Thickness of the rim of an expanding lamella near the splash threshold

Abstract

The evolution of the ejected liquid sheet, or lamella, created after impact of a liquid drop onto a solid surface is studied using high-speed video in order to observe the detailed time evolution of the thickness of the rim of the lamella. Since it has been suggested that splashing behavior is set at very early times after impact, we study early times up to D 0 / U 0 , where D 0 and U 0 are the diameter and speed of the impacting drop, respectively, for different liquid viscosities and impact speeds below the splashing threshold. Within the regime of our experiments, our results are not consistent with the idea that the lamella rim grows similar to the boundary layer thickness. Rather, we find that the rim thickness is always much larger than the boundary layer thickness, and that the rim thickness decreases with increasing impact speed. For lower impact speeds, the increase in the rim thickness is consistent with a ͱ t response over the limited time range available, but the dependence is not simply proportional to ͱ , where is the kinematic viscosity, and there is a strong dependence of the rim thickness on the impact speed U 0 . Scaling of the rim height using a balance of inertial and surface tension forces provides some collapse of the data at lower impact speeds. We also observe an unusual plateau behavior in thickness versus time at higher impact speeds as we approach the splash threshold.

First stages of drop impact on a dry surface: asymptotic model

“…(11), (12) in the liquid layer domain Ω. These formulas are further simplified in series for small zd/τ 0.5 , given by (13) [or by (15a, 15b) with (17) and (18)] and (14). The velocity and pressure expressions contain two free parameters: a ∼ O(1) and d 1.…”

“…This has motivated recent experimental investigations of the time-dependent thickness of the rim that develops at the edge of the lamella [17]. Recent numerical studies have also focused on the film spreading at later times after impact [3,15,19].…”

Splashing Onset in Dense Suspension Droplets

“…To our knowledge, there exists no systematic study that confirms this prediction. In fact, Nicolas observed [12] that adding particles, instead, lowered the splashing threshold K 0 .To investigate the influence of added particles, we depart from the dilute limit described above, and instead focus here on the limit of dense granular suspensions with volume packing fractions φ = 0.62 ± 0.03, where the discrepancy with the above droplet-scale splash onset criterion is most pronounced.In pure liquid droplets, the size of the ejecta depends on either the destabilization of a thin liquid sheet [5,[29][30][31][32][33][34] or, in the case of prompt splashing, on an instability at the moving contact line [5,10,35]. At splash onset in a suspension, on the other hand, the ejecta are the solid particles (see Fig.…”

“…In pure liquid droplets, the size of the ejecta depends on either the destabilization of a thin liquid sheet [5,[29][30][31][32][33][34] or, in the case of prompt splashing, on an instability at the moving contact line [5,10,35]. At splash onset in a suspension, on the other hand, the ejecta are the solid particles (see Fig.…”

“Doughnut” nuclear shapes in head-on heavy ion collisions

“…Despite that, the hydrodynamic description of HIC at intermediate and low energies has been the subject of only few theoretical studies [19]. By contrast, the behavior of colliding ordinary liquid droplets in a wide range of impact velocities and its dependence on the compressibility, surface tension, and viscosity and has been extensively studied in the literature [20][21][22]. Those studies resulted in changes of the qualitative picture of the process due to a better understanding of the underlying physics.…”