Journal Article•
Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit
TL;DR: In this article, a detailed physical description of the ejection process to model both the ejected droplet radius and its initial launch speed is provided, leading to a scaling law including both Oh and Bo.
Abstract: Jet droplets from bubble bursting are determined by a limited parametrical space: the liquid properties (surface tension, viscosity, and density), mother bubble size and acceleration of gravity. Thus, the two resulting parameters from dimensional analysis (usually, the Ohnesorge and Bond numbers, Oh and Bo) completely define this phenomenon when both the trapped gas in the bubble and the environment gas have negligible density. A detailed physical description of the ejection process to model both the ejected droplet radius and its initial launch speed is provided, leading to a scaling law including both Oh and Bo. Two critical values of Oh determine two limiting situations: one (Oh$_1$=0.038) is the critical value for which the ejected droplet size is minimum and the ejection speed maximum, and the other (Oh$_2$=0.0045) is a new critical value which signals when viscous effects vanish. Gravity effects (Bo) are consistently introduced from energy conservation principles. The proposed scaling laws produce a remarkable collapse of published experimental measurements collected for both the ejected droplet radius and ejection speed.
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TL;DR: In this article, a review deals with drop impacts on thin liquid layers and dry surfaces, referred to as splashing, and their propagation is discussed in detail, as well as some additional kindred, albeit nonsplashing, phenomena like drop spreading and deposition, receding (recoil), jetting, fingering, and rebound.
Abstract: The review deals with drop impacts on thin liquid layers and dry surfaces. The impacts resulting in crown formation are referred to as splashing. Crowns and their propagation are discussed in detail, as well as some additional kindred, albeit nonsplashing, phenomena like drop spreading and deposition, receding (recoil), jetting, fingering, and rebound. The review begins with an explanation of various practical motivations feeding the interest in the fascinating phenomena of drop impact, and the above-mentioned topics are then considered in their experimental, theoretical, and computational aspects.
2,077 citations
TL;DR: In this article, the authors studied four natural mechanisms for the production of these bubbles and concluded that the effects of the rate of solution of bubbles in sea water can, under some conditions, play a significant role in modifying the initial bubble spectrum.
Abstract: It is believed that the vast majority of the airborne salt nuclei arise from bursting bubbles at the air—sea water interface. Four natural mechanisms for the production of these bubbles have been studied. These are whitecaps, rain, snow and supersaturation of the surface waters of the sea due to spring warming. The bubble spectra from whitecaps and snowflakes have been measured and semi-quantitative and qualitative observations have been made on the bubble spectrum produced by raindrops. No evidence of bubble production by spring warming has been obtained. All of the measurements show that a majority of the bubbles are < 200 microns diameter and, in the case of bubbles from snowflakes, < 50 microns. In the vicinity of a breaking wave the bubble production rate is about 30 cm −2 sec −1 . Due to the effects of surface tension in increasing the bubble internal pressure all bubbles < 300 microns will go into solution even at sea water air saturations of 102 percent. Bubbles < 20 microns will go into solution at saturations up to 115 percent! The solution time for small bubbles of about 10 microns is about 10 sec and is not markedly affected by the water saturation percentage. It is concluded that the effects of the rate of solution of bubbles in sea water can, under some conditions, play a significant role in modifying the initial bubble spectrum. This, in turn, should influence the spectrum of airborne nuclei. DOI: 10.1111/j.2153-3490.1957.tb01867.x
470 citations
TL;DR: In this article, an exact solution for two-dimensional progressive waves of arbitrary amplitude on a fluid of unlimited depth, when only surface tension and not gravity is taken into account as the restoring force, was found in a fairly simple form.
Abstract: An exact solution is found in a fairly simple form for two-dimensional progressive waves of arbitrary amplitude on a fluid of unlimited depth, when only surface tension and not gravity is taken into account as the restoring force. The calculated wave forms are exhibited graphically for various amplitudes, and the relation between wave velocity and amplitude is plotted. The wave of greatest height occurs when the vertical distance between trough and crest is 0·730 wavelengths (compared with 0·142 for gravity waves). Higher waves are prevented from appearing by the enclosing of air bubbles in the troughs.
380 citations
TL;DR: In this article, the free-surface motion following a small air bubble burst at an equilibrium position at an air/water interface is modelled numerically using a boundary integral method.
Abstract: When a small air bubble bursts from an equilibrium position at an air/water interface, a complex motion ensues resulting in the production of a high-speed liquid jet. This free-surface motion following the burst is modelled numerically using a boundary integral method. Jet formation and liquid entrainment rates from jet breakup into drops are calculated and compared with existing experimental evidence. In order to investigate viscous effects, a boundary layer is included in the calculations by employing a time-stepping technique which allows the boundary mesh to remain orthogonal to the surface. This allows an approximation of the vorticity development in the region of boundary-layer separation during jet formation. Calculated values of pressure and energy dissipation rates in the fluid indicate a violent motion, particularly for smaller bubbles. This has important implications for the biological industry where animal cells in bioreactors have been found to be killed by the presence of small bubbles.
292 citations