Modeling of double emulsions using population balance equations

Abstract

Abstract Double emulsions are widely spread in a number of applications, such as food, cosmetics and pharmaceutics. They are usually prepared in two steps, comprising the preparation of a first emulsion that is in a second step introduced in an external continuous phase. A number of phenomena may occur during the second step including breakage, coalescence, and escape that is aimed to be reduced to keep high the encapsulation efficiency. Suitable models of these phenomena are proposed in this work and incorporated into a population balance model (PBM) to allow predicting the evolution of the droplet size distribution (DSD) of the external macro-droplets as well as the release rate. During the considered short preparation time and the slow molecular diffusion of the encapsulated salt, the release rate was assumed to be mainly governed by the leakage of internal droplets, i.e. their release due to the breakage of the macro-droplets. The proposed leakage model is thus described as a function of the breakage rate of the macro-droplets. The model parameters involved in the different sub-models of the PBMs (breakup and coalescence kernels, leakage) were identified in experiments of W/O/W double emulsions prepared using a rotor stator. Then, the model was validated under various key process conditions, such as the internal water fractions (10–40%) and stirring rate. The dependence of the leakage parameter on the concentration of salt was also investigated. The macro-DSD was measured by Laser diffraction while the leakage rate was monitored by conductivity measurements.