TITLE

The continuum approximation in nucleation theory

AUTHOR(S)
Wu, David T.
PUB. DATE
August 1992
SOURCE
Journal of Chemical Physics;8/1/1992, Vol. 97 Issue 3, p1922
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The continuum approximation in nucleation theory is reconsidered. It is shown that a minor change in indexing the discrete flux leads naturally to an approximation which is both simple and accurate. More complicated schemes are introduced using the formalism of spectral density (weighting) functions. Optimization of these functions produces additional approximations that minimize the errors in either the rate equation or the nucleation current. These new continuum approximations are compared to the traditional Frenkel form [Kinetic Theory of Liquids (Oxford University, Oxford, 1946)] and to the alternatives proposed by Goodrich [Proc. R. Soc. London, Ser. A 227, 167 (1964)] and Shizgal and Barrett [J. Chem. Phys. 91, 6505 (1989)]. Results show that the new forms are more accurate. Generalization to multipath kinetics (clustering or association) is also discussed. Finally, it is shown that within the continuum approximation, nucleation is mathematically equivalent to position-dependent diffusion.
ACCESSION #
7609055

 

Related Articles

  • Homogeneous bubble nucleation in liquids: The classical theory revisited. Delale, Can F.; Hruby, Jan; Marsik, Frantisek // Journal of Chemical Physics;1/8/2003, Vol. 118 Issue 2, p792 

    The classical theory of homogeneous bubble nucleation is reconsidered by employing a phenomenological nucleation barrier in the capillarity approximation that utilizes the superheat threshold achieved in experiments. Consequently, an algorithm is constructed for the evaluation of the superheat...

  • On a debate over the simulation and mapping of physical clusters in small cells. Reiss, Howard; Djikaev, Yuri; Bowles, Richard K. // Journal of Chemical Physics;7/8/2002, Vol. 117 Issue 2, p557 

    This paper attempts to resolve some issues in a published debate concerning the types of approximations involved, either implicitly or explicitly, in an innovative method for the simulation of small physical clusters. The method consists of first simulating the probability that a cluster will be...

  • A Wide Approximate Continuity. Lahiri, Indrajit // Vietnam Journal of Mathematics;Sep2002, Vol. 30 Issue 3, p271 

    Introducing the notion of widely approximate continuous functions we study some basic properties of such functions.

  • WHy Legendre Made a Wrong Guess About p(X), and How Laguerre's Continued Fraction for the Logarithmic Integral Improved It. Bauer, Friedrich L. // Mathematical Intelligencer;Summer2003, Vol. 25 Issue 3, p7 

    Discusses two approximation methods, mathematician Adrien-Marie Legendre's approximation about p(x), the number of primes p such that p = x and mathematician Edmond Nicolas Laguerre's continued fraction for the logarithmic integral. Factors responsible for the wrong guess made by Legendre;...

  • Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design. Yanfeng Ouyang; Daganzo, Carlos F. // Transportation Science;Feb2006, Vol. 40 Issue 1, p89 

    This paper proposes an algorithm that automatically translates the "continuum approximation" (CA) recipes for location problems into discrete designs. It applies to terminal systems, but can also be used for other logistics problems. The study also systematically compares the logistics costs...

  • Damage property of incompletely spalled aluminum under shock wave loading. Qi, Meilan; Luo, Chao; He, Hongliang; Wang, Yonggang; Fan, Duan; Yan, Shilin // Journal of Applied Physics;Feb2012, Vol. 111 Issue 4, p043506 

    The nucleation, growth, and coalescence of microscopic voids are induced inside ductile metal when it is subjected to dynamic tension, and this eventually results in a catastrophic fracture of the specimen. In the present work, this failure property is studied by using ultrapure aluminum...

  • On the closure conjectures for the Gibbsian approximation model of a binary droplet. Djikaev, Y. S.; Napari, Ismo; Laaksonen, Ari // Journal of Chemical Physics;5/22/2004, Vol. 120 Issue 20, p9752 

    Within the framework of Gibbsian thermodynamics, a binary droplet is regarded to consist of a uniform interior and dividing surface. The properties of the droplet interior are those of the bulk liquid solution, but the dividing surface is a fictitious phase whose chemical potentials cannot be...

  • Revisiting Twomey's approximation for peak supersaturation. Shipway, B. J. // Atmospheric Chemistry & Physics Discussions;2014, Vol. 14 Issue 19, p25901 

    Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly...

  • APPROXIMATION OF CONTINUOUS FUNCTIONS ON V.K. DZJADYK CURVES. Jafarov, Sadulla Z. // Studia Universitatis Babes-Bolyai, Mathematica;2009, Issue 1, p107 

    In the given paper rational approximation is studied on closed curves of a complex plane for continuous functions in terms of the k-th modulus of continuity, k ⩾ 1. Here a rational function interpolates a continuous function at definite points.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics