Complete modeling of a new ultrasonic atomizer, the Spray On Demand (SOD) printhead, was carried out to enable its optimization. The modeling was focused on various factors, including nozzle vibrations and a theoretical prediction of the SOD drop-size distribution. Assuming that the spray is generated based on Faraday instability, a prediction of the drop-size distribution within the framework of a specific and general Maximum Entropy Formalism (MEF) was developed. This prediction was formulated using the conservation laws of energy and mass, as well as the three-parameter generalized Gamma distribution. After establishing an analytical expression to estimate the Sauter Mean Diameter, a qualitative validation of the model was performed by comparing predictions with experimental measurements of the dropsize distribution. The dynamic model is shown to be sensitive to operating conditions and physical properties of the fluid. The prediction capabilities of the model were found to be adequate, paving the way for optimization of the atomizer. The evolution of the drop-size distribution, under the coalescence effect, was also assessed using a convergent Monte Carlo method to solve the distribution equation. This was formulated in a mass flow algorithm, leading to a more physically relevant distribution.