The scaling of exploding liquid jets under intense X-ray pulses

A general scaling of the evolution of an exploding liquid jet under an ultra short and intense X-ray pulse from a X-ray free electron laser (XFEL) is proposed. A general formulation of the conservation of energy for blasts in vacuum partially against a deformable object leads to a compact expression that governs the evolution of the gap produced by the explosion. The theoretical analysis contemplates two asymptotic stages for small and large times from the initiation of the blast. A complete dimensional analysis of the problem and an optimal collapse of experimental data reveal that the universal approximate analytical solution proposed is in remarkable agreement with experiments

Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit

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.Comment: 14 pages, three figures, published in 2018 in Physical Review Fluid

Unconditional jetting

Capillary jetting of a fluid dispersed into another immiscible phase is usually limited by a critical Capillary number, a function of the Reynolds number and the fluid properties ratios. Critical conditions are set when the minimum spreading velocity of small perturbations $v^*_-$ along the jet (marginal stability velocity) is zero. Here we identify and describe parametrical regions of high technological relevance, where $v^*_- > 0$ and the jet flow is always supercritical independently of the dispersed liquid flow rate: within these relatively broad regions, the jet does not undergo the usual dripping-jetting transition, so that either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or the issued flow rate can be made arbitrarily small. In this work, we provide illustrative analytical studies of asymptotic cases for both negligible and dominant inertia forces. In this latter case, requiring a non-zero jet surface velocity, axisymmetric perturbation waves ``surf'' downstream for all given wave numbers while the liquid bulk can remain static. In the former case (implying small Reynolds flow) we found that the jet profile small slope is limited by a critical value; different published experiments support our predictions.Comment: Submitted first (24-August-2008) to Physics of Fluids, withdrawn from that journal on 6-April-2008, and submitted to Physical Review E the same da

A revision on Rayleigh capillary jet breakup

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity $\hat{U}$ (negligible external forces) must be determined by the selection of normal modes with time-independent amplitude and wavelength (invariant modes, IMs). Both positive and negative group velocity IMs exist in ample ranges of the parameter domain (Weber and Ohnesorge numbers), which explains (i) the average breakup length independence on ambient conditions (long-term resonance), and (ii) its proportionality to the inverse of the spatial growth rate of the dominant positive group velocity IM. Published experimental results since Grace (1965, PhD Thesis) confirm our proposal.Comment: 9 pages, 7 figure

On the physics of transient ejection from bubble bursting

The transient ejection due to a bubble bursting at the interface of a liquid with a gas environment is here described using a dynamical scaling analysis along the process. We show here that the ejection of a liquid microjet requires the backfire of a vortex ring inside the liquid to preserve physical symmetry, which involves a non-trivial scaling. We present the first single uniformly valid expression for the size and speed of ejected droplets for the whole range of the Ohnesorge and Bond numbers where droplet ejection occurs. The evolution of the flow variables, the apparent singularity for a critical Ohnesorge number, and the dispersion of data around this point are explained. Our model generalizes or displaces other recently proposed ones, impacting for instance the statistical description of sea spray.Comment: 10 pages, 3 figure

A new device for the generation of microbubbles

In this paper we present a new method for the production of bubble-liquid suspensions (from now on BLS) composed of micron-sized bubbles and with gas to liquid volume ratios larger than unity. We show that the BLS gas fraction ʎ=Qg and Q1 , being Qg and Q1 the flow rates of gas and liquid, respectively, is controlled by a dimensionless parameter which accounts for the ratio of the gas pressure inside the device to the liquid viscous pressure drop from the orifices where the liquid is injected to the exit, where the BLS is obtained. This parameter permits the correct scaling of the BLS gas volume fraction of all the experiments presented

The ocean fine spray

A major fraction of the atmospheric aerosols come from the ocean spray originated by the bursting of bubbles from breaking waves. A theoretical framework that incorporates the latest knowledge on film and jet droplets from bubble bursting is proposed. Assuming that their relics constitute the ultimate origin of primary and secondary sea aerosols through a diversity of physicochemical routes, the model can be reduced to a single controlling parameter to predict the global probability density distribution (pdf) of the ocean spray. The bursting and collapse of small bubbles on the sea surface from about 10 to 100 microns produces an extreme energy focusing and the ejection of a rapid liquid spout whose size reaches the free molecular regime of the gaseous environment. In these rarefied conditions, simulations show that this spout yields a jet of sub-micrometer and nanometric scale droplets whose number and speed can be far beyond any previous estimation, overcoming by orders of magnitude alternative mechanisms recently proposed. The one-parameter model fits remarkably well published experimental measurements along five orders of magnitude of spray size, from about 5 nm to about 0.5 mm. According to this proposal, the majority of aerosols determining the life on our planet would have their extremely elusive birth in the uterus-like nano-shape of small bursting bubbles on the ocean surface at the very latest instants of collapse.Comment: 12 pages, 13 figure