A population balance model for the flow-induced preparation of Pickering emulsions

In this work we studied the flow-induced preparation of oil-in-water Pickering emulsions by means of a bivariate population balance model. We characterized oil droplets by their size and surface coverage by solid particles, and we took into account all phenomena responsible for their change, namely coalescence and breakup of the droplets, and particle-droplet collisions leading to surface coverage. We studied the population dynamics in a uniform shear flow and in a turbulent flow field, and stabilization was observed in both cases. Under shear, the population evolved by coalescence phenomena, which, together with particle adsorption, led to a prompt and full stabilization of the emulsion droplets. An inverse scaling between particle load and droplets Sauter diameter was found, and seen to well compare with previously reported experimental data for arrested coalescence. In turbulence, stabilization was also obtained. In this case, the droplet size evolved through a peculiar path, showing a size undershoot before equilibrium conditions were reached. We explained this as a consequence of the coalescence phenomena, that alongside breakup, affected the transient of the process. Results shed a new light onto the dynamics of preparation of Pickering emulsions and aim at constituting a reference for the set-up and interpretation of experiments.