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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 of volume fraction, which simply characterize the dispersion process and structure the resulting equation. They lead to equivalent “single-particle” (comprising the entire dispersed phase) 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 for 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 techniques to measure multivariate population distributions such as those of Bae and Tavlarides (1989) and of flow cytometry.

Photographic measurements of transient drop-size distributions from stirred liquid-liquid systems of low dispersed phase fraction in a batch vessel confirm consistency with a similarity behavior from population balance established earlier by Narsimhan et al. (1980). Moreover, breakage functions are presented in generalized dimensionless form accounting for dependence on physical properties of the system and power input through stirring. This information is essential for predicting drop-size distributions in stirred liquid-liquid systems. Experimental measurements of steady-state drip-size distributions obtained from stirred, continuous flow systems with known inlet drop sizes compare very favorably with theoretical predictions based on population balance analysis using the breakage functions obtained from batch experiments.