Analytical Solutions to Fragmenting Flows

A closed form analytical solution is developed to predict the temporal and spatial evolution of the particle size distribution in an axisymmetric particulate jet with accompanying fragmentation. Here, the particulate phase is conveyed by a carrier (continuous) phase and the fragmentation process along each stream line is modeled using population balance equations. The two dimensional nature of the particle size evolution equation of a jet is transformed into a one dimensional equation using a von Mises-like transformation, for which the solutions are in a form similar to the Reid's solution to the batch grinding equation. The analytical solution is implemented and studied for the situation of a pulsating jet as this is considered to be a model for an internal combustion engine injector.