Evolution of Drop Size Distributions in Fully Developed Turbulent Pipe Flow of a Liquid−Liquid Dispersion by Breakage

Abstract

The population balance equation for the evolution of drop size distributions in fully developed turbulent flow of a liquid−liquid dispersion in a circular pipe has been solved “exactly” using spectral expansion of the self-adjoint diffusion operator with a radially varying diffusion coefficient to obtain the number density at any location in the pipe. The breakage frequency is allowed to vary with position, although the size distribution of broken fragments is assumed to satisfy a form of similarity assumed in the work of Narsimhan et al. (AIChE J. 1980, 26, 991; 1984, 30, 457) that rids it of explicit spatial dependence. Of course, insofar as numerical methods are used to calculate the spectral data (eigenvalues and eigenvectors), such an exact solution is still to be regarded as approximate. Furthermore, because the solution is expressed in terms of a transient well-mixed batch dispersion evolving by breakage, the actual number density may be obtained by any of the methods for solving population balance...