Evaporation—Condensation Coefficient for Small Droplets

Okuyama, Masataka; Zung, Joseph T.

doi:10.1063/1.1840906

Cited by 51 publications

(16 citation statements)

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“…The sticking (condensation) and surface-tension coefficients of nanoparticles also become functions of their size [3][4][5]. It should be noted that small particles can arise in a gas phase only at sufficiently high values of the saturation ratio of vapor.…”

Section: Udc 541182mentioning

confidence: 99%

“…Generally, the condensation coefficient α, which is defined as the probability that the molecule incident on the surface will not reflect elastically back to the gas phase, depends on the particle size due to the decrease in the number of particle molecules that interact with the gas molecule incident on the particle. Here, the value of α decreases with the particle size as well [3,4]. On the basis of the expression for the dependence of the condensation coefficient on the particle size given in [3] and formula (5), the dependence of α on the particle (drop) diameter can be presented as…”

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confidence: 99%

“…Here, the value of α decreases with the particle size as well [3,4]. On the basis of the expression for the dependence of the condensation coefficient on the particle size given in [3] and formula (5), the dependence of α on the particle (drop) diameter can be presented as…”

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Influence of size effects on the critical diameter and growth of nanoparticles

Levdanskii

Smolik

Moravec

2006

J Eng Phys Thermophys

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UDC 541.182The effect exerted by the dependence between the condensation and surface-tension coefficients and the size of an aerosol nanoparticle on its growth and critical diameter is investigated theoretically.Investigation of the characteristic features of transfer processes in aerosol systems with nanosized particles is of interest both for description of the atmospheric phenomena related to the formation and growth of water drops in the atmosphere [1] and for the technological processes where nanoparticles are obtained (or used) [2].It is well known that, when the size of a particle decreases, the processes occurring on its surface begin to play an increasing role. As this takes place, in a number of cases an investigation of the processes in aerosol systems with nanoparticles necessitates taking account of the specific features in the progression of these processes due to the size effects. Thus, for example, the frequent (in phase transitions) assumption that the condensation coefficient is equal to the evaporation coefficient can lead to qualitatively incorrect results in the case of nanoparticles.The saturated vapor pressure over a small particle (drop) depends on its size [1]. The sticking (condensation) and surface-tension coefficients of nanoparticles also become functions of their size [3][4][5]. It should be noted that small particles can arise in a gas phase only at sufficiently high values of the saturation ratio of vapor. The condition of the equilibrium of such particles with a gas phase is determined by the so-called critical size of a particle. In [4], the influence exerted by the dependence between the condensation coefficient and the size of particles on their critical diameter and growth rate was discussed, with the surface-tension coefficient being supposed constant. In the present paper, we consider the joint effect of the condensation and surface-tension coefficients influenced by the size of aerosol nanoparticles on the phase transitions occurring on their surfaces.The particle growth rate v p in vapor condensation can be written as(1)We shall analyze the dependence of j e and j c on the particle size. The flux density of the molecules that evaporate from the surface of a small aerosol particle, with consideration for the Kelvin correction for the saturated vapor pressure over the particle, takes the form(2)According to [6], the evaporation coefficient α e is defined as a coefficient of proportionality between the actual (measured) flux density of evaporating molecules for a flat massive sample and the greatest possible, during evaporation into vacuum, flux density, which is equal to P e /(2πmkT s ) 1 ⁄ 2 . In other words, the evaporation coefficient is a measure of the deviation of an actual evaporation rate from the greatest possible one for a flat massive sample. With such a definition, the evaporation coefficient is independent of the particle size (the size dependence of the evaporation rate is taken into account by the exponential term in (2), which describes, according to the Kelv...

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Section: Udc 541182mentioning

confidence: 99%

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confidence: 99%

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Influence of size effects on the critical diameter and growth of nanoparticles

Levdanskii

Smolik

Moravec

2006

J Eng Phys Thermophys

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“…For the sake of simplicity, we assume that the dependence of the condensation coefficient on the particle size is the same for excited and unexcited molecules and is determined as [4] …”

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confidence: 99%

“…We note that the condensation coefficient for fairly small aerosol particles generally depends on their size [4,5]. When the radiation, which is resonant relative to vapor molecules, acts on the vapor-particle system, the condensation coefficient with the two-level model of molecular transitions from one state to another is determined by the expression [6] …”

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Influence of surface processes and external fields on transfer phenomena and phase transitions in aerosol systems with nano-size particles

Levdansky

Smolik

Moravec

2005

J Eng Phys Thermophys

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UDC 541.182The influence of dimensional effects, surface phenomena, and resonance radiation on the transfer processes and phase transitions in aerosol systems with nano-size particles is theoretically investigated.In recent years, transfer phenomena in two-phase systems, where one phase represents nano-size objects, in particular, nanoparticles, nanotubes, and fullerenes, have attracted the increasing attention of researchers. It is well known that the influence of surface processes occurring on the interfaces increases with decrease in the size of the objects. If the nano-size objects are in the gas phase, the mean free path of gas molecules in a number of cases is larger than the characteristic dimension of the objects or comparable to it. This leads to the necessity of considering transfer processes in a wide range of variation of the Knudsen number, determined by the ratio of the mean free path to the characteristic dimension. Furthermore, new regularities arise in the course of phase and chemical transformations on the particle surface with decrease in the characteristic dimension, for example, in the radius of a spherical nanoparticle. These regularities are, in particular, due the dependence of the condensation (sticking) coefficient on the particle size. Phase transitions and chemical reactions on the particle surface can also depend on the influence of the external fields (for example, of resonance laser radiation). In this work, the influence of dimensional effects, surface phenomena, and resonance radiation on the transfer processes in aerosol systems is studied theoretically using the growth of a small aerosol particle in physical deposition from a gas phase as an example.It is well known that an authentic description of the transfer processes in a gas-aerosol particle system with arbitrary Knudsen numbers and phase transitions on the particle surface can be performed only by solving the Boltzmann kinetic equation [1]. However, the arising mathematical difficulties do not enable one to obtain fairly simple expressions for the resulting molecular flux into the particle. Such relations can be found either from an approximate solution of the Boltzmann equation or by the use of simpler models based on the diffusion equation. Thus, for example, in [2] the possibility of using the diffusion equation was discussed, including the case where the particle radius is smaller than the mean free path of the gas molecules.We will not dwell on the numerous theoretical approaches available in the literature that enable us to obtain an approximate expression for the resulting flux of vapor molecules into the particle. Based on what has been said above, we will describe the problem of mass transfer in the vapor-buffer gas-particle system by the diffusion equation with boundary conditions set at r = R and r → ∞. The distribution of the number density of vapor molecules in the vicinity of a spherical particle in the quasisteady approximation has the form [1]where A and B are the integration constants determined from the b...

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