Statistical Characteristics of the Process of Homogeneous Nucleation in the Vapor–Gas Medium during Free Molecular Regime of the Growth of Forming Droplets

Statistical approach to the study of the process of homogeneous nucleation of droplets in the vapor–gas medium in the presence of originally generated growing droplet at free molecular regime of droplet growth after the instantaneous creation of initial vapor supersaturation is proposed. The probability density of the creation of a new droplet in the vicinity of originally generated droplet is found. The mean distance between two neighboring droplets and the relative scatter of this distance are determined. The mean expectation time for the appearance of neighboring droplet estimating the duration of the droplet nucleation stage is found. The average number of droplets in a unit volume of the vapor–gas medium by the end of the droplet nucleation stage is estimated. The results obtained are compared with the predictions of the theory based on the assumption of the homogeneity of metastable phase.     

Statistical Regularities of Homogeneous Boiling-Up of Gas-Supersaturated Solutions

Statistical regularities of homogeneous boiling-up of liquid solutions supersaturated with gas are studied. The local gas concentration and local rate of homogeneous boiling-up of the solution are found in the vicinity of the bubble emerging in the solution at low gas solubility. The probability of the emergence of new bubbles in addition to the bubble originally emerged in the solution is calculated. The mean distance between two neighboring bubbles and the relative statistical scatter of this distance are found. The mean number of bubbles in a solution unit volume by the end of the stage of their emergence is estimated. The mean expectation time of the emergence of the neighboring bubble estimating the duration of the stage of bubble emergence is established. The proposed theory is extended to the case of homogeneous nucleation in the vapor–gas medium.     

Statistico-probabilistic approach to taking account of the vapor depletion in the kinetics of homogeneous nucleation: a free-molecular regime of droplet growth

We propose a statistico-probabilistic approach to investigate the process of homogeneous formation of droplets in a vapor phase in the presence of an already formed and growing droplet under free-molecular regime of droplet growth after the instantaneous creation of initial vapor supersaturation. We find the probability density for the formation of a new, nearest (neighbor) droplet in the vicinity of an initially formed droplet. The mean distance between two neighboring droplets is also determined, as well as the average time lag for the formation of the nearest (neighbor) droplet; the latter quantity serves as an estimate for the duration of the nucleation stage. An estimate for the average number of droplets forming in unit volume by the end of the nucleation stage is also given. Our results are compared with the predictions of classical nucleation theory which assumes the density uniformity of a metastable phase. Where the proposed approach is applicable, there is observed qualitative agreement between the results. The underlying cause of this agreement is analyzed and the limits of applicability of the uniformity approximation are clarified.     

Analytical and Numerical Study of Equilibrium Characteristics of a Droplet with Charged Condensation Nucleus in the External Electric Field

The equilibrium parameters of small dielectric droplet with charged condensation nucleus in the external uniform electric field are studied. Two typical cases are considered: (i) the droplet with charged nucleus suspended by external uniform electric field in the gravitational field and (ii) the droplet moves steadily under the action of external electric field with allowance for the resistance of surrounding vapor–gas medium. It is taken into account that the charged condensation nucleus can be displaced from the mass center of the droplet to new equilibrium position inside the droplet under the action of external electric field and response field. The scheme of the numerical solution of a nonlinear system of differential equations for the droplet equilibrium profile and electric potentials inside the droplet and in the vapor–gas medium at the arbitrary values of droplet size, strength of external field, and the charge of condensation nucleus is formulated and realized. Dependences of an equilibrium profile and the thermodynamic characteristics of a droplet such as the chemical potential of condensate and formation work on the droplet size, mass, and charge of condensation nucleus, the strength of external field and ratio of permittivities of droplet and the vapor–gas medium are plotted. Results of numerical calculations are supplemented by the analytical relations for equilibrium droplet characteristics in the first orders of the perturbation theory for a weak external field.     

Vapor phase nucleation on neutral and charged nanoparticles: condensation of supersaturated trifluoroethanol on Mg nanoparticles

A new technique is described to study the condensation of supersaturated vapors on nanoparticles under well-defined conditions of vapor supersaturation, temperature, and carrier gas pressure. The method is applied to the condensation of supersaturated trifluoroethanol (TFE) vapor on Mg nanoparticles. The nanoparticles can be activated to act as condensation nuclei at supersaturations significantly lower than those required for homogeneous nucleation. The number of activated nanoparticles increases with increasing the vapor supersaturation. The small difference observed in the number of droplets formed on positively and negatively charged nanoparticles is attributed to the difference in the mobilities of these nanoparticles. Therefore, no significant charge preference is observed for the condensation of TFE vapor on the Mg nanoparticles.     

New design of a sorption device for the preconcentration of organic impurities and their subsequent determination by gas chromatography

A new design of a sorption device for the preconcentration of impurities is proposed, and its characteristics are studied. The device is a flat microconcentrator that operates based on the principle of solid-phase extraction and is intended for the subsequent gas-chromatographic determination without cryofocusing. The new device was tested in the analysis of model vapor—gas mixtures of benzene, toluene, ethylbenzene, and o-xylene. The proposed device with adsorbents such as Tenax GC and polydiphenylphthalide-1 under the conditions of exhaustive extraction reliably determines the simplest aromatic hydrocarbons in vapor—gas mixtures at a level of ~0.01 mg/m³ (lower than MPC); the precision of the results is characterized by a relative standard deviation of 14% or better.Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 1, 2005, pp. 11–16.Original Russian Text Copyright © 2005 by Makarov, Stolyarov, Berezkin, Bychinskaya, Zenkevich.Deceased.     

Supersaturated vapor recondensation: Analytical theories and numerical calculation

The time dependences of droplet size within the period from the end of nucleation until the onset of asymptotic regime of recondensation are determined by the numerical integration of equations describing droplet growth in a supersaturated vapor. The obtained dependences are compared with those derived in terms of the analytical theories of condensation. The character of variations in the final self-similar size distribution of droplets is studied as depending on variations in their initial distribution function and in the system parameters.     

Computer Simulation of the Initial Stage of Water Vapor Nucleation on a Silver Iodide Crystal Surface: 1. Microstructure

The nucleation of water vapors on the surface of a fragment of silver iodide crystal is simulated by the Monte Carlo method under the conditions similar to natural conditions in a humid atmosphere. A stable monolayer island of water molecules with clearly pronounced features of hexagonal symmetry and low orientational order is formed at the initial stage, when the vapor pressure is still lower than the saturating pressure. The island readily grows over the surface and, in the unsaturated vapor, does not grow in the direction perpendicular to the surface. The formed monolayer represents a substrate for further growth of a condensed phase and, eventually, is responsible for the mechanism of nucleation on the crystal surface. Water molecules are held by the substrate mainly owing to the directional electrostatic interaction between the negatively charged oxygen atoms and positively charged silver ions. The interaction with iodine ions lowers the binding of the island (nucleus) and the substrate. A point defect in the form of an extra ion on the surface does not change the planar shape of the nucleus and virtually does not distort its hexagonal structure. Indirect experimental data supporting the formation of a water monolayer at the stage preceding nucleation, as well as the data of observations indicating the important role of defects on a crystal surface, are reported.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 548–560.Original Russian Text Copyright © 2005 by Shevkunov.     

Growth and motion of heterogeneous water droplets in laminar diffusion chambers: 2. High nanoparticle concentrations

The heterogeneous condensation of water vapor on nanoparticles and the growth of formed droplets are numerically studied under conditions of laminar diffusion chamber (LDC) of a new type with a hot porous wall. The main attention is focused on the growth of heterogeneous droplets in the gas flow at high number densities of nanoparticles exceeding 10⁸ droplet/m³. Under these conditions, there is an interrelation between the growth of droplets and processes of heat and mass transfer in LDC due to vapor depletion and the release of latent heat of phase transition on growing droplets. The efficiency of the coverage of nanoparticles with water film is studied under LDC nonuniform conditions. It is shown that, at initial number densities of nanoparticles (N _d > 10¹¹ droplet/m³), heterogeneous droplets do not grow to optically detected sizes.     

Role of nearest-neighbor drops in the kinetics of homogeneous nucleation in a supersaturated vapor

A theory of simultaneous nucleation and drop growth in a supersaturated vapor is developed. The theory makes use of the concept of "nearest-neighbor" drops. The effect of vapor heterogeneity caused by vapor diffusion to a growing drop, formed previously, is accounted for by considering the nucleation of the nearest-neighbor drop. The diffusional boundary value problem is solved through the application of a recent theory that maintains material balance between the vapor and the drop, even though the drop boundary is a moving one. This is fundamental to the use of the proper time and space dependent vapor supersaturation in the application of nucleation theory. The conditions are formulated under which the mean distance to the nearest-neighbor drop and the mean time to its appearance can be determined reliably. Under these conditions, the mean time provides an estimate of the duration of the nucleation stage, while the mean distance provides an estimate of the number of drops formed per unit volume during the nucleation stage. It turns out, surprisingly, that these estimates agree fairly well with the predictions of the simpler and more standard approach based on the approximation that the density of the vapor phase remains uniform during the nucleation stage. Thus, as a practical matter, in many situations, the use of the simpler and less rigorous method is justified by the predictions of the more rigorous, but more complicated theory.     

Effect of transient condensation of a supercooled gas on the size distribution of new-phase particles

The homogeneous nucleation of the liquid phase upon rapid cooling of a gas is considered in the framework of the Zel'dovich–Frenkel theory, and the time-dependent distribution function of nuclei in size space and the nucleation rate are determined. It is shown that in the transient case a certain modification must be made to the basic kinetic equation at high supersaturations of the gas to allow for the discrete number of molecules in a nucleus. The form of the distribution function is found in the leading and next-higher approximations in the reciprocal of the activation barrier. Comparison with a numerical simulation shows that the results are quite accurate.     

Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis

Particle nucleation and growth are simulated for iron vapor in a thermal plasma reactor with an assumed one-dimensional flow field and decoupled chemistry and aerosol dynamics. Including both evaporation and coagulation terms in the set of cluster-balance rate equations, a sharply defined homogeneous nucleation event is calculated. Following nucleation the vapor phase is rapidly depleted by condensation, and thereafter particle growth occurs purely by Browntan coagulation. The size and number of nucleated particles are found to be affected strongly by the cooling rate and by the initial monomer concentration. An explanation is presented in terms of the response time of the aerosol to changing thermodynamic conditions.This work appears in abbreviated from in the proceedings of the International Symposium on Combustion and Plasma Synthesis of High Temperature Materials, San Francisco, Oct. 24–26, 1988, to be published asCombustion and Plasma Synthesis of Hig Temperature Materials, Z. A. Munir and J. B. Holt (eds.), VCH, New York (in press).     

On the Problem of Nucleation in a Supersaturated Vapor in the Presence of Heterogeneous Centers of Different Natures

The rules for constructing the analytical approximation are formulated for the law of the accumulation of the condensing substance by droplets that have emerged at centers of different natures. The accuracy of the suggested approximation is tested for the limiting cases of homogeneous nucleation and nucleation at centers of the same type. A general algorithm is constructed for describing the nucleation stage at centers of different natures after instantaneous creation of vapor supersaturation. Numerical calculations are conducted for the numbers of droplets formed at positively and negatively charged univalent ions in water vapors.     

Vapor–liquid equilibria and interfacial tensions for the ternary system acetone + 2,2′-oxybis[propane] + cyclohexane and its constituent binary systems

Isobaric vapor–liquid equilibrium data have been measured for the ternary system acetone + 2,2′-oxybis[propane] + cyclohexane, and its constituent binaries at 94 kPa and in the temperature range 324–350 K in a vapor–liquid equilibrium still with circulation of both phases. The dependence of the interfacial tensions of these mixtures on concentration was also determined at atmospheric pressure and 303.15 K, using the maximum bubble pressure technique.From the experimental results, it follows that both the ternary and binary mixtures exhibit positive deviations from ideal behavior and, additionally, azeotropy is present for the binaries that contain acetone. The application of a model-free approach allows conclusions about the reliability of the present vapor–liquid equilibrium data for all the indicated mixtures. Furthermore, the determined interfacial tensions exhibit negative deviation from linear behavior for all the analyzed mixtures, and aneotropy is observed for the acetone + cyclohexane mixture.The vapor–liquid equilibrium data of the binary mixtures were well correlated using the NRTL, Wilson and UNIQUAC equations. In a similar manner, the interfacial tensions of the binary mixtures were smoothed using the Redlich–Kister equation. Scaling of these models to the ternary mixture allows concluding that both the vapor–liquid equilibrium data and the interfacial tensions can be reasonably predicted from binary contributions.     

Comparative study of monomer droplet nucleation in the seeded batch and semibatch miniemulsion polymerisation of styrene

Monomer droplet nucleation in the seeded miniemulsion polymerisation of styrene under monomer-flooded and monomer-starved conditions was studied. The miniemulsion feeds were added to the reactor either batchwise or semibatchwise. The droplets preserved longer under flooded conditions. As a result, the batch operation led to a larger number of particles (N_p) than the semibatch operation. For the miniemulsion droplets containing predissolved polymer, the final N_p was independent of the way that the feed was added to the reactor and was equivalent to the number of monomer droplets in the original miniemulsion feed. The size distribution of the final latexes, however, was influenced by the operation type. For the batch operation, the rate of polymerisation (R_p) with the miniemulsion feeds was higher than that with the conventional monomer emulsion feed because of the monomer droplet nucleation. But for the semibatch operation, the opposite was true because of R_p controlled by the rate of monomer diffusion from rather stable miniemulsion droplets to the growing polymer particles.     

Isothermal vapor–liquid equilibrium at 333.15 K and excess molar volumes at 298.15 K for the ternary system di-isopropyl ether + n-propyl alcohol + toluene and its binary subsystems

Isothermal vapor–liquid equilibrium data at 333.15 K are reported for the ternary system di-isopropyl ether (DIPE) + n-propyl alcohol + toluene and the binary subsystems DIPE + n-propyl alcohol, DIPE + toluene and n-propyl alcohol + toluene by using headspace gas chromatography. The excess molar volumes at 298.15 K for the same binary and ternary systems were also determined by directly measured densities. The experimental binary and ternary vapor–liquid equilibrium data were correlated with different G^E models and the excess molar volumes were correlated with the Redlich–Kister equation for the binary systems and the Cibulka equation for the ternary system, respectively.     

The stage of nonisothermal nucleation of supercritical particles of a new phase under nonstationary conditions of particle diffusion growth and heat transfer to a medium

An analytical theory has been formulated for the stage of nonisothermal nucleation of supercritical particles in a metastable medium with instantaneously generated initial supersaturation. The theory takes into account the nonuniformities of metastable substance concentration and temperature, which result from the nonstationary diffusion of the substance to growing particles and the nonstationary transfer of the heat of the phase transition from the particles to the medium. The formulated theory extends the approach based on the concept of excluded volume that has recently been used in the theory of the stage of nucleation under isothermal conditions. This approach implies that the nucleation intensity of new particles is suppressed in spherical diffusion regions with certain sizes that surround previously nucleated supercritical particles and remaining unchanged in the rest of the medium. It has been shown that, when self-similar solutions are used for nonstationary equations of substance diffusion to particles and heat transfer from the particles, the ratio between the excluded volume and the particle volume is independent of particle size, thereby enabling one to analytically solve the integral equation for the excluded volume throughout a system as a time function at the stage of nucleation. The main characteristics of the phase transition have been found for the end of the stage of nucleation. Comparison has been carried out with the characteristics obtained in terms of the isothermal and nonisothermal nucleation theory upon uniform vapor consumption and heat dissipation (the mean-field approximation of vapor supersaturation and temperature).     

Effect of spatial inhomogeneities on the rate of homogeneous nucleation in systems with aerosol particles

The presence of growing particles in a system leads to spatial inhomogencities in the vapor concentration. The effect of these spatial variations on the rate of formation of new particles by homogeneous nucleation is examined theoretically using a cell model. Results indicate that the presence of these inhomogeneities in systems both with and without initial aerosol has generally little effect on the final number concentration of particles following a nucleation “event.”     

Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids

At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner.