Analysis of Dispersed-Phase Fresh Perspective Systems: zy Doraiswami Ramkrishna and Arun Sathyagal zyxw School of Chemical Engineering G. Narsimhan Dept. of Agricultural Engineering Purdue University, West Lafayette, IN 47907 zyxwv Dispersed-phase systems are analyzed with a fresh perspective where the volume fraction of the dispersed phase is emphasized, not particle numbers as in population balance. Such volume fraction balances are more pertinent to engineering because they deal with the amount of the dispersed phase relative to that of the continuous phase. Although it is easy to make detailed volume fraction balances directly or from population balance, many interesting features are identified here with balance equations in terms zyxwvut of volume fraction, which simply characterize the dispersion process and structure the resulting equation. They lead to equivalent “single-par- ticle” {comprising the entire dispersed phase zyxwv f processes which can be simulated with great simplicity allowing rapid calculation of quantities associated with the dispersed phase and dispersion. The techniques can solve an inverse problem f o r mass-transfer coefficients of individual droplets from (simulated) measurements of the bivariate distribution of drop size and concentration of a transferring solute. Such inverse problem method is important in developing experimental techniques to measure multivariate population distributions such as those of Bae and Tavlarides (1989) and of flow cytometry. Introduction Dispersed-phase systems form a significant part of the chem- ical process industry. The high interfacial area characteristic of the dispersed phase is generally an attractive feature for many separation and reaction processes. Liquid-liquid extrac- tion, distillation, crystallization, nitration and sulfonation of many organic chemicals, alkylation reactions, and phase trans- fer catalytic reactions are some of the well-known examples of such processes. Possible use of dispersed-phase systems for carrying out multicomponent precipitation reactions in the manufacture of ceramic mixtures (Kumar, 1990) represents promising areas of future application. The design and control of process equipment in which the dispersed phase is present hinge crucially on methods of anal- ysis of both the dispersion process and physico-chemical proc- esses in the system which occur concurrently. The population Correspondence concerning this article should be addressed to D. Ramkrishna. balance framework has been an indispensable tool in this re- gard (Hulburt and Katz, 1964; Randolph and Larson, 1964; Ramkrishna and Borwanker, 1973). The status of population balance was assessed recently by Ramkrishna (1985). Popu- lation balance is concerned with the zyxw number of particles of the dispersed phase expressed in terms of a density in physical space, as well as in an abstract property space. The abstract property space may consist of several variables characterizing the particle state including primarily a measure of particle size such as the volume or mass of the particle. This article shows that the analysis of dispersed-phase sys- tems is better accomplished by a curnufatiue volume (or mass) distribution (rather than a number density function) of the dispersed phase for several reasons. This viewpoint, although conceptually simple, deserves special expression in the litera- ture because the cumulative volume fraction has many attri- butes too compelling to be ignored. AIChE Journal January 1995 Vol. 41, No. 1 35