Droplet breakage and coalescence models for the flow of water-in-oil emulsions through a valve-like element

An experimental and theoretical study was carried out regarding the evolution of droplet size distributions for the flow of water in oil emulsions through a valve-like element that simulates a mixing valve. The water droplets had diameters in the 0.1–100 μm range, which includes droplets that are either smaller or larger than the Kolmogorov length scale for the experimental conditions. Droplet breakage and coalescence models that can be used for this size range were proposed. A simplified population balance model was developed to interpret the experimental data and solved by the method of classes. The model parameters were estimated by the orthogonal distance regression method. The simplifying assumption of the model was verified by global optimization using a parallel implementation of the particle swarm optimization method. The agreement between simulated and experimental droplet volume size distributions was good. The predictions of the DeBroukere mean diameter, d₄₃, were unbiased with mean errors of 8%.