Fragmentation of inviscid liquid and destination of satellite droplets

Abstract

The breakup process of the inviscid liquid bridge sandwiched between two coaxial and equal-sized rods is investigated by tracking its profile. Here, the focus is on the quasi-static profile of the liquid bridge close to rupture and its influence on the subsequent dynamic breakup behaviors. With the increasing distance between the two rods, the profile of the liquid bridge close to rupture undergoes a transition from symmetry to asymmetry. We found there exists a critical slenderness above which the liquid bridge will be asymmetric and present a profile that can be well fitted by one cycle of the sine wave. It is demonstrated both experimentally and theoretically that the ratio of the length of the bridge to its equivalent radius, defined as geometric mean of the radii at the peak and trough of the bridge, is always 2π for the asymmetric bridge close to rupture. Different with the symmetric evolution of the short bridge, the long asymmetric bridge pinches off first from the side near the bigger sessile drop and then from the other side, which endows the satellite droplet with a lateral momentum, resulting in the satellite re-collected by the sessile drop. The influence of the slenderness on the time interval among the asymmetric pinch-off, velocity, destination, and size of the satellite was investigated. A scaling law was proposed to describe the relationship between the lateral momentum of the satellite and the time interval between two pinch-off. This work is expected to benefit the utilizing or suppressing the satellite in practice.