On the Threshold of Drop Fragmentation under Impulsive Acceleration

Secondary fragmentation of an impulsively accelerated drop depends on fluid properties and velocity of the ambient. The critical Weber number $(\mathit{We}_{cr})$, the minimum Weber number at which a drop undergoes non-vibrational breakup, depends on 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 $\mathit{Oh}_d$ was found to significantly influence the breakup morphology, plume formation, and $\mathit{We}_{cr}$. The balance between the pressure difference between the poles and the periphery, and the shear stresses on the upstream surface, was found to be controlled by $\rho$ and $\mathit{Oh}_o$. These 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 inclusion of the data from the expanded parameter-space, the traditional $\mathit{We}_{cr}-\mathit{Oh}_d$ diagram used to illustrate 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 the forces driving the drop deformation and the forces resisting the drop deformation. Tested using available experimental data and current simulations, $C_{breakup}$ is found to be a robust predictor for the threshold of drop fragmentation.