Exactly solvable model for cluster-size distribution in a closed system.
Phys Rev E
; 95(1-1): 012135, 2017 Jan.
Article
en En
| MEDLINE
| ID: mdl-28208403
We obtain an exact solution for the cluster-size distributions in a closed system described by nonlinear rate equations for irreversible homogeneous growth with size-linear agglomeration rates of the form K_{s}=D(a+s-1) for all s≥1, where D is the diffusion coefficient, s is the size, and a is a positive constant. The size spectrum is given by the Pólya distribution times a factor that normalizes the first moment of the distribution to unity and zeroes out the monomer concentration at tâ∞. We show that the a value sets a maximum mean size that equals e for large a and tends to infinity only when aâ0. The size distributions are monotonically decreasing in the initial stage, converting to different monomodal shapes with a maximum at s=2 in the course of growth. The variance of the distribution is narrower than Poissonian at large a and broader than Poissonian at small a, with the threshold occurring at aâ
1. In most cases, the sizes present in the distributions are small and hence can hardly be described by continuum equations.
Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
Phys Rev E
Año:
2017
Tipo del documento:
Article
País de afiliación:
Rusia
Pais de publicación:
Estados Unidos