Influence of the intensity of mixing on the droplet size distribution of emulsions: Theory and experiment

Abstract

We use a stochastic model to predict the droplet size distribution of emulsions generated in a mixer. The emulsions are made of two immiscible liquids, and do not contain surfactants. The intensity of mixing is measured by the speed of rotation of the propeller stirrer. - The model depends on the two extreme diameters (d _min, d _max) of the states in which the droplets are classified during the formation of the emulsion. It predicts a lognormal stationary distribution, the two independent parameters of which can be analytically related to d _min and d _max, by assuming that during the emulsification the breaking/coalescence probabilities of the droplets are time independent and linear functions of the droplet diameter. It can also be related to the speed of rotation of the stirrer by means of the isotropic turbulence theory. — The predicted volume median diameters and standard deviations of the lognormal stationary distributions are in agreement with experiments especially designed to test the model.