Liquid jet eruption from hollow relaxation

Abstract

A cavity hollowed out on a free liquid surface is relaxing, forming an intense liquid jet. Using a model experiment where a short air pulse sculpts an initial large crater, we depict the different stages in the gravitational cavity collapse and in the jet formation. Prior eversion, all cavity profiles are found to exhibit a shape similarity. Following hollow relaxation, a universal scaling law establishing an unexpected relation between the jet eruption velocity, the initial cavity geometry and the liquid viscosity is evidenced experimentally. On further analysing the jet forms we demonstrate that the stretched liquid jet also presents shape similarity. Considering that the jet shape is a signature of the initial flow focusing, we elaborate a simple model capturing the key features of the erupting jet velocity scaling. IntroductionVertical-take-off-and-landing craft can experience loss of visibility or damage when landing over water or a soft terrain, such as mud or sand, as a consequence of the soil erosion by a gaseous jet (Barton & Edwards 1968). In the steel industry, the basic oxygen conversion process utilizes a supersonic jet of oxygen impinging on molten iron to convert it into steel. The generic occurrence of such gaseous jets shaping steady cavities has sparked a number of studies involving model experiments for the last 50 years (Banks & Chandrasekhara 1963;Cheslak et al. 1969).Violent free surface deformation can also be observed when an object impacts a liquid surface and induces an unsteady cavity whose collapse often exhibits an intense liquid jet (Worthington 1883). This phenomenon has been extensively studied, from the initial stages of contact (Korobkin & Pukhnachov 1988) et al. 1998;Gekle et al. 2009). Such a jet is a classic signature of hollow crater-like relaxation, and appears at scales ranging from champagne bubbles (Liger-Belair et al. 2009) to geological craters central peak (Melosh 1989).In this paper, we propose to investigate the characteristics of the erupting jet following large hollow relaxation in relation with the initial cavity geometry. We consider a model experiment where the crater, shaped using a short air pulse, relaxes sparking a fast inertial liquid jet (see Fig. 1). After a description of the important stages in the jet development, we explore the dependence of the erupting jet velocity with the liquid properties and the cavity geometry. As a result we propose a universal scaling law for the jet velocity. We further demonstrate that both the initial cavities and the outcoming jet exhibit shape similarity. We build up on this observation and finally propose a simple model capturing the key features of the jet velocity dependence with the cavity shape.arXiv:1312.6136v1 [physics.flu-dyn]

Jet dynamics post drop impact on a deep pool

“…As a consequence, this shows that the variation of velocity with cavity depth is different from previous studies. Indeed, with increasing cavity depth, jet velocity decreases for submillimeter cavities(V j ∝ H −1/3 ) [29], and increases for centimeter cavities (V j ∝ H 3/2 ) [31]; and here, for intermediate cavity sizes, the jet velocity is constant (V j ∝ H 0 ).…”

“…On the other hand, when a cavity is larger than a few centimeters, the relaxation process is a priori gravity driven since capillarity should become irrelevant [31,32]. In our drop impact experiments, typical cavity dimensions (heights H and widths 2R) range from 5 to 15 mm, so that both gravity and capillarity might play a role in the relaxation process.…”

“…This defines Fr = 300 as the limit for having a real singular jet. Note that for much larger cavities such as those obtained by large interface deformation [31], capillary wave collapse and cavity retraction are obviously expected to be decorrelated as well.…”

“…2). It is thus tempting to question whether the collapse of this gravitational cavity is also gravity dominated, as observed for a much bigger cavity [31], or is still dominated by surface tension. We have thus performed experiments with a liquid which has a different surface tension than water, namely ethanol whose surface tension is γ = 0.022 mN m −1 .…”

“…While jet dynamics and droplet ejection have been characterized for the collapse of cavities obtained by the bursting of bubbles [23,29,30] or large interface deformation [31,32], ours is a systematic study of cavities induced by drop impacts. In particular, in this configuration, the shape of the cavity is different, but above all, the cavity sizes are different, intermediate, typically between what has been studied so far, and we will see that this changes the subsequent jet dynamics.…”