Multi-scale analysis of atomizing liquid ligaments

• The temporal evolution of individual atomizing ligaments is visualized.
• The analysis uses a multi-scale approach and introduces the notion of scale diameter.
• Low surface tension ligaments are more sensitive to elongation constraint.
• The atomization process cascades in the scale space when surface tension decreases.
• The scale distribution of the produced droplets is modeled.

The atomization of individual liquid ligaments appearing during the disintegration of liquid sheets issuing from a triple-disk injector is investigated. High-speed visualizations report a temporal evolution of the ligaments from their production to their disintegration into drops. The parameter of the experiments is the surface tension of the liquid. A multi-scale analysis consisting in describing the temporal evolution of the ligament shape by measuring the scale-distribution is performed. This analysis introduces the notion of scale-diameter whose temporal variation leads to the following conclusion. The ligaments are subject to elongation, capillary deformation and break up and relaxation mechanisms. These mechanisms appear concomitantly on different scales. This concomitancy depends on the surface tension, i.e., on a Weber number based on the ligament initial elongation rate and initial size: the decrease of the surface tension favor the propensity of the atomization process to cascade in the scale space towards the small scale region. A mathematical scale-distribution of the final drops is satisfactorily derived from an atomization model of the literature. Furthermore, the parameters introduced by this model are well correlated to initial ligament Weber number and size.