Exact solution of a kinetic equation of one step processes of growth and decay

TL;DR

This paper derives exact solutions for kinetic equations describing growth and decay processes with sources, revealing how sources influence size distribution and aiding in modeling nucleation under supersaturation.

Contribution

It provides the first exact solutions for growth and decay kinetic equations with sources for arbitrary rate dependencies.

Findings

Sources cause broadening of size distribution.

Solutions enable approximate nucleation size distribution modeling.

Applicable for large vapor supersaturation conditions.

Abstract

The exact solution of the kinetic equation of the one step process of a growth (birth) in the presence of sources (runs-off) is found for arbitrary dependence of the rate of the growth on the number of the state (or size). It is shown that the presence of the source leads on the broadening of the state (or size) distribution. It is shown also that the solution obtained can be used for approximate definition of the size distribution of nuclei for the case of large supersaturation of the vapor. The exact solution of the kinetic equation of the one step process of a decay in the presence of sources (runs-off) is found also for arbitrary dependence of the rate of the decay on the number of the state (or size).