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 20mm, 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 ∼ 3.328 ms 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 (12mm and 20mm in diameter), reveal that a second pinch-off event can also be
observed in pairings where the smaller sphere is hydrophilic.