Deformation of soap bubbles in uniform magnetic fields

The deformation of hemispherical sessile bubbles made of ferrofluid soap under vertical uniform magnetic fields was studied using Helmholtz coils. The deformation and the shape of the bubbles were monitored according to the amplitude of the magnetic field, the initial volume of the bubbles and the ferrofluid volume used to create them. The meniscus was found to bear most of the deformation, reshaping into a cylinder, with the remainder of the bubble forming a spherical cap, mainly adapting to the meniscus transformation. The growth of the meniscus height was rationalised using a simple model. More precisely, the meniscus shape depends on the competition between capillary, gravity and magnetic effects. These three ingredients can be rewritten to highlight two characteristic lengths of the system: the capillary and the magnetic lengths. Depending on the magnetic field intensity, the shape of the meniscus is described by one of the two lengths, thus revealing the existence of two distinct regimes.

Thermal Antibubbles: When Thermalization of Encapsulated Leidenfrost Drops Matters

Antibubbles are ephemeral objects composed of a liquid drop encapsulated by a thin gas shell immersed in a liquid medium. When the drop is made of a volatile liquid and the medium is superheated, the gas shell inflates at a rate governed by the evaporation flux from the drop. This thermal process represents an alternate strategy for delaying the antibubble collapse. We model the dynamics of such "thermal" antibubbles by incorporating to the film drainage equation the heat-transfer-limited evaporation of the drop, which nourishes the gas shell with vapor, as for Leidenfrost drops. We demonstrate that the inflation of the gas shell is drastically inhibited by the thermalization of the initially colder drop. Because of this thermalization effect, smaller drops evaporate much faster than larger ones.

Disordering two-dimensional magnet-particle configurations using bidispersity

In various types of many-particle systems, bidispersity is frequently used to avoid spontaneous ordering in particle configurations. In this study, the relation between bidispersity and disorder degree of particle configurations is investigated. By using magnetic dipole-dipole interaction, magnet particles are dispersed in a two-dimensional cell without any physical contact between them. In this magnetic system, bidispersity is introduced by mixing large and small magnets. Then, the particle system is compressed to produce a uniform particle configuration. The compressed particle configuration is analyzed by using Voronoi tessellation for evaluating the disorder degree, which strongly depends on bidispersity. Specifically, the standard deviation and skewness of the Voronoi cell area distribution are measured. As a result, we find that the peak of standard deviation is observed when the numbers of large and small particles are almost identical. Although the skewness shows a non-monotonic behavior, a zero skewness state (symmetric distribution) can be achieved when the numbers of large and small particles are identical. In this ideally random (disordered) state, the ratio between pentagonal, hexagonal, and heptagonal Voronoi cells becomes roughly identical, while hexagons are dominant under monodisperse (ordered) conditions. The relation between Voronoi cell analysis and the global bond orientational order parameter is also discussed.

The wetting properties of frosted glass

Frosted glass is a common, low cost material. Its roughness can be used to control how it is wet by water. In this paper, the wetting properties of silicone oil and water are investigated. For the oil, wetting is total since the oleophilic character of the glass is enhanced by its roughness. Due to the remarkable optical properties of frosted glass, the spreading of oil droplets on its surface was recorded over three months. Frosted glass is a parahydrophilic surface because of its large contact angle hysteresis (up to 80° ). The behaviour of oil and water droplets was compared on a long piece of inclined frosted glass. The trajectories (and the spreading) of the droplets were studied and phenomenological laws were deduced to describe the dependence of the droplet speed on the initial volume of the droplet and the angle of inclination. Such dependences of speed at long travel distances (100 times the capillary length) were deduced and rationalised with a simple model that takes into account the thickness of the wake. Moreover, we analysed the flow inside the wake of water droplets sliding on inclined frosted glass. Suggestions are given on how to exploit drainage of the water droplet wake and the high hysteresis of water within the framework of open microfluidics.

Erratum: Leidenfrost effect: Accurate drop shape modeling and refined scaling laws [Phys. Rev. E 90, 053011 (2014)]

This corrects the article DOI: 10.1103/PhysRevE.90.053011.

Wave Turbulence on the Surface of a Fluid in a High-Gravity Environment

We report on the observation of gravity-capillary wave turbulence on the surface of a fluid in a high-gravity environment. By using a large-diameter centrifuge, the effective gravity acceleration is tuned up to 20 times Earth's gravity. The transition frequency between the gravity and capillary regimes is thus increased up to one decade as predicted theoretically. A frequency power-law wave spectrum is observed in each regime and is found to be independent of the gravity level and of the wave steepness. While the timescale separation required by weak turbulence is well verified experimentally regardless of the gravity level, the nonlinear and dissipation timescales are found to be independent of the scale, as a result of the finite size effects of the system (large-scale container modes) that are not taken currently into account theoretically.

Controlling the lifetime of antibubbles

An antibubble is a liquid droplet wrapped by a thin layer of gas, inside a bulk liquid usually of the same composition. The lifetime of an antibubble is governed by the drainage of the gas between the two liquid-gas interfaces populated by surfactants. Depending on the relative magnitude of surface viscosity and elastic moduli, which directly depend on or are determined by the nature of surfactants, the lifetime of an antibubble may vary a lot, from few seconds to few minutes. While such a difference can be predicted with models that include the role of interfacial properties, they were not observed experimentally in previous studies, due to important sources of dispersion. In this review, the main sources of dispersion are identified, such as (i) the initial amount of gas embedded in the antibubble, (ii) the level of saturation of gas in the bulk liquid, (iii) the presence of dust particles (<0.5 μm) in the gas, and (iv) three-dimensional flow effects. By accounting for these various effects, we obtain a coherent view on the lifetime of an antibubble, as a function of its radius and the surface rheology, with excellent consistency between experiments and modeling. Results thus demonstrate that controlling the size and lifetime of antibubbles is achievable.

Rotation of melting ice disks due to melt fluid flow

We report experiments concerning the melting of ice disks (85 mm in diameter and 14 mm in height) at the surface of a thermalized water bath. During the melting, the ice disks undergo translational and rotational motions. In particular, the disks rotate. The rotation speed has been found to increase with the bath temperature. We investigated the flow under the bottom face of the ice disks by a particle image velocimetry technique. We find that the flow goes downwards and also rotates horizontally, so that a vertical vortex is generated under the ice disk. The proposed mechanism is the following. In the vicinity of the bottom face of the disk, the water eventually reaches the temperature of 4 °C for which the water density is maximum. The 4 °C water sinks and generates a downwards plume. The observed vertical vorticity results from the flow in the plume. Finally, by viscous entrainment, the horizontal rotation of the flow induces the solid rotation of the ice block. This mechanism seems generic: any vertical flow that generates a vortex will induce the rotation of a floating object.

Displacement of an Electrically Charged Drop on a Vibrating Bath

In this work, the manipulation of an electrically charged droplet bouncing on a vertically vibrated bath is investigated. When a horizontal, uniform, and static electric field is applied to it, a motion is induced. The droplet is accelerated when the droplet is small. On the other hand, large droplets appear to move with a constant speed that depends linearly on the applied electrical field. In the latter regime, high-speed imaging of one bounce reveals that the droplet experiences an acceleration due to the electrical force during the flight and decelerates to 0 when interacting with the surface of the bath. Thus, the droplet moves with a constant average speed on a large time scale. We propose a criterion based on the force necessary to move a charged droplet at the surface of the bath to discriminate between constant speed and accelerated droplet regimes.

Droplets climbing a rotating helical fiber

A liquid droplet is placed on a rotating helical fiber. We find that the droplet may slide down, attach or climb up the fiber. We inspect experimentally the domain of existence of these three behaviors as a function of the geometrical characteristics of the fiber, its angle relatively to the horizontal, the wetting properties of the fluid and the rotating speed of the helix. A theoretical model is proposed in order to capture the boundaries of the experimental phase diagram.

Bernal random loose packing through freeze-thaw cycling

We study the effect of freeze-thaw cycling on the packing fraction of equal spheres immersed in water. The water located between the grains experiences a dilatation during freezing and a contraction during melting. After several cycles, the packing fraction converges to a particular value η(∞)=0.595 independently of its initial value η(0). This behavior is well reproduced by numerical simulations. Moreover, the numerical results allow one to analyze the packing structural configuration. With a Voronoï partition analysis, we show that the piles are fully random during the whole process and are characterized by two parameters: the average Voronoï volume μ(v) (related to the packing fraction η) and the standard deviation σ(v) of Voronoï volumes. The freeze-thaw driving modify the volume standard deviation σ(v) to converge to a particular disordered state with a packing fraction corresponding to the random loose packing fraction η(BRLP) obtained by Bernal during his pioneering experimental work. Therefore, freeze-thaw cycling is found to be a soft and spatially homogeneous driving method for disordered granular materials.

Resonant and antiresonant bouncing droplets

When placed onto a vibrating liquid bath, a droplet may adopt a permanent bouncing behavior, depending on both the forcing frequency and the forcing amplitude. The relationship between the droplet deformations and the bouncing mechanism is studied experimentally and theoretically through an asymmetric and dissipative bouncing spring model. Antiresonance phenomena are evidenced. Experiments and theoretical predictions show that both resonance at specific frequencies and antiresonance at Rayleigh frequencies play crucial roles in the bouncing mechanism. In particular, we show that they could be exploited for bouncing droplet size selection.

Leidenfrost effect: Accurate drop shape modeling and refined scaling laws

We here present a simple fitting-parameter-free theory of the Leidenfrost effect (droplet levitation above a superheated plate) covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. The geometry of this film is found to be in excellent quantitative agreement with the interferometric measurements of Burton et al. [Phys. Rev. Lett. 109, 074301 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.074301]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632 (2003)PHFLE61070-663110.1063/1.1572161] as far as the effect of plate superheat is concerned and highlight the relative role of evaporation, gravity, and capillarity in the vapor film. To further substantiate these findings, a treatment of the problem by matched asymptotic expansions is also presented.

Gas dissolution in antibubble dynamics

Antibubbles are ephemeral objects. Their lifetime is driven by the slow drainage of the air shell from the bottom to the top of the antibubble under the action of hydrostatic pressure. We show in this paper that this argument is only valid if the water used to make the surfactant mixture is saturated in air. Otherwise, two paths are used by the air, which conduct to the thinning and the eventual collapse of the air shell: the drainage from the bottom to the top of the antibubble and the dissolution of the air into the liquid. Using degassed water dramatically shortens the lifetime of the antibubbles, as observed experimentally and rationalised by time-dependent simulations. Consequently, the antibubble lifetime is not only correlated with physical and chemical properties of the air-liquid interface but also with the gas content of the liquid. We also show that pure gas dissolution does not depend on the antibubble radius, a behaviour that allows to rationalise unexplained experimental data found in literature.

Dynamics of a grain-filled ball on a vibrating plate

We study experimentally how the bouncing dynamics of a hollow ball on a vibrating plate is modified when it is partially filled with liquid or grains. Whereas empty and liquid-filled balls display a dominant chaotic dynamics, a ball with grains exhibits a rich variety of stationary states, determined by the grain size and filling volume. In the collisional regime, i.e., when the energy injected to the system is mainly dissipated by interparticle collisions, an unexpected period-1 orbit appears independently of the vibration conditions, over a wide range. This is a self-regulated state driven by the formation and collapse of a granular gas within the ball during one cycle. In the frictional regime (dissipation dominated by friction), the grains move collectively and generate different patterns and steady modes: oscillons, waves, period doubling, etc. From a phase diagram and a geometrical analysis, we deduce that these modes are the result of a coupling (synchronization) between the vibrating plate frequency and the trajectory followed by the particles inside the cavity.

Organization of microbeads in Leidenfrost drops

We investigated the organization of micrometric hydrophilic beads (glass or basalt) immersed in Leidenfrost drops. Starting from a large volume of water compared to the volume of the beads, while the liquid evaporates, we observed that the grains are eventually trapped at the interface of the droplet and accumulate. At a moment, the grains entirely cover the droplet. We measured the surface area at this moment as a function of the total mass of particles inserted in the droplet. We concluded that the grains form a monolayer around the droplet assuming (i) that the packing of the beads at the surface is a random close packing and (ii) that the initial surface of the drop is larger than the maximum surface that the beads can cover. Regarding the evaporation dynamics, the beads are found to reduce the evaporation rate of the drop. The slowdown of the evaporation is interpreted as being the consequence of the dewetting of the particles located at the droplet interface which makes the effective surface of evaporation smaller. As a matter of fact, contact angles of the beads with the water deduced from the evaporation rates are consistent with contact angles of beads directly measured at a flat air-water interface of water in a container.

Experimental study of a vertical column of grains submitted to a series of impulses

We report physical phenomena occurring in a vertical Newton's cradle system. A dozen of metallic spheres are placed in a vertical tube. Therefore, the gravity induces a non-uniform pre-compression of the beads and a restoring force. An electromagnetic hammer hits the bottom bead at frequencies tuned between 1 and 14Hz. The motion of the beads are recorded using a high-speed camera. For low frequencies, the pulses travel through the pile and expel a few beads from the surface. Then, after a few bounces of these beads, the system relaxes to the chain of contacting grains. When the frequency is increased, the number of fluidized beads increases. In the fluidized part of the pile, adjacent beads are bouncing in opposition of phase. This phase locking of the top beads is observed even when the bottom beads experience chaotic motions. While the mechanical energy increases monotically with the bead vertical position, heterogeneous patterns in the kinetic energy distribution are found when the system becomes fluidized.

Rebound of a confined granular material: combination of a bouncing ball and a granular damper

A ball dropped over a solid surface bounces several times before a complete stop. The bouncing can be reduced by introducing a liquid into the ball; however, the first rebound remains largely unaffected by the fluid. Granular materials can also work as dampers. We investigated the rebound of a container partially filled with a given mass of grains mi. During the collision, the kinetic energy of the container is partially transferred to the grains, the rebound is damped, and the fast energy dissipation through inter-particle collisions and friction decreases the bouncing time dramatically. For grain-filled cylinders, a completely inelastic collision (zero rebound) is obtained when mi ≥ 1.5εomc, where εo and mc are the coefficient of restitution and mass of the empty container. For grain-filled spheres, the first rebound is almost undamped, but the second collision is completely inelastic if mi ≫ mc. These findings are potentially useful to design new granular damping systems.

Antibubble dynamics: the drainage of an air film with viscous interfaces

An antibubble is a spherical air film that is immersed in a surfactant mixture and drains under the action of hydrostatic pressure. A dynamical model of this film is proposed that accounts for the surface shear viscosity effects in the case of purely viscous interfaces, which applies for surfactants whose adsorption rate is much larger than advection rate and at a concentration much above the critical micelle concentration. Our model shows that the lifetime of the antibubbles in this case increases with surface shear viscosity, denoted ε, whose value is measured independently, all in agreement with experimental measurements. We also found that the critical thickness, h(c), at film rupture due to van der Waals interactions slightly depends on the surface shear viscosity, namely h(c) ∝ ε(1/6).

Bouncing of polymeric droplets on liquid interfaces

The effect of polymers on the bouncing behavior of droplets in a highly viscous, vertically shaken silicone oil bath was investigated in this study. Droplets of a sample liquid were carefully placed on a vibrating bath that was maintained well below the threshold of Faraday waves. The bouncing threshold of the plate acceleration depended on the acceleration frequency. For pure water droplets and droplets of aqueous polymer solutions, a minimum acceleration amplitude was observed in the acceleration threshold curves as a function of frequency. The bouncing acceleration amplitude for a droplet of a dilute aqueous polymer solution was higher than the acceleration amplitude for a pure water droplet. Measurements of the center of mass trajectory and the droplet deformations showed that the controlling parameter in the bouncing process was the oscillating elongational rate of the droplet. This parameter can be directly related to the elongational viscosity of the polymeric samples. The large elongational viscosity of the polymer solution droplets suppressed large droplet deformations, resulting in less chaotic bouncing.

Sculpting sandcastles grain by grain: self-assembled sand towers

We study the spontaneous formation of granular towers produced when dry sand is poured on a wet sand bed. When the liquid content of the bed exceeds a threshold value W*, the impacting grains have a nonzero probability to stick on the wet grains due to instantaneous liquid bridges created during the impact. The trapped grains become wet by the capillary ascension of water and the process continues, giving rise to stable narrow towers. The growth velocity is determined by the surface liquid content which decreases exponentially as the tower height augments. This self-assembly mechanism (only observed in the funicular and capillary regimes) could theoretically last while the capillary rise of water is possible; however, the structure collapses before reaching this limit. The collapse occurs when the weight of the tower surpasses the cohesive stress at its base. The cohesive stress increases as the liquid content of the bed is reduced. Consequently, the highest towers are found just above W*.

How does an ice block assembly melt?

The melting of an assembly of ice blocks contained in a vertical cylinder and under an unidirectional load was investigated. The total volume occupied by the ice blocks and the volume of ice were simultaneously measured which allowed one to determine the volume fraction of the ice in the cylinder. While the ice volume continuously decreases, sudden breakdowns of the total volume were observed. Large reorganizations of the whole assembly occur. However, the maximal volume fraction found just after a large reorganization decreased with time. In addition, the modifications of the pile structure were investigated using an x-ray tomography imaging before and after one collapse. As the packing is better ordered along the walls, we suggest that the motion of the piston is governed by the layer of ice blocks located along the container wall. This layer was modeled by a two-dimensional assembly of disks. The model supports the idea that the geometrical frustrations explain the dynamics of the successive reorganization due to the shrinkage of the grains. Finally, numerical simulations allow one to conclude that the dynamics of the melting of the ice blocks is governed (i) by the confinement effect which induces defects in the packing and (ii) by the low friction between the ice blocks.

Symmetry breaking in a few-body system with magnetocapillary interactions

We have experimentally investigated the interactions between floating magnetic spheres which are submitted to a vertical magnetic field, ensuring a tunable repulsion, while capillary forces induce attraction. We emphasize the complex arrangements of floating bodies. The equilibrium distance between particles exhibits hysteresis when the applied magnetic field is modified. Irreversible processes are evidenced. Symmetry breaking is also found for three identical floating bodies when the strength of the magnetic repulsion is tuned. We propose a Dejarguin-Landau-Verwey-Overbeek (DLVO)-like potential, i.e., an interaction potential with a primary and a secondary minimum, capturing the main physical features of the magnetocapillary interaction, which is relevant for self-assembly.

Impact of liquid droplets on granular media

The crater formation due to the impact of a water droplet onto a granular bed has been experimentally investigated. Three parameters were tuned: the impact velocity, the size of the droplet, and the size of the grains. The aim is to determine the influence of the kinetic energy on the droplet pattern. The shape of the crater depends on the kinetic energy at the moment the droplet starts to impact the bed. The spreading and recession of the liquid during the impact were carefully analyzed from the dynamical point of view, using image analysis of high-speed video recordings. The different observed regimes are characterized by the balance between the impregnation time of the water by the granular bed by the water and the capillary time responsible for the recession of the drop.

Influence of a reduced gravity on the volume fraction of a monolayer of spherical grains

Centrifuge force is used to study granular materials in low gravity conditions. We consider a monolayer of noncohesive spherical grains placed on a plate. Reduced gravity conditions can be simulated in the plane by tilting or by rotating the plate. We compare both approaches experimentally. The volume fraction is found to increase with the apparent gravity and saturates. A model based on the exponential distribution of the Voronoi cell areas has been built and is in excellent agreement with the experimental data by extrapolating the fits of the data. Moreover, numerical simulations exhibit that more arches can be maintained at low apparent gravities than at high.

Single thermal plume in locally heated vertical soap films

A vertical soap film is maintained by injection of a soap solution from the top. The film is then locally heated. Thermal plumes may be observed to rise in the film, depending on the magnitude of the heating and injected flows. The nearly two-dimensional nature of the system allows to visualize the motion of the plumes using an infrared camera. A model is proposed to describe the growth, emergence, and stationarity of the plumes in the film by taking into account both magnitudes of the heating ΔT and injected flow Q.

Wave turbulence on the surface of a ferrofluid in a horizontal magnetic field

We report observations of wave turbulence on the surface of a ferrofluid submitted to a magnetic field parallel to the fluid surface. The magnetic wave turbulence shows several differences compared to the normal field case reported recently. The inertial zone of the magnetic wave turbulence regime is notably found to be strongly increased with respect to the normal field case and to be well described by our theoretical predictions. The dispersion relation of linear waves is also measured and differs from the normal field case due to the absence of the Rosensweig instability.

Hysteretic behavior in three-dimensional soap film rearrangements

We report experiments on soap film configurations in a triangular prism for which the shape factor can be changed continuously. Two stable configurations can be observed for a range of the shape factor h, being the prism-height/edge-length ratio. A hysteretic behavior is found, due to the occurrence of another local minima in the free energy. Contrary to a common belief, soap films can be trapped in a particular configuration being different from a global surface minimization. This metastability can be evidenced from a geometrical model based on idealized structures. Depending on the configuration, the transition is either first or second order, providing clues on the structural relaxations taking place into three-dimensional foams, such as T1 rearrangements.

From a bouncing compound drop to a double emulsion

We show that a double emulsion (oil in water in oil) can be created starting from a compound droplet (surfactant solution in oil). The compound drop bounces on a vertically vibrated liquid surface. When the amplitude of the vibration exceeds a threshold value, the oil layer penetrates the water content and leaves a tiny oil droplet within. As this phenomenon occurs at each vigorous impact, the compound drop progressively transforms into a double emulsion. The emulsification threshold, which is observed to depend on the forcing frequency but not on the drop size, is rationalized by investigating the impact of compound drops onto a static liquid surface. The droplet creation occurs when the kinetic energy released at impact is larger than the energy required to deform the compound drop, namely when the Weber number is higher than a given threshold value.

Compaction dynamics of a magnetized powder

We have investigated experimentally the influence of a magnetic interaction between the grains on the compaction dynamics of a granular pile submitted to a series of taps. The granular material used to perform this study is a mixture of metallic and glass grains. The packing is immersed in homogeneous external magnetic field. The magnetic field induces an interaction between the metallic grains that constitutes the tunable cohesion. The compaction characteristic time and the asymptotic packing fraction have been measured as a function of the Bond number which is the ratio between the cohesive magnetic force and the grain weight. These measurements have been performed for different fractions of metallic beads in the pile. When the pile is only made of metallic grains, the characteristic compaction time increases as the square root of the Bond number. While the asymptotic packing fraction decreases as the inverse of the Bond number. For mixtures, when the fraction of magnetized grains in the pile is increased, the characteristic time increases while the asymptotic packing fraction decreases. A simple mesoscopic model based on the formation of granular chains along the magnetic field direction is proposed to explain the observed macroscopic properties of the packings.

Completely inelastic ball

This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter Gamma. A pseudochaotic behavior, consisting in arbitrarily long and complex periodic sequences, is observed through this generic system.

Dynamics of a bouncing droplet onto a vertically vibrated interface

Low viscosity (<100 cSt) silicon oil droplets are placed on a high viscosity (1000 cSt) oil bath that vibrates vertically. The viscosity difference ensures that the droplet is more deformed than the bath interface. Droplets bounce periodically on the bath when the acceleration of its sinusoidal motion is larger than a threshold value. The threshold is minimum for a particular frequency of excitation: droplet and bath motions are in resonance. The bouncing droplet has been modeled by considering the deformation of the droplet and the lubrication force exerted by the air layer between the droplet and the bath. Threshold values are predicted and found to be in good agreement with our measurements.

Lifetime of a bouncing droplet

When a droplet is gently laid onto the surface of the same liquid, it stays at rest for a moment before coalescence. The coalescence can be delayed and sometimes inhibited by injecting fresh air under the droplet. This can happen when the surface of the bath oscillates vertically. In this case the droplet basically bounces on the interface. The lifetime of the droplet has been studied with respect to the amplitude and the frequency of the excitation. The lifetime decreases when the acceleration increases. The thickness of the air film between the droplet and the bath has been investigated using interference fringes obtained when the system is illuminated by low-pressure sodium lamps. Moreover, both the shape evolution and the motion of the droplet center of mass have been recorded in order to evidence the phase offset between the deformation and the trajectory. A short lifetime is correlated to a small air-film thickness and to a large phase offset between the maximum of deformation and the minimum of the vertical position of the center of mass.

Controlling the partial coalescence of a droplet on a vertically vibrated bath

A method is proposed to stop the cascade of partial coalescences of a droplet laid on a liquid bath. The strategy consists of vibrating the bath in the vertical direction in order to keep small droplets bouncing. Since large droplets are not able to bounce, they partially coalesce until they reach a critical size. The system behaves as a low pass filter: droplets smaller than the critical size are selected. This size has been investigated as a function of the acceleration and the frequency of the bath vibration. Results suggest that the limit size for bouncing is related to the first mode of the droplet deformation.

Some aspects of electrical conduction in granular systems of various dimensions

We report on measurements of the electrical conductivity in both a 2D triangular lattice of metallic beads and in a chain of beads. The voltage/current characteristics are qualitatively similar in both experiments. At low applied current, the voltage is found to increase logarithmically in good agreement with a model of widely distributed resistances in series. At high enough current, the voltage saturates due to the local welding of microcontacts between beads. The frequency dependence of the saturation voltage gives an estimate of the size of these welded microcontacts. The DC value of the saturation voltage ( approximately 0.4 V per contact) gives an indirect measure of the number of welded contact carrying the current within the 2D lattice. Also, a new measurement technique provides a map of the current paths within the 2D lattice of beads. For an isotropic compression of the 2D granular medium, the current paths are localized in few discrete linear paths. This quasi-one-dimensional nature of the electrical conductivity thus explains the similarity between the characteristics in the 1D and 2D systems.

Critical parameters for the partial coalescence of a droplet

The partial coalescence of a droplet onto a planar liquid-liquid interface is investigated experimentally by tuning the viscosities of both liquids. The problem mainly depends on four dimensionless parameters: The Bond number (gravity vs surface tension), the Ohnesorge numbers (viscosity in both fluids vs surface tension), and the density relative difference. The ratio between the daughter droplet size and the mother droplet size is investigated as a function of these dimensionless numbers. Global quantities such as the available surface energy of the droplet have been measured during the coalescence. The capillary waves propagation and damping are studied in detail. The relation between these waves and the partial coalescence is discussed. Additional viscous mechanisms are proposed in order to explain the asymmetric role played by both viscosities.

Precursors to avalanches in a granular monolayer

We investigate the stability of a granular monolayer composed of spherical grains on an inclined plate. When the tilt angle alpha increases, some reorganizations are observed throughout the pile. The packing fraction rho of the packing evolves by successive jumps. Those discontinuous events precede the collapse of the pile at a critical angle alphac. The occurrence of precursors before avalanches is modeled by stop-and-go motions of blocks due to the competition between sliding friction and the Janssen effect [J. Durand, (Springer-Verlag, New York, 2000)].

Dynamics of a bouncing dimer

We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited mode has a novel horizontal drift in which one end of the dimer stays on the plate during most of the cycle, while the other end bounces in phase with the plate. The speed and direction of the drift depend on the aspect ratio of the dimer. We employ event-driven simulations based on a detailed treatment of frictional interactions between the dimer and the plate in order to elucidate the nature of the transport mechanism in the drift mode.

Stability limit of a granular monolayer

A granular monolayer is composed by spherical grains on a horizontal plate. The plate is then tilted until the monolayer breaks down. This critical angle has been measured for different widths and heights of the rectangular monolayer. The highest critical angles are found when one of these two characteristic lengths is less than about 30 bead diameters. When the polydispersity is less than one percent, the monolayer may be stable till angles close to 90( degrees ). Arches induce large critical angles. On the other hand, for a large and high monolayer, the critical angle saturates towards a lower value. This angle is related to the static friction of a grain on the plate. A model based on the block dynamics is proposed to describe the behavior of the avalanche angle as a function of the size of the monolayer and the polydispersity of the beads.

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.

Rolling and slipping motion of Euler's disk

We present an experimental study of the motion of a circular disk spun onto a table. With the help of a high speed video system, the temporal evolution of (i) the inclination angle alpha, (ii) the angular velocity omega, and (iii) the precession rate Omega are studied. The influence of the mass of the disk as well as the friction between the disk and the supporting surface are considered. Both inclination angle and angular velocity are observed to decrease according to a power law. We also show that the precession rate diverges as the motion stops. Measurements are performed very near the collapse as well as on long range times. Times to collapse have been also measured. Results are compared with previous theoretical and experimental works. The major source of energy dissipation is found to be the slipping of the disk on the plane.

Reexamination of the Branly effect

The electrical resistance of a metallic granular packing has been recorded at room temperature. A nearby burster between which sparks are produced, induces a decrease in the resistance of the granular packing as described in the works of Branly. Our measurements emphasize that the decrease is continuous and the resistance variations behave like a stretched exponential law due to the creation of new electrical paths as in nucleation-growth soldering processes. This behavior has been identified to be a diffusionlike process.