Moment and Fokker-Planck equations for the growth and decay of small objects

Abstract
Some aspects of the growth and decay of distributions of small objects, such as particles, bubbles, or droplets, that are governed by discrete rate equations, are investigated. Differential equations for the moments of the distribution are derived and are solved in an equilibrium model both for the static moments and for the approach to equilibrium. Comparisons with numerical and exact analytical results show that the method gives fairly accurate values for the moments. The method also indicates types of growth and decay problems where the replacement of the discrete equations by the continuity equation is justified. The accuracy of static solutions of various Fokker-Planck equations is also examined in the equilibrium model. It is found that a form proposed by Goodrich gives by far the best representation of the solution of the discrete equations.

This publication has 0 references indexed in Scilit: