Determination of the aerodynamic droplet breakup boundaries based on a total force approach

The determination of the critical Weg number separating the different breakup regimes has been extensively studied in several experimental and numerical works, while empirical and semi-analytical approaches have been proposed to relate the critical Weg number with the Ohl number. Nevertheless, under certain conditions, the Reg number and the density ratio ε may become important. The present work provides a simple but reliable enough methodology to determine the critical Weg number as a function of the aforementioned parameters in an effort to fill this gap in knowledge. It considers the main forces acting on the droplet (aerodynamic, surface tension and viscous) and provides a general criterion for breakup to occur but also for the transition among the different breakup regimes. In this light, the present work proposes the introduction of a new set of parameters named as Weg,eff and Cal monitored in a new breakup plane. This plane provides a direct relation between gas inertia and liquid viscosity forces, while the secondary effects of Reg number and density ratio have been embedded inside the effective Weg number (Weg,eff)