A self-similar model for shear flows in dense granular materials

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 tex

Inviscid coalescence of drops

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 $r_b \propto t^{1/2}$

Granular Pressure and the Thickness of a Layer Jamming on a Rough Incline

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 figure

A 2-D asymmetric exclusion model for granular flows

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 change

Cavitation induced by explosion in a model of ideal fluid

We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent view for rebound bubbles in superfluid and we indentify the loss of energy between the successive rebounds as radiated waves. We compute self-similar solution of the explosion for the early stage, when no bubbles have been nucleated. The solution also gives the wave number of the excitations emitted through the shock wave.Comment: 21 pages,13 figures, other comment

A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates

International audienceThin plates vibrating at large amplitudes may exhibit a strongly nonlinear regime that has to be studied within the framework of wave turbulence. Experimental studies have revealed the importance of the damping on the spectra of wave turbulence , which precludes for a direct comparison with the theoretical results, that assumes a Hamiltonian dynamics. A phenomenological model is here introduced so as to predict the effect of the damping on the turbulence spectra. Self-similar solutions are found and the cutoff frequency is expressed as function of the damping rate and the injected power

Making superhydrophobic splashes by surface cooling

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