Prediction of drop size distributions in sprays using the maximum entropy formalism : the effect of satellite formation

The droplet size distribution function for sprays is derived using the maximum entropy formalism (MEF) to link the end stage of the atomization process to an intermediate state, characterized by unstable liquid cylinders. The probability density function, PDF, for droplet diameter, d, is mainly governed by conservation of mass and the energy equation. Many of the small droplets are supposedly created together with a much larger droplet, i.e. are supposed to be satellites. A dual PDF, f1(d,d*), represents the number of satellites of diameter d corresponding to a central or primary drop with diameter d*. The representation space is extended with the primary droplet diameter d* and the MEF is applied to derive the function f1. The physical constraints are first related to parts of the liquid cylinders only, and some higher moments of the primary size distribution function, f0(d*), have to be known in order to be able to apply the MEF. Some problems inherent in the application of this formalism are examined. Without invoking fitting parameters or ad-hoc constraints the predicted PDFs are close to measured ones.