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We study experimentally the enhancement of splashing due to solidification. Investigating the impact of water drops on dry smooth surfaces, we show that the transition velocity to splash can be drastically reduced by cooling the surface below the liquid melting temperature. We find that at very low temperatures (below $-60 ^\circ \rm C$), the splashing behaviour becomes independent of surface undercooling and presents the same characteristics as on ambient temperature superhydrophobic surfaces. This resemblance arises from an increase of the dynamic advancing contact angle of the lamella with surface undercooling, going from the isothermal hydrophilic to the superhydrophobic behaviour. We propose that crystal formation can affect the dynamic contact angle of the lamella, which would explain this surprising transition. Finally, we show that the transition from hydrophilic to superydrophobic behaviour can also be characterized quantitatively on the dynamics of the ejecta.

In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible change of topology while retaining a high-order representation of the gradients on the interface and the capability of properly applying boundary conditions on the interface. This leads to a two-fluid conservative second-order numerical method. The ability of the method to correctly solve Stefan problems, onset dendrite growth with and without anisotropy is demonstrated through a variety of test cases. Finally, we take advantage of the two-fluid representation to model a Rayleigh--B\'enard instability with a melting boundary.

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. Modelling 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, Comment: Physical Review Letters, 22 juin 2022

We investigate numerically the influence of a weak current on wind-generated surface deformations for wind velocity below the onset of regular waves. In that regime, the liquid surface is populated by small disorganised deformations elongated in the wind direction, referred to as wrinkles. These wrinkles are the superposition of incoherent wakes generated by the pressure fluctuations traveling in the turbulent boundary layer in the air. In this work, we account for the effect of a weak sheared current in the liquid, either longitudinal or transverse, by introducing a modified Doppler-shifted dispersion relation to lowest order in viscosity and current in the spectral theory previously derived by Perrard et al (2019). This theory describes the simplified one-way problem of surface deformations excited by a prescribed turbulent forcing, thereby neglecting the retroaction of waves on turbulence in the air. The forcing is taken from a set of direct numerical simulations of a turbulent channel flow. We determine the wrinkle properties (size and amplitude) as a function of the liquid viscosity and current properties (surface velocity, thickness and orientation). We find significant modifications of the wrinkle geometry by the currents: the wrinkles are tilted for a transverse current, and show finer scales for a longitudinal current. However, their characteristic size is weakly affected, and their amplitude remains independent of the current. We discuss the implications of these results on the onset of regular waves at larger wind velocity. In this work, we introduce a spectral interpolation method to evaluate the surface deformation fields, based on a refined meshing close to the dispersion relation of the waves. This method, which can be extended to any dispersive system excited by a random forcing, strongly reduces the discretization effects at a low computational cost.

A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of energy, as well as the Kolmogorov-Zakharov spectrum of wave turbulence. In the Wave Turbulence Theory framework, the model is used to investigate the self-similar, non-stationary solutions of forced and free turbulent vibrations. Frequency-dependent damping laws can easily be accounted for. Their effects on the characteristics of the stationary spectra of turbulence are then investigated. Thanks to this analysis, self-similar universal solutions are given, relating the power spectrum to both the injected power and the damping law., Comment: 22 pages, 9 figures

Modeling and simulating overland flow fed by rainfall is a common issue in watershed surface hydrology. Modelers have to choose among various friction models when defining their simulation framework. The purpose of this work is to compare the simulation quality for the Manning, Darcy-Weisbach, and Poiseuille friction models on the simple case of a constant rain on a thin experimental flume. Results show that the usual friction law of Manning is not suitable for this type of flow. The Poiseuille friction model gave the best results both on the flux at the outlet and the velocity and depth profile along the flume. The Darcy-Weisbach model shows good results for laminar flow. Additional testing should be carried out for turbulent cases., Comment: in Journal of Hydrology 2016

We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than $\ell_{\nu} = \rho\nu^2/\sigma$, which is $10 nm$ for water. Using a high-precision boundary integral method, we show that the walls of the thin retracting sheet of air between the drops reconnect in finite time to form a toroidal enclosure. After the initial reconnection, retraction starts again, leading to a rapid sequence of enclosures. Averaging over the discrete events, we find the minimum radius of the liquid bridge connecting the two drops to scale like $r_b \propto t^{1/2}$.

Theoretical and experimental study of high-acceleration patterns in vibrated granular layers is presented. The order parameter model based on parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including hexagons, interface between flat anti-phase domains and new localized objects, super-oscillons. The experiments confirmed the existence of super-oscillons and bound states of super-oscillons and interfaces. On the basis of order parameter model we predict analytically and confirm experimentally that the additional subharmonic driving results in controlled motion of the interfaces., Comment: 18 pages, 16 figures, submitted to Phys. Rev. E

A 2-D version of the asymmetric exclusion model for granular sheared flows is presented. The velocity profile exhibits two qualitatively different behaviors, dependent on control parameters. For low friction, the velocity profile follows an exponential decay while for large friction the profile is more accurately represented by a Gaussian law. The phase transition occurring between these two behavior is identified by the appearance of correlations in the cluster size distribution. Finally, a mean--field theory gives qualitative and quantitative good agreement with the numerical results., Comment: 13 pages, 5 figures; typos added, one definition changed

The present article represents part of the PhD. dissertation by C. Josserand. We discuss the nucleation of quantized vortices in the nonlinear Schr\"{o}dinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field $\psi$ gives an Euler-Tricomi type equation for the stationary solutions below threshold. This equation is closely related to the one known in shock wave dynamics for gas. Then using solvability condition, we extract a time-dependent scenario for the evolution of the amplitude of the solution, which we, finally, relate to a known family solution of NLS which gives rise to a vortex nucleation. We also give a first order correction at the Landau velocity of nucleation, taking into account the geometry of the flow., Comment: 25 pages, 9 figures

We propose a model to describe the quasistatic shearing of dry granular materials, which notably captures the differences in velocity profiles recently observed in 2 and 3-D Couette flow experiments. In our scheme, the steady-state flow is due to the intermittent motion of particle clusters moving together with the wall. The motion of a cluster is associated with the transient formation of a fracture inside the sheared pack. The model is based on the existence of a persistence length for the fractures, which imposes a self-similar structure on the clusters. Through a probabilistic approach, we can evaluate the rate of appearance of a cluster of a given size and obtain a prediction for the average velocity profiles. We also predict the existence of large stress fluctuations at the moving wall, which characteristics are in good agreement with experimental data., Comment: 7 pages, 2 figures, correction of the text