Theoretical prediction of stretching separation–coalescence boundary in droplet collisions with DNS verification

In combustion chambers, fuel droplet collisions alter droplet size and velocity distributions, significantly influencing subsequent combustion processes. Droplet–droplet collision outcomes are categorized into five regimes: minor deformation coalescence, bouncing, major deformation coalescence, head on collision (reflexive separation), and off center collision (stretching separation). These originate from five regions in the impact parameter-Weber number map using extensive experimental data, where the impact parameter characterizes droplet pair eccentricity and the Weber number is the dimensionless number defined as the ratio of inertial to surface tension forces. Subsequent research has focused on boundary lines between these regimes in such maps. For specific droplet pairs (fixed density, viscosity, surface tension), outcomes can be predicted from given impact parameter and Weber number. This study addresses the boundary between stretching separation and coalescence. Numerical simulations with the volume of fluid method were conducted for dodecane, tetradecane, and hexadecane droplet pairs across varying impact parameter and Weber number. We plotted collision outcomes in impact parameter-Weber number maps, emphasizing cases near the boundary between stretching separation and coalescence. Three boundary expressions distinguishing these states were theoretically derived. To validate the proposed expressions, we performed both internal and external calibration. Internal calibration used our numerical simulation data, quantifying predictive accuracy via mean absolute errors for three criteria (time-ratio criterion, aspect-ratio criterion, and force-ratio criterion). Compared with classical models, the mean absolute errors of the time ratio and aspect ratio criteria are reduced by 66%–78%, and that of the force ratio criterion by 16%–46%. External calibration employed the experimental data to determine a fixed set of coefficients in our expressions. These coefficients were then directly applied to the independent experimental data, where the proposed expressions still effectively discriminate the stretching separation and coalescence boundary, demonstrating good generalizability. The physical meanings of the parameters in our theoretical expressions are analyzed, and adaptability comparisons across variations in fluid properties show that our boundary expressions exhibit stronger robustness. • Direct numerical simulations of alkane droplet collisions are performed over varied impact parameters and Weber numbers. • Three theoretical boundary criteria are derived to distinguish stretching separation from coalescence for droplet collisions. • The influence of Ohnesorge number on the transition boundary is systematically analyzed and quantified. • Improved models show robust viscosity adaptability and outperform classical droplet collision models.