Parallel water entry of hydrophobic-hydrophilic sphere pairings: particle image velocimetry and High-Speed camera analysis

This study provides further investigation on parallel water entry of pairings of hydrophobic-hydrophilic spheres. In a prior publication by the current authors (Akbarzadeh et al., 2023), a distinct phenomenon termed “second pinch-off” was observed for certain scenarios of parallel water entry of equally-sized hydrophobic-hydrophilic spheres. This experimental study examines this event more comprehensively. Experiments with differently-sized spheres are also conducted and analyzed. In the equally-sized cases, two spheres with a diameter of $20\text{mm}$, positioned in a lateral distance of 1.5 times the diameter, are released simultaneously from heights ranging from 25 to 55cm. This corresponds to impact velocities of $2.21\sim 3.328m{s}^{-1}$. In these configurations, the vortex shedding behind the hydrophilic sphere significantly influences the air cavity produced by the hydrophobic sphere. A high-speed photography system, coupled with an image processing technique, is employed to analyze the event dynamics. Additionally, a Particle Image Velocimetry system is utilized to capture the flow field, extracting both velocity and vorticity fields. The analysis demonstrates that a vortex ring forms behind the hydrophilic sphere and causes some waviness in the cavity interface. This vortex ring is shed and migrates towards the cavity wall causing an indentation which grows over time and finally completely severs the air cavity (second pinch-off). Furthermore, the results highlight that the second pinch-off time, in non-dimensional form, correlates linearly with the impact Weber number. The findings for the case of differently-sized spheres ($12\text{mm}$ and $20\text{mm}$ in diameter), reveal that a second pinch-off event can also be observed in pairings where the smaller sphere is hydrophilic.