Prediction and evolution of drop-size distribution of an ultrasonic vibrating microchannel

We report in this paper the evolution of a physically-based drop size-distribution coupling the Maximum Entropy Formalism and the Monte Carlo method to solve the distribution equation of a spray. The atomization is performed by a new Spray On Demand (SOD) device which exploits ultrasonic generation via a Faraday instability. The Modified Hamilton's principle is used to describe the fluid structure/interaction with a vibrating micro-channel conveying fluid excited by a pointwise piezoactuator. We combine to the fluid/structure description a physically based approach for predicting the drop-size distribution within the framework of the Maximum Entropy Formalism (MEF) using conservation laws of energy and mass coupling with the three-parameter generalized Gamma distribution. The prediction and experimental validation of the drop size distribution of a new Spray On Demand print-head is performed. The dynamic model is shown to be sensitive to operating conditions, design parameter and physico-chemical properties of the fluid and its prediction capability is good. We also report on a model allowing the evolution of drop size- distribution. Deriving the discrete and continuous population balance equation, the Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After proposing a kernel for coalescence, we solve the time dependent drop size distribution using a Monte Carlo Method which is shown to be convergent. The drops size distribution upon time shows the effect of spray droplets coalescence.