Analytical criterion for droplet breakup

We studied the problem of a liquid droplet in a high-speed trajectory through ambient gas. The fate of such a droplet is of importance to the overall spray characteristics, in the context of secondary breakup. A theoretical analysis of the problem is presented in which we examine an overall energy balance that includes surface and dissipation energies. Transformation between a droplet to its breakup products under trajectory conditions that include drag forces is a spontaneous process that occurs at a characteristic finite time. The transformation involves reversible surface energy transitions and irreversible viscous dissipation energy. The results provide a simple algebraic equation that shows the inter-relationships between the pertinent parameters and constitutes the minimum essential conditions for droplet breakup.