We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different gas phase conditions and types of liquid mixtures. The equilibrium distribution function of the clusters is determined in terms of the variables g and x. We obtain an approximate analytical solution for the steady-state binary nucleation rate that has the correct limit in the transition to unary nucleation. To further illustrate our description, the nonequilibrium steady-state cluster concentrations are found by numerically solving the reformulated kinetic equation. For the reformulated transient problem, the relaxation or induction time for binary nucleation was calculated using Galerkin's method. This relaxation time is affected by processes in both size and composition space, but the contributions from each process can be separated only approximately.




United States. Department of Energy

Keywords and Phrases

Boundary Conditions; Free Energy; Kinetic Theory; Approximation theory; Astrophysics; Brownian movements; Differential equations; Galerkin methods; Nucleation; Problem solving; Vapors

International Standard Serial Number (ISSN)

1539-3755; 2470-0045

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2004 American Physical Society (APS), All rights reserved.

Publication Date

01 Jan 2004

Included in

Physics Commons