Submicron drops from flapping bursting bubbles.

Tiny water drops produced from bubble bursting play a critical role in forming clouds, scattering sunlight, and transporting pathogens from water to the air. Bubbles burst by nucleating a hole at their cap foot and may produce jets or film drops. The latter originate from the fragmentation of liquid ligaments formed by the centripetal destabilization of the opening hole rim. They constitute a major fraction of the aerosols produced from bubbles with cap radius of curvature (R) > ∼0.4 × capillary length (a). However, our present understanding of the corresponding mechanisms does not explain the production of most submicron film drops, which represent the main number fraction of sea spray aerosols. In this study, we report observations showing that bursting bubbles with R < ∼0.4a are actually mainly responsible for submicron film drop production, through a mechanism involving the flapping shear instability of the cap with the outer environment. With this proposed pathway, the complex relations between bubble size and number of drops produced per bubble can be better explained, providing a fundamental framework for understanding the production flux of aerosols and the transfer of substances mediated by bubble bursting through the air-water interface and the sensitivity of the process to the nature of the environment.

Bubbles spray aerosols: Certitudes and mysteries.

Ocean spray aerosol formed by bubble bursting are at the core of a broad range of atmospheric processes: they are efficient cloud condensation nuclei and carry a variety of chemical, biological, and biomass material from the surface of the ocean to the atmosphere. The origin and composition of these aerosols is sensibly controlled by the detailed fluid mechanics of bubble bursting. This perspective summarizes our present-day knowledge on how bursting bubbles at the surface of a liquid pool contribute to its fragmentation, namely to the formation of droplets stripped from the pool, and associated mechanisms. In particular, we describe bounds and yields for each distinct mechanism, and the way they are sensitive to the bubble production and environmental conditions. We also underline the consequences of each mechanism on some of the many air-sea interactions phenomena identified to date. Attention is specifically payed at delimiting the known from the unknown and the certitudes from the speculations.

Architecture of a self-fragmenting droplets cascade.

We report quantitative imaging experiments describing the three-dimensional (3D) bursting cascade of droplets from a liquid melt reacting with the oxygen of air which explode sequentially to produce ever smaller fragments. The 3D space-time resolved trajectories of the fragmenting drops reveal an arborescent structure of branchings defining the cascade steps, each random in direction and shortening along the cascade, in a way we determine. The phenomenon is a unique and prototypical illustration of the so-called Richardson regime, namely, an accelerated cascade towards smaller scales. The phenomenon, which coincides with the early time dispersion period of a Brownian motion, featuring here ever shrinking steps, is well captured by a Langevin dynamics.

Controlling fracture cascades through twisting and quenching.

Fracture fundamentally limits the structural stability of macroscopic and microscopic matter, from beams and bones to microtubules and nanotubes. Despite substantial recent experimental and theoretical progress, fracture control continues to present profound practical and theoretical challenges. While bending-induced fracture of elongated rod-like objects has been intensely studied, the effects of twist and quench dynamics have yet to be explored systematically. Here, we show how twist and quench protocols may be used to control such fracture processes, by revisiting Feynman's observation that dry spaghetti typically breaks into three or more pieces when exposed to large pure bending stresses. Combining theory and experiment, we demonstrate controlled binary fracture of brittle elastic rods for two distinct protocols based on twisting and nonadiabatic quenching. Our experimental data for twist-controlled fracture agree quantitatively with a theoretically predicted phase diagram, and we establish asymptotic scaling relations for quenched fracture. Due to their general character, these results are expected to apply to torsional and kinetic fracture processes in a wide range of systems.

Direct Self-Sustained Fragmentation Cascade of Reactive Droplets.

A traditional hand-held firework generates light streaks similar to branched pine needles, with ever smaller ramifications. These streaks are the trajectories of incandescent reactive liquid droplets bursting from a melted powder. We have uncovered the detailed sequence of events, which involve a chemical reaction with the oxygen of air, thermal decomposition of metastable compounds in the melt, gas bubble nucleation and bursting, liquid ligaments and droplets formation, all occurring in a sequential fashion. We have also evidenced a rare instance in nature of a spontaneous fragmentation process involving a direct cascade from big to smaller droplets. Here, the self-sustained direct cascade is shown to proceed over up to eight generations, with well-defined time and length scales, thus answering a century old question, and enriching, with a new example, the phenomenology of comminution.

Luminescence from Collapsing Centimeter Bubbles Expanded by Chemical Reaction.

We report on a new method for realizing an exceptionally strong inertial confinement of a gas in a liquid: A centimetric spherical bubble filled with a reactive gaseous mixture in a liquid is expanded by an exothermic chemical reaction whose products condense in the liquid at the bubble wall. Hence, the cavity formed in this way is essentially empty as it collapses. The temperatures reached at maximum compression, inferred from the cavity radius dynamics and further confirmed by spectroscopic measurements exceed 20 000 K. Because the cavity is typically big, our findings also provide unique space and time resolved sequences of the events accompanying the collapse, notably the development of the inertial instability notoriously known to deter strong compression.

Star-shaped crack pattern of broken windows.

Broken thin brittle plates like windows and windshields are ubiquitous in our environment. When impacted locally, they typically present a pattern of cracks extending radially outward from the impact point. We study the variation of the pattern of cracks by performing controlled transverse impacts on brittle plates over a broad range of impact speed, plate thickness, and material properties, and we establish from experiments a global scaling law for the number of radial cracks incorporating all these parameters. A model based on Griffith's theory of fracture combining bending elastic energy and fracture energy accounts for our observations. These findings indicate how the postmortem shape of broken samples are related to material properties and impact parameters, a procedure relevant to forensic science, archaeology, or astrophysics.

Superdiffusive trajectories in Brownian motion.

The Brownian motion of a microscopic particle in a fluid is one of the cornerstones of statistical physics and the paradigm of a random process. One of the most powerful tools to quantify it was provided by Langevin, who explicitly accounted for a short-time correlated "thermal" force. The Langevin picture predicts ballistic motion, ~t(2) at short-time scales, and diffusive motion ~t at long-time scales, where x is the displacement of the particle during time t, and the average is taken over the thermal distribution of initial conditions. The Langevin equation also predicts a superdiffusive regime, where ~t(3), under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air and indeed find t(3) dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin.

Stretching, coalescence, and mixing in porous media.

We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed, depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses toward uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion, and random overlaps, holding for all field heterogeneities, residence times, and Péclet numbers.

Radial cracks in perforated thin sheets.

When a rigid cone is slowly pushed through a thin elastic sheet, the material breaks, exhibiting a network of cracks expanding in the radial direction. Experiments conducted with aluminum sheets show that the number of cracks is selected at the beginning of the perforation process and then remains stable. A simple model predicts the number of cracks as the result of a competition between the elastic energy stored in the sheet, and the energy dissipated during crack extension. We also evidence the subtle rearrangements of randomly distributed cracks into uniform radial patterns with fewer cracks. In that respect, this study exemplifies how relaxation mechanisms in fragmenting solids can attenuate the influence of defects in the material.

Soap films burst like flapping flags.

When punctured, a flat soap film bursts by opening a hole driven by liquid surface tension. The hole rim does not, however, remain smooth but soon develops indentations at the tip of which ligaments form, ultimately breaking and leaving the initially connex film into a mist of disjointed drops. We report on original observations showing that these indentations result from a flaglike instability between the film and the surrounding atmosphere inducing an oscillatory motion out of its plane. Just like a flag edge flaps in the wind, the film is successively accelerated on both sides perpendicularly to its plane, inducing film thickness modulations and centrifuging liquid ligaments that finally pinch off to form the observed spray. This effect exemplifies how the dynamics of fragile objects such as thin liquid films is sensitive to their embedding medium.

'Infotaxis' as a strategy for searching without gradients.

Chemotactic bacteria rely on local concentration gradients to guide them towards the source of a nutrient. Such local cues pointing towards the location of the source are not always available at macroscopic scales because mixing in a flowing medium breaks up regions of high concentration into random and disconnected patches. Thus, animals sensing odours in air or water detect them only intermittently as patches sweep by on the wind or currents. A macroscopic searcher must devise a strategy of movement based on sporadic cues and partial information. Here we propose a search algorithm, which we call 'infotaxis', designed to work under such conditions. Any search process can be thought of as acquisition of information on source location; for infotaxis, information plays a role similar to concentration in chemotaxis. The infotaxis strategy locally maximizes the expected rate of information gain. We demonstrate its efficiency using a computational model of odour plume propagation and experimental data on mixing flows. Infotactic trajectories feature 'zigzagging' and 'casting' paths similar to those observed in the flight of moths. The proposed search algorithm is relevant to the design of olfactory robots, but the general idea of infotaxis can be applied more broadly in the context of searching with sparse information.

Simple ideas on mixing and fragmentation.

The mechanisms building the overall concentration distribution in a scalar mixture, and the drops in a spray, are examined successively. In both cases, the distributions belong to a unique family of distributions stable by self-convolution, the signature of the aggregation process from which they originate.