Entrapping an impacting particle at a liquid–gas interface

Abstract

We numerically investigate the mechanism leading to the entrapment of spheres at the gas–liquid interface after impact. Upon impact onto a liquid pool, a hydrophobic sphere is seen to follow one of the three regimes identified in the experiment (Lee & Kim, Langmuir, vol. 24, 2008, pp. 142–145): sinking, bouncing or being entrapped at the interface. It is important to understand the role of wettability in this process of flow–structure interaction with dynamic wetting, and in particular, to what extent the wettability can determine whether the sphere is entrapped at the interface. For this purpose, a diffuse-interface immersed boundary method is adopted in the numerical simulations. We expand the parameter space considered previously, provide the phase diagrams and identify the key phenomena in the impact dynamics. Then, we propose the scaling models to interpret the critical conditions for the occurrence of sphere entrapment, accounting for the wettability of the sphere. The models are shown to provide a good correlation among the impact inertia of the drop, the surface tension, the wettability and the density ratio of the sphere to the liquid.

Oblique impact of microspheres on the surface of quiescent liquid

“…Based on this, we can deduce that . The same relationship was also found in the numerical studies on the vertical impact of millimetre-sized spheres by Kintea et al (2016) and Chen et al (2018). Since the decay ratios of the kinetic energies of the spheres during the slamming stage have little difference regarding the impacts at different and values, the remaining kinetic energy after the slamming stage is consumed mostly by the work expended by the surface tension given that of an oscillating sphere is relatively very small.…”

“…The average of an oblique submergence mode with is approximately of that of a vertical submergence mode in figure 8(). For the submerging microspheres after impacting on the surfaces of water and propanol solution, is approximately and , respectively, which is larger than that of a millimetre-sized sphere reported by Chen et al (2018).

Figure 8.Variations of the dimensionless penetration depth of the microsphere with after impacting on the surfaces of () water and () propanol solution with different impact angles, whereby the solid and hollow points represent the submergence and oscillation modes, respectively.

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“…The average h p /d p of an oblique submergence mode with α = 17 ± 3 • is approximately 75 % of that of a vertical submergence mode in figure 8(a). For the submerging microspheres after impacting on the surfaces of water and propanol solution, h p /d p is approximately 1.84 and 1.65, respectively, which is larger than that of a millimetre-sized sphere reported by Chen et al (2018).…”

“…Thus, we can find that in our experiment). The simulations conducted by Chen et al (2018) on the impact of millimetre-sized spheres with elicited the characteristic penetration time of , which corresponds to the time taken for a capillary–gravity wave to travel the capillary length . This expression was also suggested to characterize the pinch-off time of millimetre-sized spheres (Lee & Kim 2008).…”

“…The experiment on the impact of superhydrophobic millimetre-sized spheres on liquid surfaces by Lee & Kim (2008) observed three impact modes, namely, oscillation, rebound and submergence, with the increase in . Subsequently, Chen et al (2018) numerically investigated the effect of wettability on the impact behaviour of millimetre-sized spheres and proposed a criterion to distinguish different impact modes. Spheres with a large and will sink uniformly after impact the liquid surface owing to their large inertia (Aristoff & Bush 2009), while spheres with a small or experience a deceleration process after impact (Aristoff et al 2010), which means that the sphere dynamics and fluid dynamics are coupled.…”