An Examination of the Maximum Entropy Formalism for Secondary Atomization*

The maximum entropy formalism (MEF) is an attractive approach to predict the size and velocity distributions of daughter droplets resulting from secondary atomization because it is based on satisfying physical conservation laws. However, a critical examination of the method shows that it cannot reliably predict secondary atomization statistics due to a multitude of reasons. Firstly, the MEF cannot predict the multi-modal nature of droplet size distributions as evidenced by experimentally obtained size distributions in the literature. Secondly, it over-predicts velocity distributions of daughter droplets because of its inability to capture the temporal nature of the breakup process. Efforts to improve the velocity predictions by the MEF through a variation of the parameters in its formulation show little to no improvement. Finally, mathematical inconsistencies in the properties of the continuous form of the information entropy function used in the MEF pose challenges to the validity of its utilization for secondary atomization.