Droplet impact on a microhole through a partially wetting surface

In this study, we thoroughly investigate the impact dynamics of water droplets on a partially wetting substrate with a single hole. By conducting experiments using de-ionized water droplets and high-speed imaging, we observe various outcomes, including downward jetting without pinch-off, jetting with single and multiple pinch-offs, and the intriguing emergence of an upward jet during droplet recoil. A regime map is constructed to establish the relationship between the dynamics of the jet and the Weber number. We find the small amount of liquid leakage through the hole has a negligible effect on the maximum spreading of the droplet. We analyze the behavior of the downward jet resulting from droplet impact in terms of its length, speed, and breakup characteristics. The scaling relation between the maximum jet length before its breakup and the Weber number is derived and compared with experimental data. We find that the growth of the downward jet length follows a consistent power-law relationship with time regardless of impact velocity, while the maximum jet velocity scales linearly with the impact velocity, confirming the hydrodynamic focusing theory. The size of the head satellite droplet formed during the jet pinch-off process remains nearly constant across different Weber numbers. Additionally, we investigate the volume of ejected liquid through the microhole, observing an initial increase with the Weber number followed by a saturation point. The occurrence of the upward jet during droplet recoil is a significant finding, and we analyze its diameter, height, and velocity in relation to the Weber number.