Self-preserving theory of particulate systems

Abstract

The similarity solution of the population balance equation for pure kinetic coagulation (coalescence) has proved to be a useful means of representing the evolution of size distributions of homogeneous particulate systems. The resulting solution is termed self-preserving since neither particle size nor time appears explicitly in the solution. In the present work similarity solutions are developed for a wide class of particulate processes that are governed by a general population balance equation for the inhomogeneous size distribution density function. The general theory has application to the analysis of size spectra of atmosphere aerosols undergoing simultaneous coagulation, turbulent diffusion, and growth by gas-to-particle condensation, to the analysis of size spectra during grinding processes, and to several other physical systems of interest.

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