Marangoni effect on the impact of droplets onto a liquid-gas interface

Abstract

The impact dynamics and internal mixing of a droplet onto a liquid-gas interface of lower surface tension was studied both experimentally and numerically, with both the Ohnesorge number (Oh) and the Bond number (Bo) being fixed. Compared to the droplet impact onto a pool of identical liquid, the interfacial Marangoni flow entrains abundant fluid upward and hence induces an additional jet breakup during crater formation (the first breakup), and it facilitates the emergence of the Rayleigh jet breakup (the second breakup) during crater restoration and enhances the vortical mixing beneath the liquid surface. Specifically, with the increase of the impact inertia, the first breakup manifests a nonmonotonic trend of "absence-presence-absence." The former transition of "absencepresence" at a low droplet-based Weber number (We d ) is caused by the shortened path of the Marangoni flow on the faster-growing liquid bridge, and the later transition of "presence-absence" at a high We d is resulted from the reduced displacement velocity of the pool fluid on the expanding crater surface. The second breakup corresponds to the Rayleigh jet breakup without surface tension difference and occurs monotonically beyond a certain We d . Due to the relatively short displacement time of the Marangoni flow on the crater surface compared to the time for crater formation, the critical condition for the emergence of the second jet breakup could be described by the critical reservoir-fluid-based We number (We r ). The critical We r contains two parts: the Bo-dependent critical We r0 without surface tension difference, and the increased viscous dissipation from the wrap-up motion of the Marangoni flow. Furthermore, capillary waves are also induced by the Marangoni flow during crater restoration, and the accompanied vorticity generation causes the mixing pattern to exhibit multiple vortex rings and even a clawlike structure, which is substantially enhanced compared to the vortical mixing without surface tension difference.

Impact of a microfluidic jet on a pendant droplet

“…Comparable mixing patterns were observed (data not shown) for the rest of the Newtonian liquids containing surfactants, and weaker mixing is seen for water, ethanol and glycerine 25% droplets. Similar mixing patterns have been described in the literature, for example, Jia et al in 2020 40 reported an interfacial Marangoni flow enhancing the mixing of an impacting droplet and a liquid pool with different surface tensions.…”

“…Indeed, Marangoni stresses have been shown to retard cavity collapse and slow the velocity of Worthington jets. 40,41 Therefore, we can assume that U cr ∝ U γ , indicating that the retraction of the cavity is surface tension driven. 42 The origin of the dispersion in U cr is associated with the jet tail breakup, where the Matryoshka effect or the creation of an antibubble may arise, like in Fig.…”

“…The lower average values of U cr for the AOT and Triton solutions can possibly be explained by the Marangoni stresses generated by the flow from areas with low surface tension to those with high surface tension. Indeed, Marangoni stresses have been shown to retard cavity collapse and slow the velocity of Worthington jets 40,41 . Therefore, we can assume that U cr ∝ U γ , indicating that the retraction of the cavity is surface tension driven 42 .…”

“…Extensive studies of the length, speed and breakup time of a Worthington jet formed after droplet and solid impact on a liquid pool have been widely reported, and are outside of the scope of this paper 1,40,[42][43][44][45][46][47] . Moreover, given the random breakup of the impacting jet in our experiments, the Worthington jets are observed to vary widely in size and shape, even when droplet and impacting jet consist of the same liquids.…”

Cavity dynamics after the injection of a microfluidic jet onto capillary bridges

“…See DOI: 10.1039/cXsm00000x/ cused on the critical energy necessary for air entrainment into the pool, the collapse of the entrained air cavity and the subsequent formation of a liquid jet that travels in the opposite direction of impact, i.e., a Worthington jet [14][15][16] . The time of collapse, cavity geometry and Worthington jet, depend on both, the properties of the liquid pool and the impacting object 9,[17][18][19][20][21] . The phenomena is usually well described by the ratio between the surface tension, inertia and hydrostatics.…”