The Kelvin equation and self-consistent nucleation theory

Wilemski, G

doi:10.1063/1.469822

Title: The Kelvin equation and self-consistent nucleation theory

Full Record
Other Related Research

Abstract

Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplifymore »« less

Authors:

Wilemski, G ^[1]

Lawrence Livermore National Laboratory, Livermore California 94551-9900 (United States)

Publication Date:: Sat Jul 15 00:00:00 EDT 1995

OSTI Identifier:: 69055

DOE Contract Number:: FG02-92ER14257; W-7405-ENG-48

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 103; Journal Issue: 3; Other Information: PBD: 15 Jul 1995

Country of Publication:: United States

Language:: English

Subject:: 66 PHYSICS; NUCLEATION; MATHEMATICAL MODELS; EVAPORATION; KINETICS; MOLECULAR CLUSTERS; SIZE; THERMODYNAMICS; STATISTICAL MECHANICS

Citation Formats


                    Wilemski, G, and Physical Sciences Inc., Andover, Massachusetts 01810-1077. The Kelvin equation and self-consistent nucleation theory.  United States: N. p., 1995. 
        Web.  doi:10.1063/1.469822.

Copy to clipboard


                    Wilemski, G, & Physical Sciences Inc., Andover, Massachusetts 01810-1077. The Kelvin equation and self-consistent nucleation theory.  United States.  https://doi.org/10.1063/1.469822

Copy to clipboard


                    Wilemski, G, and Physical Sciences Inc., Andover, Massachusetts 01810-1077. 1995.  
        "The Kelvin equation and self-consistent nucleation theory".  United States.  https://doi.org/10.1063/1.469822.

Copy to clipboard


                    
@article{osti_69055,

  title        = {The Kelvin equation and self-consistent nucleation theory},

  author       = {Wilemski, G and Physical Sciences Inc., Andover, Massachusetts 01810-1077},

  abstractNote = {Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplify the calculation of nucleation rates for this model. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.},

  doi          = {10.1063/1.469822},

  url          = {https://www.osti.gov/biblio/69055},
  journal      = {Journal of Chemical Physics},
number       = 3,

  volume       = 103,

  place        = {United States},

  year         = {Sat Jul 15 00:00:00 EDT 1995},

  month        = {Sat Jul 15 00:00:00 EDT 1995}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.469822

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Binary nucleation kinetics. I. Self-consistent size distribution

Journal Article Wilemski, G; Wyslouzil, B - Journal of Chemical Physics

Using the principle of detailed balance, we derive a new self-consistency requirement, termed the kinetic product rule, relating the evaporation coefficients and equilibrium cluster distribution for a binary system. We use this result to demonstrate and resolve an inconsistency for an idealized Kelvin model of nucleation in a simple binary mixture. We next examine several common forms for the equilibrium distribution of binary clusters based on the capillarity approximation and ideal vapor behavior. We point out fundamental deficiencies for each expression. We also show that each distribution yields evaporation coefficients that formally satisfy the new kinetic product rule but aremore »« less
https://doi.org/10.1063/1.469823
LARGE-SCALE MAGNETIC FIELD GENERATION VIA THE KINETIC KELVIN-HELMHOLTZ INSTABILITY IN UNMAGNETIZED SCENARIOS

Journal Article Alves, E; Grismayer, T; Martins, S; ... - Astrophysical Journal Letters

Collisionless plasma instabilities are fundamental in magnetic field generation in astrophysical scenarios, but their role has been addressed in scenarios where velocity shear is absent. In this work we show that velocity shears must be considered when studying realistic astrophysical scenarios, since these trigger the collisionless Kelvin-Helmholtz instability (KHI). We present the first self-consistent three-dimensional particle-in-cell simulations of the KHI in conditions relevant for unmagnetized relativistic outflows with velocity shear, such as active galactic nuclei and gamma-ray bursts. We show the generation of a strong large-scale DC magnetic field, which extends over the entire shear-surface, reaching thicknesses of a fewmore »« less
https://doi.org/10.1088/2041-8205/746/2/L14
A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

Journal Article Schilling, Oleg - Physica. D, Nonlinear Phenomena

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying amore »« less
https://doi.org/10.1016/j.physd.2019.132238

Full Text Available
Two-dimensional kinetics of binary nucleation in sulfuric acid--water mixtures

Journal Article McGraw, R - Journal of Chemical Physics; (United States)

Homogeneous nucleation theory for binary mixtures is developed as a two-component extension of the classical multistate kinetics rate theory. A matrix formulation, based on the stochastic model of Shugard and Reiss [J. Chem. Phys. [bold 65], 2827 (1976)], provides the framework for solving the strongly coupled two-dimensional flux network associated with tracking the evaporation and growth kinetics of each component for several thousand binary clusters, of varying composition, throughout the region of critical size. This approach avoids the assumption of a single nucleation path, e.g., through the saddle point of the binary free-energy surface, and considers, instead, all possible pathsmore »« less
https://doi.org/10.1063/1.468731
The energetics of prenucleation clusters in lattice solutions

Journal Article Legg, Benjamin; De Yoreo, James - Journal of Chemical Physics

According to classical nucleation theory, nucleation from solution involves the formation of small atomic clusters. Most formulations of classical nucleation use continuum “droplet” approximations to describe the properties of these clusters. However, the discrete atomic nature of very small clusters may cause deviations from these approximations. Here, we present a self-consistent framework for describing the nature of these deviations. We use our framework to investigate the formation of “polycube” atomic clusters on a cubic lattice, for which we have used combinatoric data to calculate the thermodynamic properties of clusters with 17 atoms or less. We show that that the classicalmore »« less
Cited by 8
https://doi.org/10.1063/1.4964489

Similar Records