Droplet breakup modelling in spraying

We study the problem of a liquid droplet in 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. Results propose a simple algebraic equation that shows the inter-relationships between the pertinent parameters, and constitutes the minimum essential conditions for the droplet breakup. Breakup times and travel distances are also evaluated.