A New Model for the Dynamics of Dispersions in a Batch Reactor

A new model for coalescence and breakage of liquid-liquid dispersion is presented. The main features are: (i) the introduction of an efficiency factor which controls the time rate of the various processes affecting the size distribution function of droplets, (ii) a new effect — that we call volume scattering — which is consistent with the experimentally observed circumstance of the existence of a top size limit for droplets depending on the general dynamical conditions. The model is proved to be mathematically and physically correct by proving existence and uniqueness of a regular solution to the Cauchy problem.