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We investigate experimentally the receding of a contact line when a Peltier module is pulled out of a water bath at constant speed, while a ice layer is also growing at constant speed on the Peltier module. A steady regime is therefore reached for all the parameters used in this studied, corresponding to a dynamical stationnary meniscus. We show that the height of the meniscus provides most of the properties of the flow. For high pulling rate, it is related to the amount of liquid of the equivalent Landau-Levich (LL) film that would be extracted from the bath, which is eventually freezing as the plate is lifted upward. For smaller velocity, so that no LL film would be formed without freezing, the meniscus height is directly linked to the contact angle of water on ice in these conditions. Solving numerically the meniscus equation taking into account the solidifcation of water, our results suggest that the contact angle of water on ice should be around $6^\circ$.

The present study reports experiments of water droplet impacting on ice or on a cold metallic substrate, with the aim of understanding the effect of phase change on the impingement process. Both liquid and substrate temperatures are varied, as well as the height of fall. The dimensionless maximum spreading diameter, $\beta_m$, is found to increase with both temperatures as well as with the impact velocity. Furthermore, $\beta_m$ is reduced when solidification, which enhances dissipation, is present, whereas fusion favours the liquid film spreading. These observations are rationalized by extending an existing model of effective viscosity, in which phase change alters the size and shape of the developing viscous boundary layer, thereby modifying the value of $\beta_m$. The use of this correction allows to adapt a scaling law existing for isothermal drop impacts to propose a universal law giving the maximum diameter of an impacting water droplet in the presence of melting or solidification., Comment: 10 pages, 4 figures

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor-Couette test case. To impose the boundary condition when the fluid-fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

We investigate the three-dimensional flow around and through a porous screen for various porosities at high Reynolds number Re = O(10000). Historically, the study of this problem was focused on two-dimensional cases and for a screen spanning completely or partially a channel. Since many recent problems have involved a porous object in a three-dimensional free flow, we present a three-dimensional model for porous screens, initially based on Koo & James (1973) and Steiros & Hultmark (2018), accounting for viscous effects at the vicinity of the screen, from which we can derive velocities, pressure distribution as well as aerodynamic forces. We then characterize experimentally the aerodynamic drag coefficient for a porous square screen, composed of fibers, immersed in a laminar air flow with different angles of attack. We test various fiber diameters to explore the effect of the space between the pores on the drag force. The drag prediction from the model is in good agreement with our experimental results. Our theoretical and experimental results suggest that for high solidity, a homogeneous porous screens composed of fibers can have a higher drag coefficient than a flat plate with the same dimensions. We also show that local viscous effects are important: at the same solidity and with the same air flow, the drag coefficient strongly depends on the Reynolds number based on the fiber diameter. The model, taking into account three-dimensional effects and the shape of the porous screen, may have many applications including the prediction of water collection efficiency for fog harvesters., Comment: Submitted to JFM, revised version, 43 pages, 18 figures

Due to their morphology, the dynamics of bacteria suspended in media can exhibit complex behaviors. In the presence of a shear, swimming bacteria experience a drift perpendicular to the shear plane. This drift, termed rheotaxis, is studied here semi-analytically, numerically and experimentally. We find the dependency of bacterial orientation and bacterial speed on the shear rate, in the presence of rotational diffusion. This enables us to show that the drift speed of bacteria perpendicular to the shear is predominantly due to bacterial propulsion, and not rheotactic forces. Comparing the drift speed of bacteria and diffusion leads to the definition of a P\'{e}clet number. The rheotactic effect increases with the shear, reaching a plateau at very large P\'{e}clet numbers, in good agreement with experiments of rheotaxis performed in microfluidic droplets., Comment: 15 pages, 9 figures

Compound drop impacting on a solid surface is of considerable importance in industrial applications, such as combustion, food industry, and drug encapsulation. An intriguing phenomenon associated with this process is the occurrence of singular jets that are up to dozens of times faster than the impact velocity. These jets break into micro-droplets, which can produce aerosols and affect the quality of printing technologies. Here, we investigate experimentally and numerically the jetting process after a coaxial water-in-oil compound drop impacts on a glass substrate with different releasing heights and volumetric ratios. After impact, the water core spreads and retracts, giving rise to a vertical jet initially made of oil. For certain values of the impacting velocity, high speed and very thin jets are observed, the so-called singular jets. Depending on the volumetric ratio, one or two velocity peaks can be observed when varying the impact velocity, triggered by the contraction dynamics of a deep and cylindrical cavity. The self-similar time-evolution of the collapse for the first singularity regime follows a 1/2 power law in time, which can be derived from bubble pinch-off. In contrast, the collapse at the second peak follows a 2/3 power law, which can be accounted for by a balance between inertial and capillary forces.

We experimentally investigate the effect of freezing on the spreading of a water drop. Whenever a water drop impacts a cold surface, whose temperature is lower than 0{\deg}C, a thin layer of ice grows during the spreading. This freezing has a notable effect on the impact: at given Reynolds and Weber numbers, we show that lowering the surface temperature reduces the drop maximal extent. Using an analogy between this ice layer and the viscous boundary layer, which also grows during the spreading, we are able to model the effect of freezing as an effective viscosity. The scaling laws designed for viscous drop impact can therefore be applied to such a solidification problem, avoiding the recourse to a full and complex modelling of the thermal dynamics., Comment: Seven pages, five figures

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.

The freezing of a water rivulet begins with a water thread flowing over a very cold surface, is naturally followed by the growth of an ice layer and ends up with a water rivulet flowing on a static thin ice wall. The structure of this final ice layer presents a surprising linear shape that thickens with the distance. This paper presents a theoretical model and experimental characterisation of the ice growth dynamics, the final ice shape and the temperature fields. In a first part, we establish a 2D model, based on the advection-diffusion heat equations, that allows us to predict the shape of the ice structure and the temperature fields in both the water and the ice. Then, we study experimentally the formation of the ice layer and we show that both the transient dynamics and the final shape are well captured by the model. In a last part, we characterise experimentally the temperature fields in the ice and in the water, using an infrared camera. The model shows an excellent agreement with the experimental fields. In particular, it predicts well the linear decrease of the water surface temperature observed along the plane, confirming that the final ice shape is a consequence of the interaction between the thermal boundary layer and the free surface.

We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these singularities are regularized, and the inclusion of an external forcing results in a chaotic fluctuating state. The strong events appear randomly in space and time, making the dissipation rate highly fluctuating. The model shows that: i) dissipation takes place near the singularities only, ii) such intense events are random in space and time, iii) the mean dissipation rate is almost constant as the viscosity varies, and iv) the observation of an Obukhov-Kolmogorov spectrum with a power law dependence together with an intermittent behavior using structure functions correlations, in close correspondence with fluid turbulence., Comment: 5 pages, 6 figues

We investigate experimentally the formation of the particular ice structure obtained when a capillary trickle of water flows on a cold substrate. We show that after a few minutes the water ends up flowing on a tiny ice wall whose shape is permanent. We characterize and understand quantitatively the formation dynamics and the final thickness of this ice structure. In particular, we identify two growth regimes. First, a 1D solidification diffusive regime, where ice is building independently of the flowing water. And second, once the ice is thick enough, the heat flux in the water comes into play, breaking the 1D symmetry of the problem, and the ice ends up thickening linearly downward. This linear pattern is explained by considering the confinement of the thermal boundary layer in the water by the free surface.

This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1D solidification setup, using different liquids and substrates. In a second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate, and pins the contact line at its edge when the drop reaches its maximal diameter. The liquid film then remains still on its ice and keeps freezing. This configuration lasts until the contact line eventually depins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop main thickness, using the drop impact and liquid parameters., Comment: 17 pages, 6 figures

In fluid turbulence, energy is transferred from a scale to another by an energy cascade that depends only on the energy dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Remarkably the normal modes of vibrations in elastic plates manifests an energy cascade with the same K41 spectrum in the fully non-linear regime. Moreover, the elastic deformations present large "eddies" together with a myriad of small "crumpling eddies", such that folds, developable cones, and more complex stretching structures, in close analogy with spots, swirls, vortices and other structures in hydrodynamic turbulence. We characterize the energy cascade, the validity of the constant energy dissipation rate over the scales and the role of intermittency via the correlation functions.

We investigate both experimentally and numerically the impact of liquid drops on deep pools of aqueous glycerol solutions with variable pool viscosity and air pressure. 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 in particular on the viscosity ratio between the two liquids., Comment: 5 pages, 3 figures

We investigate the mechanical response of a compressed monolayer of large and dense particles at a liquid-fluid interface: a granular raft. Upon compression, rafts first wrinkle; then, as the confinement increases, the deformation localizes in a unique fold. This characteristic buckling pattern is usually associated to floating elastic sheets and as a result, particle laden interfaces are often modeled as such. Here, we push this analogy to its limits by comparing the first quantitative measurements of the raft morphology to a theoretical continuous elastic model of the interface. We show that although powerful to describe the wrinkle wavelength, the wrinkle-to-fold transition and the fold shape, this elastic description does not capture the finer details of the experiment. We describe an unpredicted secondary wavelength, a compression discrepancy with the model and a hysteretic behavior during compression cycles, all of which are a signature of the intrinsic discrete and frictional nature of granular rafts. It suggests also that these composite materials exhibit both plastic transition and jamming dynamics., Comment: 10 pages, including Supplementary Information. Submitted to Physical Review Materials

The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for increasing the dissipation are used. The main observable consequence of increasing the damping is a significant modification in the slope of the power spectral density, so that the observed power laws are not in a pure inertial regime. However, the system still displays a turbulent behavior with a cut-off frequency that is determined by the injected power which does not depend on damping. By using the measured damping power-law in numerical simulations, similar conclusions are drawn out., Comment: 6 pages, 6 figures

The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of generating function and of multi-point pdf, for weakly interacting waves with initial random phases. When also initial amplitudes are random, the 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 Schroedinger equation (NLSE) and of a vibrating plate prove that: (i) generic Hamiltonian 4-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 timescale 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, like the vibrating plates, that also show some intermittency at very strong forcings.

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These tests are applied to real Eulerian data of a turbulent velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype model equation for wave turbulence. First we demonstrate the irreversible character of the flow by using multi-time correlation function at a given point of space. Moreover the unexpected behavior of the test function leads us to connect irreversibility and finite time singularities (intermittency). Secondly we show that turbulent cascade exists, and is a dynamical process, by using a test function depending on time and frequency. The cascade shows up only in the inertial domain where the kinetic energy is transferred more rapidly (on average) from the wavenumber $k_{1}$ to $k_{2}$ than from $k_{1}$ to $k'_{2}$ larger than $k_{2}$.

We investigate experimentally the quenching of a liquid pancake, obtained through the impact of a water drop on a cold solid substrate ($0$ to $-60^\circ$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 is stronger. 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.

Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and high mesh resolution is only used near the interface. Parametric studies are performed on the droplet horizontal radius and the capillary number. For droplets with an horizontal radius larger than half the channel height the droplet overfills the channel and exhibits a pancake shape. A lubrication film is formed between the droplet and the wall and particular attention is paid to the effect of the lubrication film on the droplet velocity. The computed velocity of the pancake droplet is shown to be lower than the average inflow velocity, which is in agreement with experimental measurements. The numerical results show that both the strong shear induced by the lubrication film and the three-dimensional flow structure contribute to the low mobility of the droplet. In this low-migration-velocity scenario the interfacial flow in the droplet reference frame moves toward the rear on the top and reverses direction moving to the front from the two side edges. The velocity of the pancake droplet and the thickness of the lubrication film are observed to decrease with capillary number. The droplet velocity and its dependence on capillary number cannot be captured by the classic Hele--Shaw equations, since the depth-averaged approximation neglects the effect of the lubrication film.

We investigate the dynamics of drop impact on a thin liquid film at short times in order to identify the mechanisms of splashing formation. Using numerical simulations and scaling analysis, we show that the splashing formation depends both on the inertial dynamics of the liquid and the cushioning of the gas. Two asymptotic regimes are identified, characterized by a new dimensionless number $J$: when the gas cushioning is weak, the jet is formed after a sequence of bubbles are entrapped and the jet speed is mostly selected by the Reynolds number of the impact. On the other hand, when the air cushioning is important, the lubrication of the gas beneath the drop and the liquid film controls the dynamics, leading to a single bubble entrapment and a weaker jet velocity.

Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in the limit of small nonlinearity. Here, we explore the possible deviations from this mean-field framework, in terms of anomalous scaling, focusing on the case of elastic plates. We establish the picture of the possible behaviors at varying the extent of nonlinearity, and we show that the mean-field theory is appropriate when all excited scales remain dominated by linear dynamics. The other picture is non-trivial and our results suggest that, when large scales contain much energy, the cascade sustains extreme events at small scales and the system displays intermittency.

We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, gfs.sourceforge.net) we compute solutions of the bubble dynamics (i.e. shape and terminal velocity) induced by the interaction between the bubble movement, the Laplace pressure variation, and the lubrication film near the channel wall. Quantitative and qualitative results are presented and compared against both theory and experimental data for small Capillary numbers. We discuss the technical issues of explicit integration methods on small Capillary numbers computations, and the possibility of adding Van der Walls forces to give a more precise picture of the Droplet-based microfluidic problem., Comment: in 1st Pan-American Congress on Computational Mechanics - PANACM 2015, 2015, Buenos Aires, Argentina

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 {\gr 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 behaviour in the short wavelength limit which is significantly different 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.

We present a study of viscous fingering using the Volume Of Fluid method and a central injection geometry, assuming a Laplacian field and a simple surface tension law. As in experiments we see branched structures resulting from the Saffman-Taylor instability. We find that the area $A$ of a viscous-fingering cluster varies as a simple power law $A \sim L^{\alpha}$ of its interface length $L$. Our results are compared to previously published simulations in which the viscosity of the invading fluid is vanishing. We find differences in exponent $\alpha$ and in the appearance of detached droplets and bubbles.

Bubbles at a free surface surface usually burst in ejecting myriads of droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we propose a simple scaling for the jet velocity and we unravel experimentally the intricate roles of bubble shape, capillary waves, gravity and liquid properties. We demonstrate that droplets ejection unexpectedly changes with liquid properties. In particular, using damping action of viscosity, self-similar collapse can be sheltered from capillary ripples and continue closer to the singular limit, therefore producing faster and smaller droplets.These results pave the road to the control of the bursting bubble aerosols.

We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study to the strongly non linear regime described in a previous letter by N. Yokoyama & M. Takaoka. At small forcing, a weakly non linear regime is compatible with the Weak Turbulence Theory when the dissipation is localized at high wavenumber. When the forcing intensity is increased, a strongly non linear regime emerges: singular structures dominate the dynamics at large scale 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., Comment: accepted for publication in Physical Review Letters

We study the non-continuous correction in the dynamics of drop impact on a solid substrate. Close to impact, a thin film of gas is formed beneath the drop so that the local Knudsen number is of order one. We consider the first correction to the dynamics which consists of allowing slip of the gas along the substrate and the interface. We focus on the singular dynamics of entrapment that can be seen when surface tension and liquid viscosity can be neglected. There we show that different dynamical regimes are present that tend to lower the singularity strength. We finally suggest how these effects might be connected to the influence of the gas pressure in the impact dynamics observed in recent experiments.

The splashing of a drop impacting onto a liquid pool produces a range of different sized micro-droplets. 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 ultra-high-speed video imaging in combination with high-resolution numerical simulations to show how the ejecta gives way to irregular splashing. At higher Reynolds number, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von K\'arm\'an vortex street, thus breaking the ejecta sheet as it forms., Comment: 5 pages, 4 figure, 2 supplemental videos

We study the rotational inertia of a model of supersolid in the frame of the mean field Gross-Pitaevskii theory in one space dimension. We discuss the ground state of the model and the existence of a non classical inertia (NCRI) under rotation that models an annular geometry. An explicit formula for the NCRI is deduced. It depends on the density profil of the ground state, in full agreement with former theories. We compare the NCRI computed through this theory with direct numerical simulations of rotating 1D systems.

We review the main properties of a supersolid. We describe first the macroscopic equation that satisfies a supersolid based on general arguments and symmetries and show that such solids might exhibit simultaneously or independently both elastic behavior and superfluidity. We then explain why a supersolid state should exist for solids at very low temperature but with a very small superfluid fraction. Finally, we propose a mean-field model, based on the Gross-Pitaevski\u{\i} equation, which presents the general properties expected for a supersolid and should therefore provide a consistent framework to study its dynamical properties., Comment: Lecture notes of the 4th Warsaw School on Statistical Ohysics

The distribution engendered by successive splitting of one point vortex are considered. The process of splitting a vortex in three using a reverse three-point vortex collapse course is analysed in great details and shown to be dissipative. A simple process of successive splitting is then defined and the resulting vorticity distribution and vortex populations are analysed.

We study the influence of the surrounding gas in the dynamics of drop impact on a smooth surface. We use an axisymmetric 3D model for which both the gas and the liquid are incompressible; lubrication regime applies for the gas film dynamics and the liquid viscosity is neglected. In the absence of surface tension a finite time singularity whose properties are analysed is formed and the liquid touches the solid on a circle. When surface tension is taken into account, a thin jet emerges from the zone of impact, skating above a thin gas layer. The thickness of the air film underneath this jet is always smaller than the mean free path in the gas suggesting that the liquid film eventually wets the surface. We finally suggest an aerodynamical instability mechanism for the splash., Comment: 5 figures

We simulate the impact of a viscous liquid drop onto a smooth dry solid surface. As in experiments, when ambient air effects are negligible, impact flattens the falling drop without producing a splash. The no-slip boundary condition at the wall produces a boundary layer inside the liquid. Later, the flattening surface of the drop traces out the boundary layer. As a result, the eventual shape of the drop is a "pancake" of uniform thickness except at the rim, where surface tension effects are significant. The thickness of the pancake is simply the height where the drop surface first collides with the boundary layer., Comment: 5 pages, 3 figures, submitted to Physical Review Letters

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is modeled by generalizing the porous diffusion equation with a time-dependent diffusion coefficient equivalent to a nonlinear rescaling of time, Comment: 4 pages

We propose the first continuous model with long range screening (shadowing) that described columnar growth in one space dimension, as observed in plasma sputter deposition. It is based on a new continuous partial derivative equation with non-linear diffusion and where the shadowing effects apply on all the different processes., Comment: Fast Track Communication

We present the mechanics of a model of supersolid in the frame of the Gross-Pitaevskii equation at $T=0K$ that do not require defects nor vacancies. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The mechanical equilibrium is studied under external constrains as steady rotation or external stress. Our model displays a paradoxical behavior: the existence of a non classical rotational inertia fraction in the limit of small rotation speed and no superflow under small (but finite) stress nor external force. The only matter flow for finite stress is due to plasticity., Comment: 6 pages, 2 figures

We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence a nonlinear wave system evolves in long-time creating a slow transfer of energy from one mode to another. We derive this kinetic equation for the spectral transfer in terms of the second order moment. We show explicitly that such a non-equilibrium theory describes the approach to an equilibrium wave spectrum, and describes also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations confirming this scenario.

We study the impact and subsequent retraction dynamics of liquid droplets upon high-speed impact on hydrophobic surfaces. Performing extensive experiments, we show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that when increasing the Ohnesorge number, $\Oh=\eta/\sqrt{\rho R_{\rm I} \gamma}$, the retraction, i.e. dewetting, dynamics crosses over from a capillaro-inertial regime to a capillaro-viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid-liquid contact line dynamics inspired by the standard theories for thin film dewetting.

We study the dewetting of a porous plate withdrawn from a bath of fluid. The microscopic contact angle is fixed to zero and the flow is assumed to be parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a critical value of the capillary number $\eta U / \gamma$, above which no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, that reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal for large control parameters (3/2 power law).

Dense granular media have a compaction between the random loose and random close packings. For these dense media the concept of a granular pressure depending on compaction is not unanimously accepted because they are often in a "frozen" state which prevents them to explore all their possible microstates, a necessary condition for defining a pressure and a compressibility unambiguously. While periodic tapping or cyclic fluidization have already being used for that exploration, we here suggest that a succession of flowing states with velocities slowly decreasing down to zero can also be used for that purpose. And we propose to deduce the pressure in \emph{dense and flowing} granular media from experiments measuring the thickness of the granular layer that remains on a rough incline just after the flow has stopped., Comment: 10 pages, 2 figures

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the simulations.