Contraction of an air cone vs a liquid cone

The universality of the pinch-off of inviscid liquid threads is well known and scales with capillary-inertial dynamics. Recent work by Brasz et al. (2018)¹ investigates the repeated droplet formation from the tip of a retracting liquid cone, using a discrete self-similar formalism. Interchanging the air and liquid to form the contraction of an air-cone within a liquid pool is geometrically similar, but the dynamics will resemble more the purely inertial pinch-off of a bubble. Here we use the volume-of-fluid computational code Gerris to investigate the retraction of such an air cone over a range of different cone angles and initial perturbation levels, using refinement levels up to 20. We find that the parameter space for the air cone is significantly different from that of the liquid cone, showing regions of no pinch-off and regular pinch-off, with an irregular regime in between. The irregular pinch-off regime shows a much faster contraction speed and stronger jets emerging. The pinch-off radius follows inertial time-scaling with a power-law exponent close to 0.5, while overall discrete self-similarity is still approximately preserved.