An acoustic-field assisted process intended to recover the oil phase from aqueous emulsions has been previously developed. It applies a resonant ultrasonic wavefield to the emulsion flowing through a rectangular chamber. The oil droplets migrate to pressure antinodes of the standing wave-field. Rapid coalescence and plating out of droplets on the internal surfaces of the chamber occurs.; To obtain a fundamental understanding of the bulk coalescence of droplets away from any solid surface in acoustic field, a microscopic mathematical model was developed that predicts the relative trajectory of a pair of droplets in an acoustic field by considering pertinent body forces and interdroplet effects. This trajectory analysis was used to compute the rate of volume cleared by the coalescence of different droplet pairs as a function of various operating conditions.; The results of the droplet pair model were used as a basis to develop a global model for coalescence rates. The expressions for volume cleared by coalescence of different droplet pairs were incorporated into standard population balance equations to determine the rate of collisions of different droplet pairs. This analysis led to the formulation of a predictive model that could track evolution of drop sizes in a given droplet population coalescing in an acoustic field.; The droplet pair model was validated by designing an experimental system to visualize the interaction between two coalescing droplets in an emulsion subjected to a standing acoustic field. The experimentally observed trajectories were compared with those determined by the droplet-pair model. The predicted and observed trajectories matched reasonably well without any model parameter adjustment. The match between relative trajectories predicted by the model and those observed experimentally was further improved via adjustments in the energy density values used in the model.; The predictions of the global model were validated by experimentally tracking the size-evolution of emulsions subjected to an acoustic field and comparing it with the predictions of the global model. It was observed that the model consistently underpredicted the coalescence rate in the experimental system. This was attributed to energy density gradients within the chamber that could give rise to lateral acoustic forces. These forces tend to concentrate the droplets in the regions of local energy density maxima, thereby enhancing the rate of coalescence over that predicted by the model.; The existence of energy density gradients in the experimental system was confirmed by performing parallel band line-up and disruption experiments with polystyrene suspensions. An effective energy density value was computed for each of the experiments, and this enabled the model predictions to agree very well with the experimental observations. The inclusion of lateral acoustic forces in the model may improve the accuracy of its predictions.
展开▼
