François Ludewig

The role of the droplet deformations in the bouncing droplet dynamics

Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion, and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical bouncing dynamics by neglecting the deformation of the surface of the bath. To be under this favorable condition, low viscous oil droplets are dropped over a highly viscous oil bath that is vibrated. These droplets bounce vertically on the surface of the bath and exhibit many periodic trajectories and resonant modes when tuning the forcing parameters, i.e., the oscillation of the bath. This complex dynamics emphasizes the interplay between elastic energy storage and energy dissipation in droplets at each bounce. We propose to model droplets using a bouncing mass-spring-damper system that mimics a deformable droplet bouncing on a non-deformable liquid bath. From the experimental measurements, we constructed bifurcation diagrams of the bouncing trajectories and challenge...

Energetic approach for the characterization of taps in granular compaction

We report numerical investigations for the compaction dynamics of dense granular assemblies. The studies are based on the non-smooth contact dynamics model. Our work suggests that the dimensionless acceleration parameter Γ, used by a large majority of authors, is not appropriate for rescaling the data. We prove that the dimensionless energy Ξ, injected in the granular system at lift-off, is more appropriate and leads to robust interpretations of the compaction dynamics. Indeed, the injected energy allows to pass energy barriers that separate local equilibrium states. Using the Eyring picture of relaxation dynamics, we show that the consideration of Ξ leads to a new law for compaction.

Dynamical clustering in driven granular gas

Driven granular gases present rich dynamical behaviors. Due to inelastic collisions, particles may form dense and slow regions. These clusters emerge naturally during a cooling phenomenon but another dynamical clustering is observed when the system is continuously excited. In this paper, the physical processes that trigger the transition from a granular gas to a dynamical cluster are evidenced through numerical simulations. At the granular scale, the transition is evidenced by the observation of caging effects. At the scale of the system, the transition is emphasized by density fluctuations. Physical arguments, based on relaxation times, provide an analytical prediction for the edge between dynamical regimes.

Effect of friction in a toy model of granular compaction.

A toy model of granular compaction which includes some resistance due to granular arches is proposed. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold omega(c) is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point omega*(c) of the slipping threshold have been emphasized: (i) a slow compaction with lots of paralyzed regions and (ii) an inverse logarithmic dynamics with a power-law scaling of grain mobility. Below the critical point omega*(c) , the physical properties of this frozen system become independent of omega(c) . Above the critical point omega*(c) --i.e., for low friction values--the packing properties behave as described by the classical Janssen theory for silos.

Granular transport in driven granular gas

We numerically and theoretically investigate the behavior of a granular gas driven by asymmetric plates. The injection of energy in the dissipative system differs from one side to the opposite one. We prove that the dynamical clustering which is expected for such a system is affected by the asymmetry. As a consequence, the cluster position can be fully controlled. This property could lead to various applications in the handling of granular materials in low-gravity environment. Moreover, the dynamical cluster is characterized by natural oscillations which are also captured by a model. These oscillations are mainly related to the cluster size, thus providing an original way to probe the clustering behavior.Graphical abstract

Bouncing trimer: a random self-propelled particle, chaos and periodical motions

A trimer is an object composed of three centimetrical stainless steel beads equidistant from each other and is predestined to show richer behaviour than a bouncing ball or a bouncing dimer. A rigid trimer was placed on the plate of an electromagnetic shaker and was vertically vibrated according to a sinusoidal signal. The horizontal translational and rotational motions of the trimer were recorded for a range of frequencies between 25 and 100Hz, while the amplitude of the forcing vibration was tuned to obtain maximal acceleration of the plate up to 10 times gravity. Several modes have been detected such as, e.g., rotational and pure translational motions. These modes are found at determined accelerations of the plate and do not depend on the frequency. Chaotic behaviour is observed for other accelerations. By recording the time delays between two successive contacts when the frequency and the amplitude are fixed, a map of the bouncing regime was constructed and compared with that of the dimer and the bouncing ball. Period-2 and period-3 orbits were experimentally observed. In these modes, according to observations, the contact between the trimer and the plate is persistent between two successive jumps. This persistence erases the memory of the jump preceding the contact. A model based on the conditions for obtaining persistent contact is proposed and allows us to explain the values of the particular accelerations for which period-2 and period-3 modes were observed. Finally, numerical simulations allow us to reproduce the experimental results. This allows us to conclude that the friction between the beads and the plate is the major dissipative process.

Clustering and segregation in driven granular fluids.

In microgravity, the successive inelastic collisions in a granular gas can lead to a dynamical clustering of the particles. This transition depends on the filling fraction of the system, the restitution of the used materials and on the size of the particles. We report simulations of driven bi-disperse gas made of small and large spheres. The size as well as the mass difference imply a strong modification in the kinematic chain of collisions and therefore alter significantly the formation of a cluster. Moreover, the different dynamical behaviors can also lead to a demixing of the system, adding a few small particles in a gas of large ones can lead to a partial clustering of the taller type. We realized a detailed phase diagram recovering the encountered regimes and developed a theoretical model predicting the possibility of dynamical clustering in binary systems.Graphical abstract

Compaction of granular materials: experiments and contact dynamics simulations

We present an original experimental study of the slow compaction dynamics for two dimensional isotropic granular systems. Compaction dynamics is measured at three different scales : the macroscopic scale through the normalized packing fraction , the mesoscopic scale through the normalized fraction of domains ideally ordered in the system, and the microscopic scale through the grain mobility µ. The domains ideally ordered are found to obey a growth process dominated by the displacement of domain boundaries. We present also preliminary results of three-dimensional simulations with a model of contact dynamics. These results allow to discuss the difference between the two-dimensional and the three-dimensional cases.

Influence of cohesive forces on the macroscopic properties of granular assemblies

The influence of cohesive forces inside a granular material is analyzed with compaction experiments. To begin, a model cohesive granular material is considered. This granular material is made of millimetric grains with a cohesion induced by an external magnetic field. Therefore, the cohesion between the grains is adjusted through the intensity of the applied magnetic field. Afterward, the cohesion induced by capillary bridges are considered. In the first study concerning capillary forces, the cohesion between neighboring grains is induced by liquid bridges in a wet granular material. The cohesiveness is tuned using different liquids having specific surface tension values. The second study performed with capillary forces concerns initially dry granular materials surrounded by a well controlled air humidity. Then, the cohesion inside the packing is controlled through the relative humidity which influence both triboelectric and capillary effects. The evolution of the parameters extracted from the compaction ...

Dynamical regimes of a granular gas in microgravity : a molecular dynamics study

We propose a numerical model, based on molecular dynamics, which is able to reproduce the behavior of a dissipative granular gas in microgravity. Granular material is confined in a cubic box of side length L following a sinusoidal motion of amplitude A and angular velocity ω = 2πf along the z-axis. The simulations are performed using the parameters of earlier Texus experiments [15]. Our results are in excellent agreement with experimental data. Moreover, we discovered various dynamical regimes and the physical conditions for their appearance : a gaseous state, the formation of either small or large clusters, the collective motion of grains. Phase diagrams are drawn where transitions between these different granular states are emphasized. Transitions are discussed by considering Statistical Physics models.