Contact Line Catch Up by Growing Ice Crystals.

The effect of freezing on contact line motion is a scientific challenge in the understanding of the solidification of capillary flows. In this Letter, we experimentally investigate the spreading and freezing of a water droplet on a cold substrate. We demonstrate that solidification stops the spreading because the ice crystals catch up with the advancing contact line. Indeed, we observe the formation and growth of ice crystals along the substrate during the drop spreading, and show that their velocity equals the contact line velocity when the drop stops. Modeling the growth of the crystals, we predict the shape of the crystal front and show that the substrate thermal properties play a major role on the frozen drop radius.

Modeling of aerosol transmission of airborne pathogens in ICU rooms of COVID-19 patients with acute respiratory failure.

The COVID-19 pandemic has generated many concerns about cross-contamination risks, particularly in hospital settings and Intensive Care Units (ICU). Virus-laden aerosols produced by infected patients can propagate throughout ventilated rooms and put medical personnel entering them at risk. Experimental results found with a schlieren optical method have shown that the air flows generated by a cough and normal breathing were modified by the oxygenation technique used, especially when using High Flow Nasal Canulae, increasing the shedding of potentially infectious airborne particles. This study also uses a 3D Computational Fluid Dynamics model based on a Lattice Boltzmann Method to simulate the air flows as well as the movement of numerous airborne particles produced by a patient's cough within an ICU room under negative pressure. The effects of different mitigation scenarii on the amount of aerosols potentially containing SARS-CoV-2 that are extracted through the ventilation system are investigated. Numerical results indicate that adequate bed orientation and additional air treatment unit positioning can increase by 40% the number of particles extracted and decrease by 25% the amount of particles deposited on surfaces 45s after shedding. This approach could help lay the grounds for a more comprehensive way to tackle contamination risks in hospitals, as the model can be seen as a proof of concept and be adapted to any room configuration.

Scaling laws in turbulence.

Following the idea that dissipation in turbulence at high Reynolds number is dominated by singular events in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows, scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the drag law deduced by Newton for a projectile moving quickly in a fluid at rest. Inspired by this Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between the Reynolds stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space). This model takes the form of an integrodifferential equation for the velocity which is eventually solved for a Poiseuille flow in a circular pipe.

Dimple drainage before the coalescence of a droplet deposited on a smooth substrate.

Thin liquid or gas films are everywhere in nature, from foams to submillimetric bubbles at a free surface, and their rupture leaves a collection of small drops and bubbles. However, the mechanisms at play responsible for the bursting of these films is still in debate. The present study thus aims at understanding the drainage dynamics of the thin air film squeezed by gravity between a millimetric droplet and a smooth solid or a liquid thin film. Solving coupled lubrication equations and analyzing the dominant terms in the solid- and liquid-film cases, we explain why the drainage is much faster in the liquid-film case, leading often to a shorter coalescence time, as observed in recent experiments.

Pinching Dynamics and Satellite Droplet Formation in Symmetrical Droplet Collisions.

In head-on collisions between two droplets, reflexive separation is frequently formed, showing tentative coalescence followed by disintegration into two primary drops. With higher impact inertia relative to surface tension, characterized by a Weber number (We), more satellite droplets are created between the primary drops. In the symmetric configuration, the existing phenomenological models indicate the absence of satellite droplets at the onset We when the coalesced drops start to break. Supported by experimental and simulation evidence, here we demonstrate the exclusive formation of at least one droplet after pinch of the thread connecting the colliding drops. In accordance with the universal features of a thinning liquid filament approaching singularity as predicted by scaling theories of pinch-off, the mechanism of satellite droplet formation in the symmetrical impact of droplets is clarified. Via slight breaking of the symmetry, no satellite droplet can be observed, thus providing a possible interpretation for the discrepancy in the literature and implications for controlling undesirable drop formation.

The capillary interaction between pairs of granular rafts.

When an object is placed at the surface of a liquid, its weight deforms the interface. For two identical spherical objects, such a deformation creates an attractive force, leading to the aggregation of the two-body system. Here, we experimentally investigate the interaction between two granular rafts, formed by the aggregation of dense millimeter-sized beads placed at an oil-water interface. The interfacial deformation created by such a two-dimensional object exceeds by at least an order of magnitude the deformation of a single bead. This leads to unusually high capillary forces which strongly depend on the number of particles. Likewise, because the raft grows in size as more particles are added, the viscous drag experienced increases along with the capillary attraction, leading to a non-trivial dependence of the balance of forces on the number of beads. By studying the relative motion of two granular rafts in relation with the interfacial deformation they generate, we derive a model for the observed speed profiles. With this work, we generalize how the capillary interaction between two non-identical complex structures evolves with their respective geometry.

Ejecta, Corolla, and Splashes from Drop Impacts on Viscous Fluids.

We investigate the impact of liquid drops on deep pools of aqueous glycerol solutions with variable pool viscosity and air pressure both experimentally and numerically. With this approach, we are able to address drop impacts on substrates that continuously transition from low-viscosity liquids to almost solids. We show that the generic corolla spreading out from the impact point consists of two distinct sheets, namely an ejecta sheet fed by the drop liquid and a second sheet fed by the substrate liquid, which evolve on separated timescales. These two sheets contribute to a varying extent to the corolla overall dynamics and splashing, depending on the viscosity ratio between the two liquids.

Oscillating path between self-similarities in liquid pinch-off.

Many differential equations involved in natural sciences show singular behaviors; i.e., quantities in the model diverge as the solution goes to zero. Nonetheless, the evolution of the singularity can be captured with self-similar solutions, several of which may exist for a given system. How to characterize the transition from one self-similar regime to another remains an open question. By studying the classic example of the pinch-off of a viscous liquid thread, we show experimentally that the geometry of the system and external perturbations play an essential role in the transition from a symmetric to an asymmetric solution. Moreover, this transient regime undergoes unexpected log-scale oscillations that delay dramatically the onset of the final self-similar solution. This result sheds light on the strong impact external constraints can have on predictions established to explain the formation of satellite droplets or on the rheological tests applied on a fluid, for example.

Drops Floating on Granular Rafts: A Tool for Liquid Transport and Delivery.

Solid particles can modify the properties of liquid interfaces and are therefore widely used to coat drops, bubbles, and stabilize emulsions and foams. Here, we propose a new, easy, and affordable method to produce millimetric to centimetric water-in-water capsules using solid particles. We prevent the coalescence of a water drop at an oil-water interface using a monolayer of large, dense, and hydrophobic particles: a "granular raft". The capsule is then formed by a mechanical instability occurring when the interface collapses under the combined load of the floating drop and particle weight. During the destabilization, the water drop sinks into the water subphase through an oil-particle film which covers it to produce the armored capsule. By modeling the raft as a heavy membrane, we predict the floating drop shape, the raft deformation, its destabilization and highlight the complex dual nature (solid- and liquid-like) of the capsule shell. Because armored capsules' content is isolated, transportable, and easily releasable, they are great candidates for applications requiring transport of water-soluble compounds in aqueous systems such as green chemistry or cell biology.

Wave-turbulence theory of four-wave nonlinear interactions.

The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of a generating function and of a multipoint probability density function (PDF), for weakly interacting waves with initial random phases. When the initial amplitudes are also random, a one-point PDF equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions. Numerical investigations of the two-dimensional nonlinear Schrödinger equation (NLSE) and of a vibrating plate prove the following: (i) Generic Hamiltonian four-wave systems rapidly attain a random distribution of phases independently of the slower dynamics of the amplitudes, vindicating the hypothesis of initially random phases. (ii) Relaxation of the Fourier amplitudes to the predicted stationary distribution (exponential) happens on a faster time scale than relaxation of the spectrum (Rayleigh-Jeans distribution). (iii) The PDF equation correctly describes dynamics under different forcings: The NLSE has an exponential PDF corresponding to a quasi-Gaussian solution, as the vibrating plates, that also shows some intermittency at very strong forcings.

Modal active control of Chinese gongs.

Instruments that belong to the gong family exhibit nonlinear dynamics at large amplitudes of vibration. In the specific case of the xiaoluo gong, this nonlinear behavior results in a pitch glide of several modes of the instrument in addition to harmonic distortion and internal resonances. This study applies a linear modal active control to a xiaoluo gong in an attempt to change its sound properties. First, a modal damping control of the fundamental mode based on a linear identification and a state space controller is applied in the small amplitude regime (no pitch glide). Results indicate that modal control influences not only the controlled mode but also the frequency components involved in distortion or internal resonance phenomena. Second, a modal damping control is performed in the large amplitude regime (in the presence of pitch glide). Results show that modal control does not affect the pitch glide. However, the controller becomes effective at a time trigger which is related to the instantaneous frequency.

Sinking a Granular Raft.

We report experiments that yield new insights on the behavior of granular rafts at an oil-water interface. We show that these particle aggregates can float or sink depending on dimensionless parameters taking into account the particle densities and size and the densities of the two fluids. We characterize the raft shape and stability and propose a model to predict its shape and maximum length to remain afloat. Finally we find that wrinkles and folds appear along the raft due to compression by its own weight, which can trigger destabilization. These features are characteristics of an elastic instability, which we discuss, including the limitations of our model.

Frozen Impacted Drop: From Fragmentation to Hierarchical Crack Patterns.

We investigate experimentally the quenching of a liquid pancake, obtained through the impact of a water drop on a cold solid substrate (0 °C to -60 °C). We show that, below a certain substrate temperature, fractures appear on the frozen pancake and the crack patterns change from a 2D fragmentation regime to a hierarchical fracture regime as the thermal shock increases. The different regimes are discussed and the transition temperatures are estimated through classical fracture scaling arguments. Finally, a phase diagram presents how these regimes can be controlled by the drop impact parameters.

Elastic wave turbulence and intermittency.

We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by d cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only.

Self-similar formation of an inverse cascade in vibrating elastic plates.

The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.

Transition from wave turbulence to dynamical crumpling in vibrated elastic plates.

We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study on the strongly nonlinear regime described in a previous Letter by Yokoyama and Takaoka. At small forcing, a weakly nonlinear regime is compatible with the weak turbulence theory when the dissipation is localized at high wave number. When the forcing intensity is increased, a strongly nonlinear regime emerges: singular structures dominate the dynamics at large scales whereas at small scales the weak turbulence is still present. A turbulence of singular structures with folds and D cones develops that alters significantly the energy spectra and causes the emergence of intermittency.

von Kármán vortex street within an impacting drop.

The splashing of a drop impacting onto a liquid pool produces a range of different sized microdroplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultrahigh-speed video imaging in combination with high-resolution numerical simulations to show how this ejecta gives way to irregular splashing. At higher Reynolds numbers, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von Kármán vortex street, thus breaking the ejecta sheet as it forms.

Activated nucleation of vortices in a dipole-blockaded supersolid condensate.

We investigate theoretically and numerically a model of a supersolid in a dipole-blockaded Bose-Einstein condensate. The dependence of the superfluid fraction with an imposed thermal bath and a uniform boost velocity on the condensate is considered. Specifically, we observe a critical velocity for the nucleation of vortices in our system that is strongly linked to a steplike decrease in the superfluid fraction. We are able to use a scaling argument based on the energy required to activate a vortex, relating the critical temperature to the critical velocity, and find that this relationship is in good agreement with the numerical simulations carried out on the nonlocal Gross-Pitaevskii equation.

Patterned surfaces in the drying of films composed of water, polymer, and alcohol.

A study of the complex drying dynamics of polymeric mixtures with optical microscopy and gravimetric measurement is presented. Droplet formation is observed, followed by a collapse that leads to the residual craters in the dried film. The process is followed in situ under well-defined temperature and hygrometric conditions to determine the origin and nature of these droplets and craters. The drying process is usually completed within 1 h. The observations are explained using a simple diffusion model based on experimental results collected from mass and optical measurements as well as Raman confocal microspectrometry. Although the specific polymeric mixtures used here are of interest to the cosmetic industry, the general conclusions reached can apply to other polymeric aqueous solutions with applications to commercial and artistic painting.

Instant fabrication and selection of folded structures using drop impact.

A drop impacting a target cutout in a thin polymer film is wrapped by the film in a dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from a given target by slightly varying the impact parameters. A simplified model for a nonlinear dynamic Elastica coupled with a drop successfully explains this shape selection and yields detailed quantitative agreement with experiments. This first venture into the largely unexplored dynamics of elastocapillary assemblies opens up the perspective of mass production of 3D packages with individual shape selection.