Dynamics of the droplet size distribution function during the gradual creation of a supersaturation state under different regimes of droplet growth

The method of the direct numerical integration of kinetic equations of droplet size distribution functions that was previously proposed by the authors is employed to solve the problem of condensation relaxation in a vapor-gas mixture during the creation of a supersaturation state at a finite rate. Two relaxation regimes are considered. In the static regime, the mixture is expanded at a constant rate until a preset supersaturation ratio is achieved; in the dynamic regime, the expansion is continued. Solutions are obtained for argon-cesium and argon-ethane mixtures, thus making it possible to study the dependence of the process character on the Knudsen number. The effects of the rate of the supersaturation creation and the relaxation regime on the droplet size distribution function are analyzed.     

Study of the volume condensation process in supersaturated vapor by the direct numerical solution of the kinetic equation for the droplet size distribution function

The volume condensation of supersaturated vapor is investigated by the direct numerical solution of the basic kinetic equation for the droplet size distribution function by analogy with the corresponding solution of the Boltzmann kinetic equation. The proposed consideration of the condensation growth of droplets is applicable at any Knudsen number. The method is tested by the example of vapor condensation under the conditions of the rapid development of supersaturation in a vapor-gas mixture as a result of its adiabatic expansion. In a wide range of Knudsen numbers, the results of the modeling are compared with those obtained by the moment method.     

Selective condensation during relaxation of multicomponent gas-plasma mixtures

The physical and chemical processes taking place in multicomponent gas-plasma mixtures are considered. A theoretical model of selective condensation during relaxation of the mixture is developed. It is shown that the condensation process depends strongly on the concentration of charged particles, which appear to be condensation nuclei. The concentration of the charged nuclei isfound to be influenced by the initial conditions of gas-plasma mixture relaxation. Illustrative calculations for titanium ultrafine powder deposition during plasma-chemical processing of titanium tetrachloride are carried out.     

NMR Study of the Kinetics of Butane and Hexane Adsorption from Vapor Phase by Porous Glasses

The kinetics of butane and hexane sorption from vapor phase by porous glasses is studied by the pulsed NMR technique. The sorption process is revealed to proceed in two stages: monomolecular adsorption and capillary condensation. The rate of adsorption is limited by the rate of adsorbate transfer to the adsorbent surface, with the latter rate being described by the classical diffusion flux. It is shown that ultramicropores are filled simultaneously with the formation of a monolayer. The relative content of molecules in such pores is estimated. At the stage of monomolecular adsorption and at the initial stage of capillary condensation, when the adsorption proceeds from the vapor phase of butane-hexane or butane-deuterated hexane mixtures, butane molecules are predominantly sorbed and followed by their partial displacement by hexane molecules. The rate of the capillary condensation of butane from the mixture is 15–18-fold lower than that from the vapor phase of butane alone which is explained by a decrease in the gradient of chemical potential. It is shown that, when adsorption occurs from a nonequilibrium butane-hexane mixture, anomalous kinetic curves are observed because the driving force of adsorption changes in the course of establishing equilibrium in the liquid phase.     

Heat exchange between phases and kinetics of condensation relaxation for different regimes of droplet growth

The mathematical model and numerical solution of the problem relevant to the heat exchange between a droplet and a vapor-gas medium are described for different regimes of the condensation droplet growth. The effect of the heat exchange between phases on the kinetics of the condensation relaxation after supersaturation is instantaneously generated in a vapor-gas mixture is studied based on the results obtained. Cesium-argon and ethane-helium mixtures are considered, with the droplet growth regime being free-molecular in the former case and varying from transient to continual in the latter case. The data obtained in terms of the general formulation of the problem and those resulting from the assumptions simplifying the behavior of droplet temperature are compared to determine the applicability domain of the aforementioned assumptions.     

Dynamics of variations in size and composition of supercritical droplet at binary condensation

A general analytical solution is found in quadratures for the radius and concentration of a solution droplet, which isothermally grows or evaporates in a diffusion or free-molecular regime in a binary mixture of vapors. The obtained solution describes the dynamics of variations in the size and composition of a super-critical droplet during the binary condensation in mixed vapors at an arbitrary initial droplet composition. It is shown that, at small (linear) deviations of the growth regime and droplet composition from the stationarity, these quadratures lead to the results that were recently obtained for the composition relaxation in a growing droplet. Moreover, it is demonstrated that, in terms of the nonlinear theory, when the deviation of solution concentration in a droplet from its stationary value is not small, it is invalid to use the law of stationary variations in the size of a droplet with time to describe the relaxation process for its chemical composition.     

Nonstationary vapor concentration fields near the growing droplet of binary solution

Nonstationary vapor concentration fields near the droplet of binary solution growing in the vapor—gas mixture are revealed using the concepts of similarity. The revealed fields are determined with the exact account of the motion of droplet surface and refer to the times at which the droplet reaches sizes that provide for the diffusion regime of droplet growth. To obtain the self-similar solution of the problem of binary condensation, it is necessary to ensure a constant (in time) concentration of binary solution in the growing droplet. The velocities of an increase in the number of molecules and the radius of two-component droplet with time are found with allowance for the equation ensuring this solution. The conditions for the transformation of the self-similar solution of the problem of the condensation of two-component mixture into the solution, which was derived previously for the condensation of one component, are elucidated.     

Kinetics of binary condensation on the droplet growing in diffusion regime

A relaxation equation determining the regular tendency of the concentration of binary solution in the growing droplet to the stationary value, at which there is a self-similar solution to the problem of the condensation in a binary mixture, is derived. An analytical solution of the relaxation equation is obtained and it is demonstrated that the stationary value of concentration is achieved via the power law. The time interval that elapses from the emergence of the droplet until the diffusion regime of droplet growth and derived relaxation equation become effective is revealed. The stationary value of concentration is found for the model of ideal solution.     

Stochastic diffusion interactions and coarsening in a system of droplets growing from a supersaturated gas mixture

In this work we study diffusion interactions among liquid droplets growing in stochastic population by condensation from supersaturated binary gas mixture. During the postnucleation transient regime collective growth of liquid droplets competing for the available water vapor decreases local supersaturation leading to the increase of critical radius and the onset of coarsening process. In coarsening regime the growth of larger droplets is prevailing noticeably broadening the droplet size-distribution function when the condensation process becomes more intensive than the supersaturation yield. Modifications in the kinetic equation are discussed and formulated for a stochastic population of liquid droplets when diffusional interactions among droplets become noteworthy. The kinetic equation for the droplet size-distribution function is solved together with field equations for the mass fraction of disperse liquid phase, mass fraction of water vapor component of moist air, and temperature during diffusion-dominated regime of droplet coarsening. The droplet size and mass distributions are found as functions of the liquid volume fraction, showing considerable broadening of droplet spectra. It is demonstrated that the effect of latent heat of condensation considerably changes coarsening process. The coarsening rate constant, the droplet density (number of droplets per unit volume), the screening length, the mean droplet size, and mass are determined as functions of the temperature, pressure, and liquid volume fraction.     

Bulk condensation in a dusty vapor–gas flow with regard to dust particle size distribution

Bulk condensation in a dusty vapor–gas flow has been numerically simulated taking into account dust particle size distribution. Two types of distribution (monodisperse and lognormal) have been used. Changes in the bulk condensation process that are relevant to the dustiness of the flow have been revealed by comparing the results obtained for dust-free and dusty flows at the monodisperse dust distribution. Variations in the relative contributions of the homogeneous and heterogeneous mechanisms with variations in the flow dustiness have been considered. The effect of the root-mean-square deviation in the dust particle sizes on the bulk condensation in the dusty flow has been illustrated by comparing the data obtained for the monodisperse and lognormal distributions.     

Vibrational energy relaxation of high density HCl fluid in the 150–345 K range

The vibrational lifetime of liquid hydrogen chloride alone the liquid—vapor coexistence curve and of high density hydrogen chloride above the critica anti-Stokes Raman scattering technique. The results obtained above the critical temperature show a gas-liKe behaviour with a larger relaxation rate con is consistent with a contribution of van der Waals dimers to vibrational relaxation. The results obtained along the liquid—vapor coexistence curve ar model.     

Study of selenium clusters

The aim of this paper is to study the properties of selenium clusters produced by vapor condensation technique. Simulation of nucleation process up to 50 atoms are in favour of a structure close to the amorphous structure. Doubly charged clusters are also obtained in the mass spectra.     

Nucleation in hydrophobic cylindrical pores: a lattice model

We consider the nucleation process associated with capillary condensation of a vapor in a hydrophobic cylindrical pore (capillary evaporation). The liquid-vapor transition is described within the framework of a simple lattice model. The phase properties are characterized both at the mean-field level and with Monte Carlo simulations. The nucleation process for the liquid to vapor transition is then specifically considered. Using umbrella sampling techniques, we show that nucleation occurs through the condensation of an asymmetric vapor bubble at the pore surface. Even for highly confined systems, good agreement is found with macroscopic considerations based on classical nucleation theory. The results are discussed in the context of recent experimental work on the extrusion of water in hydrophobic pores.     

A model of the two-stage condensation mechanism of water adsorption on nonporous carbon adsorbents

The mechanism of adsorption of water molecules on nonporous carbon adsorbents has been suggested in terms of two different states of adsorbed water; stretched liquid water and water that occupies an intermediate state between the liquid and vapor. Two stages of adsorption were distinguished: condensation and pre-condensation that assumes the formation of molecular associates. The BET model was used to describe the pre-condensation stage. The equations of the adsorption isotherm for water vapor in the region of condensation process and the expression for the determination of the specific hydrophilic surface of adsorbents were found. Examination of the experimental data on adsorption of water vapor on nongraphitized samples of carbon adsorbents shows that in the region of polymolecular adsorption, all isotherms fall into a common curve determined by the equation of the stretched liquid film and can be calculated regardless of the properties of individual liquid water. The equation for adsorption of water vapor on the hydrophobic surface was obtained. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1933–1939, October, 1998.     

The evaporation/condensation transition of liquid droplets

The condensation of a supersaturated vapor enclosed in a finite system is considered. A phenomenological analysis reveals that the vapor is found to be stable at densities well above coexistence. The system size at which the supersaturated vapor condenses into a droplet is found to be governed by a typical length scale which depends on the coexistence densities, temperature and surface tension. When fluctuations are neglected, the chemical potential is seen to show a discontinuity at an effective spinodal point, where the inhomogeneous state becomes more stable than the homogeneous state. If fluctuations are taken into account, the transition is rounded, but the slope of the chemical potential versus density isotherm develops a discontinuity in the thermodynamic limit. In order to test the theoretical predictions, we perform a simulation study of droplet condensation for a Lennard-Jones fluid and obtain loops in the chemical potential versus density and pressure. By computing probability distributions for the cluster size, chemical potential, and internal energy, we confirm that the effective spinodal point may be identified with the occurrence of a first order phase transition, resulting in the condensation of a droplet. An accurate equation of state is employed in order to estimate the droplet size and the coexisting vapor density and good quantitative agreement with the simulation data is obtained. The results highlight the need of an accurate equation of state data for the Laplace equation to have predictive power.     

Effects of conformational distributions on sigma profiles in COSMO theories

The charge density or sigma profile of a solute molecule is an essential component in COSMO (conductor-like screen model) based solvation theories, and its generation depends on the molecular conformation used. The usual procedure is to determine the conformation of an isolated molecule, and assume that this is unchanged when the molecule is placed in solution. In this paper, the conformations of 1-hexanol and 2-methoxy-ethanol in both the liquid and vapor phases obtained from Gibbs ensemble simulation and from an isolated-molecule quantum DFT optimization are used to determine the effect of realistic conformation differences on COSMO-based properties predictions. In particular, the vapor pressure at the normal boiling temperature and the binary mixture VLE (vapor-liquid equilibrium) predictions obtained using different conformations are investigated. The results show that the sigma profile for 1-hexanol varies only slightly using the different conformations, while the sigma profile of 2-methoxy-ethanol shows a significant difference between the liquid and vapor phases. Consequently, the vapor pressure predictions for 1-hexanol are similar regardless of the manner in which the conformation population was obtained, while there is a larger difference for 2-methoxy-ethanol depending on whether the liquid or vapor conformations from simulation or the DFT-optimized structure is used. These differences in predictions are seen to be largely due to differences in the ideal solvation energy term. In mixture VLE calculations involving 1-hexanol, we again see that there is little difference in the phase equilibrium predictions among the different conformations, while for the mixture with 2-methoxy-ethanol, the differences in the sigma profiles lead to a more noticeable, though not significant, difference in the phase equilibrium predictions.     

On the analyses of mixture vapor pressure data: the hydrogen peroxide/water system and its excess thermodynamic functions

Reported here are some aspects of the analysis of mixture vapor pressure data using the model-free Redlich-Kister approach that have heretofore not been recognized. These are that the pure vapor pressure of one or more components and the average temperature of the complex apparatuses used in such studies can be obtained from the mixture vapor pressures. The findings reported here raise questions regarding current and past approaches for analyses of mixture vapor pressure data. As a test case for this analysis approach the H2O2-H2O mixture vapor pressure measurements reported by Scatchard, Kavanagh, and Tickner (G. Scatchard, G. M. Kavanagh, L. B. Ticknor, J. Am. Chem. Soc. 1952, 74, 3715-3720; G. M. Kavanagh, PhD. Thesis, Massachusetts Institute of Technology (USA), 1949) have been used; there is significant recent interest in this system. It was found that the original data is fit far better with a four-parameter Redlich-Kister excess energy expansion with inclusion of the pure hydrogen peroxide vapor pressure and the temperature as parameters. Comparisons of the present results with the previous analyses of this suite of data exhibit significant deviations. A precedent for consideration of iteration of temperature exists from the little-known work of Uchida, Ogawa, and Yamaguchi (S. Uchida, S. Ogawa, M. Yamaguchi, Japan Sci. Eng. Sci. 1950, 1, 41-49) who observed significant variations of temperature from place to place within a carefully insulated apparatus of the type traditionally used in mixture vapor pressure measurements. For hydrogen peroxide, new critical constants and vapor pressure-temperature equations needed in the analysis approach described above have been derived. Also temperature functions for the four Redlich-Kister parameters were derived, that allowed calculations of the excess Gibbs energy, excess entropy, and excess enthalpy whose values at various temperatures indicate the complexity of H2O2-H2O mixtures not evident in the original analyses of this suite of experimental results.     

An electrothermal vaporization unit with axially focusing convection upstream. Part II: Modeling of the condensation process

A model is presented that describes quantitatively the condensation of analytes in pico- and nanogram masses sampled with electrothermal vaporization (ETV). It presumes that the analyte vapor condensation of such low amounts occurs mainly heterogeneously, predominantly on growing carbon particulates originating from the graphite furnace before the analyte vapor achieves saturation via cooling. The model regards the coagulation of carbon particles and the diffusion of analyte atoms. The criterion whether or not an analyte atom sticks to a colliding particle is chosen as a function depending on its temperature and on the common GFAAS pretreatment temperatures. Heterogeneous condensation of six analytes with different volatilities, Ag, Cu, Fe, Ni, Mn, and Pb, is calculated for the ETV unit with an axially focusing convection upstream described in Part I. Modifier effects are taken into account. The results are compared to measured data.     

Molecular dynamics simulation of liquid-solid transition. I. Response function model

Molecular dynamics simulation of stimulated condensation of supercooled liquid is discussed. The results of the calculations show that in the initial period, after an external potential is switched on, the sytem responds with relaxation even below the stability limit. It is found that the entire process of stimulated condensation is not on the scale of molecular dynamics calculations.     

Analytical investigation of simultaneous effects of convergent section heating of Laval nozzle,steam inlet condition,and nozzle geometry on condensation shock

Rapid expansion and supercooling of dry vapor in low-pressure steam turbines trigger nucleation phenomenon. Subsequently, following the occurrence of vapor condensation, a vapor–liquid two-phase flow is established. Entropy generation mainly by condensation shock, blade erosion, and ultimately, destruction of equipment and efficiency reduction are among adverse effects of vapor condensation, which should be either attenuated or controlled. In the present research, which is a continuation to the research performed by original authors, a one-dimensional analytical Eulerian–Lagrangian model is used to apply convergent section heating to different supersonic nozzles under various inlet conditions. The results indicate that the flow response to the heating is well dependent on the intensity of condensation shock or inlet conditions. In order to compensate for the mass flow rate resulted from the convergent section heating, effects of simultaneous reduction of inlet stagnation temperature and convergent section heating were investigated. Finally, it was found that, maintaining constant mass flow rate, simultaneous reduction of inlet stagnation temperature and convergent section heating cannot attenuate the condensation shock significantly. Therefore, the best approach to compensate for the reduction in the mass flow rate due to convergent section heating is to simultaneously increase inlet stagnation pressure.