How vortices mix

International audienceThe advection of a passive scalar blob in the deformation field of an axisymmetric vortex is a simple mixing protocol for which the advection-diffusion problem is amenable to a near-exact description. The blob rolls-up in a spiral which ultimately fades away in the diluting medium. The complete transient concentration field in the spiral is accessible from the Fourier equations in a properly chosen frame. The concentration histogram of the scalar wrapped in the spiral presents unexpected singular transient features and its long time properties are discussed in connection with mixtures from the real world

Van Hove singularities in Probability Density Functions of scalars

A general theory for the Probability Density Function (PDF) of a scalar stirred in an axisymmetric time-dependent flow is derived. This theory reveals singularities, discontinuities and cusps occurring as soon as the spatial gradient of the scalar concentration vanishes somewhere in the field. These singularities are similar to the Van Hove singularities obtained in the density of vibration modes of a crystal. This feature, ubiquitous in convection–diffusion problems, is documented experimentally for the mixing of a dye in a Lamb–Oseen vortex

The destabilization of an initially thick liquid sheet edge

International audienceBy forcing the sudden dewetting of a free soap film attached on one edge to a straight solid wire, we study the recession and subsequent destabilization of its free edge. The newly formed rim bordering the sheet is initially thicker than the film to which it is attached, because of the Plateau border preexisting on the wire. The initial condition is thus that of an immobile massive toroidal rim connected to a thin liquid film of thickness h. The terminal Taylor-Culick receding velocity V = sqrt(2 sigma/rho h), where sigma and rho are the liquid surface tension and density, respectively, is only reached after a transient acceleration period which promotes the rim destabilization. The selected wavelength and associated growth time coincide with those of an inertial instability driven by surface tension

Fragmentation de liquides et de solides

On s'intéresse à la forme et à la dynamique d'objets déformables lors d'un impact avec une source de quantité de mouvement dirigée. On envisagera le cas d'un objet dur (élastique) choqué par un autre objet dur pour des géométries simples (tiges, feuilles), le cas d'un objet mou (liquide) impactant un solide, et le cas d'un objet mou se déformant dans un milieu encore plus mou (gaz). On soulignera l'intérêt de ces observations pour le problème de la fragmentation en général, et pour la compréhension de certains phénomènes naturels comme la pluie

Impacts on thin elastic sheets

International audienceWe study transverse impacts of rigid objects on a free elastic membrane, using thin circular sheets of natural rubber as experimental models. After impact, two distinct axisymmetric waves propagate in and on the sheet. First a tensile wave travels at sound speed leaving behind the wave front a stretched domain. Then, a transverse wave propagates on the stretched area at a lower speed. In the stretched area, geometrical confinement induces compressive circumferential stresses leading to a buckling instability, giving rise to radial wrinkles. We report on a set of experiments and theoretical remarks on the conditions of occurrence of these wrinkles, their dynamics and wavelength

Abyss Aerosols

Bubble bursting on water surfaces is believed to be a main mechanism to produce submicron drops, including sea spray aerosols, which play a critical role in forming cloud and transferring various biological and chemical substances from water to the air. Over the past century, drops production mechanisms from bubble bursting have been extensively studied. They usually involve the centrifugal fragmentation of liquid ligaments from the bubble cap during film rupture, the flapping of the cap film, and the disintegration of Worthington jets after cavity collapse. Here, we show that a dominant fraction of previously identified as 'bubble bursting' submicron drops are in fact generated via a new mechanism underwater, inside the bubbles themselves before they have reached the surface. These drops are then carried within the rising bubbles towards the water surface and are released in air at bubble bursting. Evidence suggests that these drops originate from the flapping instability of the film squeezed between underwater colliding bubbles. This finding fundamentally reshapes our understanding of sea spray aerosol production and establishes a new role for underwater bubble collisions regarding the nature of transfers through water-air interfaces.Comment: 50 pages, 4 figures, and 10 extended data figure