relationship (S−1) ∝r −1 ∝t − 1 3 is shown to hold, where ( S−1) is the supersaturation, f the average droplet radius and t the time. Using the diffusion-kinetic theory of droplet growth, which includes the effects of thermal accomodation and condensation coefficients, numerically soluble relationships are derived for ( S−1), r and t. Application of this theory is shown to increase ( S−1) mc considerably. The Maxwellian analytic solution that is obtained, the variation of Factor I under different atmospheric conditions and the effect of condensation and thermal accomoddation coefficients through the use of the diffusion-kinetic droplet growth theory suggest that maximum supersaturation may reach as high as 10% and beyond in convective clouds.