Breakup pathway selection and scaling in Rayleigh-regime air-assisted atomization

This study examines ligament formation and droplet-size variation in air-assisted twin-fluid atomizers in the Rayleigh regime (We g ≤ 0.4) using a 0.3 mm-thick planar water sheet at a liquid velocity of 1 m/s. High-speed shadowgraphy is combined with a reduced two-fluid spatial stability analysis that incorporates interfacial viscous stresses while neglecting bulk viscous diffusion. The analysis identifies the sinuous mode as the dominant amplified mode, consistent with its role in primary sheet deformation and ligament formation, while the sheet’s dilatational branch is weakly amplified and associated with long wavelengths. Ligament thinning and pinch-off are consistent with capillary (varicose) instability of the ligaments. The classification-dependent empirical metric β, the fraction of classified objects that are droplets under a projected aspect-ratio threshold, depends on that threshold. It is an empirical, classification-dependent measure and not an intrinsic breakup probability. Classical constant-ratio relations (D ≈ 0.44λ sin and L ≈ 0.77λ sin ) are leading-order approximations at low We g but show a systematic We g dependence, captured by linear corrections: D/λ sin = 0.0509 + 1.737 We g and L/λ sin = 0.0443 + 3.237 We g . We fitted these corrections to the present data (single fluid, fixed sheet thickness and velocity); their goodness of fit is in-sample, and they are not independent predictions. The spatial model, which combines potential flow with viscous interfacial stress, agrees slightly better with the measured length scales than the temporal model and provides a framework for interpreting liquid-sheet breakup in the Rayleigh regime.