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

Abstract

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 sizedistribution. 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.