On the Threshold of Drop Fragmentation under Impulsive Acceleration (2211.12017v2)

Abstract: Secondary fragmentation of an impulsively accelerated drop depends on fluid properties and velocity of the ambient. The critical Weber number $(\mathit{We}\mathit{cr})$, the minimum Weber number at which a drop undergoes non-vibrational breakup, depends on fluid density ratio $(\rho)$, the drop $(\mathit{Oh}_d)$, and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. The current study uses VoF based interface-tracking multiphase flow simulations to quantify the effect of different non-dimensional groups on the threshold at which secondary fragmentation occur. For $\mathit{Oh}_d \leq 0.1$, a decrease in $\mathit{Oh}_d$ significantly influences the breakup morphology, plume formation, and the resulting $\mathit{We}\mathit{cr}$. $\rho$ and $\mathit{Oh}o$, were found to influence the balance between the pressure differences between the poles and the periphery, and the shear stresses on the upstream surface. These external forces induce flow inside the initially spherical drop, resulting in deformation into pancakes and eventually the breakup morphology of forward/backward bag. The evolution pathways of the drop morphology based on their non-dimensional groups have been charted. With the inclusion of the new observations, the traditional $\mathit{We}\mathit{cr}-\mathit{Oh}d$ plot, used for illustrating the dependence of critical Weber number on $\mathit{Oh}_d$, was found to be inadequate in predicting the minimum initial $\mathit{We}$ required to undergo fragmentation. A new non-dimensional parameter $C{breakup}$ is derived based on the competition between forces driving drop deformation and the forces resisting drop deformation. Tested on the available experimental data and current simulations, $C_{breakup}$ is found to be a robust predictor for the threshold of drop fragmentation.