On the Threshold of Drop Fragmentation under Impulsive Acceleration

TL;DR

This study uses advanced simulations to analyze how fluid properties and acceleration influence drop fragmentation thresholds, introducing a new predictor for when drops break apart under impulsive forces.

Contribution

The paper develops a new non-dimensional parameter, $C_{breakup}$, that accurately predicts the critical conditions for drop fragmentation, improving upon traditional methods.

Findings

Decrease in Ohnesorge number affects breakup morphology and critical Weber number.

Pressure and shear forces controlled by density ratio and ambient Ohnesorge number influence deformation.

The new $C_{breakup}$ parameter reliably predicts fragmentation thresholds.

Abstract

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.