Fluctuation-Induced Interaction in Turbulent Flows

Fluctuation-induced forces are observed in numerous physical systems spanning from quantum to macroscopic scale. However, there is as yet no experimental report of their existence in hydrodynamic turbulence. Here, we present evidence of an attraction force mediated via turbulent fluctuations by using two walls locally confining 2D turbulence. This long-range interaction is a function of the wall separation and the energy injection rate in the turbulent flow. As the wall spacing decreases, the confined flow becomes less energetic and more anisotropic in the bounded domain, producing stronger attraction. The mechanism of force generation is rooted in a nontrivial fluid-wall coupling where coherent flow structures are guided by the cavity walls. For the narrowest cavities studied, a resonance phenomenon at the flow forcing scale leads to a complex short-range interaction. The results could be relevant to problems encountered in a range of fields from industrial multiphase flows to modeling of planetary formation.

From collections of independent, mindless robots to flexible, mobile, and directional superstructures

A swarm of simple active particles confined in a flexible scaffold is a promising system to make mobile and deformable superstructures. These soft structures can perform tasks that are difficult to carry out for monolithic robots because they can infiltrate narrow spaces, smaller than their size, and move around obstacles. To achieve such tasks, the origin of the forces the superstructures develop, how they can be guided, and the effects of external environment, especially geometry and the presence of obstacles, need to be understood. Here, we report measurements of the forces developed by such superstructures, enclosing a number of mindless active rod-like robots, as well as the forces exerted by these structures to achieve a simple function, crossing a constriction. We relate these forces to the self-organization of the individual entities. Furthermore, and based on a physical understanding of what controls the mobility of these superstructures and the role of geometry in such a process, we devise a simple strategy where the environment can be designed to bias the mobility of the superstructure, giving rise to directional motion. Simple tasks-such as pulling a load, moving through an obstacle course, or cleaning up an arena-are demonstrated. Rudimentary control of the superstructures using light is also proposed. The results are of relevance to the making of robust flexible superstructures with nontrivial space exploration properties out of a swarm of simpler and cheaper robots.

Near-Field Probe of Thermal Fluctuations of a Hemispherical Bubble Surface

We report measurements of resonant thermal capillary oscillations of a hemispherical liquid gas interface obtained using a half bubble deposited on a solid substrate. The thermal motion of the hemispherical interface is investigated using an atomic force microscope cantilever that probes the amplitude of vibrations of this interface versus frequency. The spectrum of such nanoscale thermal oscillations of the bubble surface presents several resonance peaks and reveals that the contact line of the hemispherical bubble is pinned on the substrate. The analysis of these peaks allows us to measure the surface viscosity of the bubble interface. Minute amounts of impurities are responsible for altering the rheology of the pure water surface.

Viscous Effects on Inertial Drop Formation

The breakup of low-viscosity droplets like water is a ubiquitous and rich phenomenon. Theory predicts that in the inviscid limit one observes a finite-time singularity, giving rise to a universal power law, with a prefactor that is universal for a given density and surface tension. This universality has been proposed as a powerful tool to determine the dynamic surface tension at short time scales. We combine high-resolution experiments and simulations to show that this universality is unobservable in practice: in contrast to previous studies, we show that fluid and system parameters do play a role; notably a small amount of viscosity is sufficient to alter the breakup dynamics significantly.

Large variability in the motility of spiroplasmas in media of different viscosities

Spiroplasmas are bacteria that do not possess flagella and their motility is linked to kink propagation coupled to changes in the cell body helicity. While the motility of bacteria with flagellar motion has been studied extensively, less work has been devoted to the motility of spiroplasmas. We first show that the motility of such bacteria has large variability from individual to individual as well as large fluctuations in time. The Brownian motion of such bacteria both in orientation and translation is also highlighted. We propose a simple model to disentangle the different components of this motility by examining trajectories of single bacteria in different viscosity solvents. The mean velocity of the bacteria turns out to depend on the viscosity of the medium as it increases with viscosity. Further, the temporal fluctuations of the bacteria motility turn out to be very strong with a direct link to tumbling events particular to this bacteria.

Boundaries Control Collective Dynamics of Inertial Self-Propelled Robots

Simple ingredients, such as well-defined interactions and couplings for the velocity and orientation of self-propelled objects, are sufficient to produce complex collective behavior in assemblies of such entities. Here, we use assemblies of rodlike robots made motile through self-vibration. When confined in circular arenas, dilute assemblies of these rods act as a gas. Increasing the surface fraction leads to a collective behavior near the boundaries: polar clusters emerge while, in the bulk, gaslike behavior is retained. The coexistence between a gas and surface clusters is a direct consequence of inertial effects as shown by our simulations. A theoretical model, based on surface mediated transport accounts for this coexistence and illustrates the exact role of the boundaries. Our study paves the way towards the control of collective behavior: By using deformable but free to move arenas, we demonstrate that the surface induced clusters can lead to directed motion, while the topology of the surface states can be controlled by biasing the motility of the particles.

Viscoelastic Drag Forces and Crossover from No-Slip to Slip Boundary Conditions for Flow near Air-Water Interfaces

The "free" water surface is generally prone to contamination with surface impurities, be they surfactants, particles, or other surface active agents. The presence of such impurities can modify flow near such interfaces in a drastic manner. Here we show that vibrating a small sphere mounted on an atomic force microscope cantilever near a gas bubble immersed in water is an excellent probe of surface contamination. Both viscous and elastic forces are exerted by an air-water interface on the vibrating sphere even when very low doses of contaminants are present. The viscous drag forces show a crossover from no-slip to slip boundary conditions while the elastic forces show a nontrivial variation as the vibration frequency changes. We provide a simple model to rationalize these results and propose a simple way of evaluating the concentration of such surface impurities.

Structure of velocity distributions in shock waves in granular gases with extension to molecular gases

Velocity distributions in normal shock waves obtained in dilute granular flows are studied. These distributions cannot be described by a simple functional shape and are believed to be bimodal. Our results show that these distributions are not strictly bimodal but a trimodal distribution is shown to be sufficient. The usual Mott-Smith bimodal description of these distributions, developed for molecular gases, and based on the coexistence of two subpopulations (a supersonic and a subsonic population) in the shock front, can be modified by adding a third subpopulation. Our experiments show that this additional population results from collisions between the supersonic and subsonic subpopulations. We propose a simple approach incorporating the role of this third intermediate population to model the measured probability distributions and apply it to granular shocks as well as shocks in molecular gases.

Taming contact line instability for pattern formation

Coating surfaces with different fluids is prone to instability producing inhomogeneous films and patterns. The contact line between the coating fluid and the surface to be coated is host to different instabilities, limiting the use of a variety of coating techniques. Here we take advantage of the instability of a receding contact line towards cusp and droplet formation to produce linear patterns of variable spacings. We stabilize the instability of the cusps towards droplet formation by using polymer solutions that inhibit this secondary instability and give rise to long slender cylindrical filaments. We vary the speed of deposition to change the spacing between these filaments. The combination of the two gives rise to linear patterns into which different colloidal particles can be embedded, long DNA molecules can be stretched and particles filtered by size. The technique is therefore suitable to prepare anisotropic structures with variable properties.

Spreading of an Oil-in-Water Emulsion on a Glass Plate: Phase Inversion and Pattern Formation

Rigid blade coating of glass plates by oil-in-water emulsions stabilized by surfactants is studied. Complete surface coverage is obtained only for speeds exceeding a threshold velocity dependent on the height between the blade end and the surface. Below this threshold, the emulsion can be inverted in the vicinity of the blade. The inversion dynamics of the oil-in-water emulsion and the deposition patterns induced by this phase inversion are studied using a microscope mounted set up. We show that these dynamics are universal for different volume fractions and deposition velocities. This inversion as well as the destabilization of the emulsion film deposited at high speeds gives rise to different patterns on the glass surface. These patterns are discussed in terms of the emulsion characteristics as well as the deposition velocity.

Scaling of near-wall flows in quasi-two-dimensional turbulent channels

The law of the wall and the log law rule the near-wall mean velocity profile of three-dimensional turbulent flows. These well-known laws, which are validated by legions of experiments and simulations, may be universal. Here, using a soap-film channel, we report the first experimental test of these laws in quasi-two-dimensional turbulent channel flows under two disparate turbulent spectra. We find that despite the differences with three-dimensional flows, the laws prevail, albeit with notable distinctions: the two parameters of the log law are markedly distinct from their three-dimensional counterpart; further, one parameter (the von Kármán constant) is independent of the spectrum whereas the other (the offset of the log law) depends on the spectrum. Our results suggest that the classical theory of scaling in wall-bounded turbulence is incomplete wherein a key missing element is the link with the turbulent spectrum.

Rheology of polymer solutions using colloidal-probe atomic force microscopy

We use colloidal-probe atomic force microscope (AFM) to study the rheological behavior of polymer solutions confined between two surfaces: the surface of a sphere and a flat surface on which the fluid is deposited. Measurements of the hydrodynamic force exerted on the sphere by the flowing liquid allowed retrieving the viscosity of the solution for different distances between the sphere and the flat surface. This method has been experimentally tested for Newtonian fluids for which the viscosity does not vary versus the gap dimensions. On the other hand, for non-Newtonian fluids, such as the large molecular weight polymer solutions used here, the measured viscosity depends on the gap height D between the flat surface and the sphere. The decrease of the viscosity versus gap height is similar to previously observed variations in colloidal suspensions. Depletion of polymers in the gap region due to the high shear rates involved is a possible cause for such a variation.

Unstable blast shocks in dilute granular flows

Shocks and blasts can be readily obtained in granular flows be they dense or dilute. Here, by examining the propagation of a blast shock in a dilute granular flow, we show that such a front is unstable with respect to transverse variations of the density of grains. This instability has a well-defined wavelength which depends on the density of the medium and has an amplitude which grows as an exponential of the distance traveled. These features can be understood using a simple model for the shock front, including dissipation which is inherent to granular flows. While this instability bears much resemblance to that anticipated in gases, it is distinct and has special features we discuss here.

Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions

The flow of polymer solutions is examined in a flow geometry where a jet is used to inject the viscoelastic solution into a cylindrical tube. We show that this geometry allows for the generation of a "turbulentlike" flow at very low Reynolds numbers with a fluctuation level which can be as high as 30%. The fluctuations increase with an increase in solution polymer concentration and flow velocity. The turbulent fluctuations decay downstream for small flow velocities but persist for high velocities. The statistical properties of the generated fluctuations indicate that this turbulentlike flow is different from previously studied flows displaying elastic turbulence and shows a direct cascade of energy to small scales with practically no intermittency.

Experimental evidence of a Rayleigh-plateau instability in free falling granular jets

A granular jet falling out of a funnel shaped container, subjected to small vertical vibrations, develops an instability farther downstream as may happen for ordinary liquid jets. Our results show that this instability is reminiscent of the Rayleigh-Plateau capillary instability leading to breakup of the jet at large scales. The first stages of this instability are captured in detail allowing a determination of the dispersion relation. Surface tensions measured in this unstable regime (of the order of mN/m) are in agreement with previously reported measurements carried out at much smaller scales. This instability and the breakup of the jet can be inhibited when the effect of the surrounding medium (air) is reduced by enclosing the jet in an evacuated chamber, showing that the effective surface tension measured is the result of a strong interaction with the surrounding air.

From intermittent to nonintermittent behavior in two dimensional thermal convection in a soap bubble

Turbulent thermal convection in half a soap bubble heated from below displays a new and surprising transition from intermittent to nonintermittent behavior for the temperature field. This transition is observed here by studying the high order moments of temperature increments. For high temperature gradients, these structure functions display Bolgiano-like scaling predicted some 60 years ago with no observable deviations. The probability distribution functions of these increments are Gaussian throughout the scaling range. These measurements are corroborated with additional velocity structure function measurements.

Drag coefficient for a circular obstacle in a quasi-two-dimensional dilute supersonic granular flow

The measurement of the drag coefficient of a dilute granular flow around a cylinder is carried out over a wide range of Knudsen numbers. The variation of this coefficient shows a smooth transition from a freely falling grains regime to a continuous flow regime. This is reminiscent of the behavior of gases in the supersonic regime. This transition is accompanied by remarkable changes of the density and velocity profiles near the cylinder. A simple model is proposed for the transition regime which is in agreement with the experimental measurements.

Effect of surface tension variations on the pinch-off behavior of small fluid drops in the presence of surfactants

It is shown experimentally that surfactants can change the thinning rate of fluid necks undergoing rupture. In the case of two-fluid pinch-off, two or three linear regimes are observed for the variation of the neck radius versus time. The surface tension in the neck region changes with time, as a result of surfactant depletion. Similar results are obtained for the case of a single fluid pinching in air. The depletion of surfactant can be either partial or complete depending on the rate of transport of the surfactant from the bulk to the surface.

Blast shocks in quasi-two-dimensional supersonic granular flows

In a thin, dilute, and fast flowing granular layer, the impact of a small sphere generates a fast growing hole devoid of matter. The growth of this hole is studied in detail, and its dynamics is found to mimic that of blast shocks in gases. This dynamics can be decomposed into two stages: a fast initial stage (the blast) and a slower growth regime whose growth velocity is given by the speed of sound in the medium used. A simple model using ingredients already invoked for the case of blast shocks in gases but including the inelastic nature of collisions between grains accounts accurately for our results. The system studied here allows for a detailed study of the full dynamics of a blast as it relaxes from a strong to a weak shock and later to an acoustic disturbance.

Shock front width and structure in supersonic granular flows

The full structure of a shock front around a blunt body in a quasi-two-dimensional granular flow is studied. Two features, a large density gradient and a very small thickness of the front, characterize this shock and make it different from shocks in molecular gases. Both of these features can be understood using a modified version of the granular kinetic theory. Our model separates the particles into two subpopulations: fast particles having experienced no collisions and randomly moving particles. This separation is motivated by direct measurements of the particle velocities which show a bimodal distribution. Our results not only shed new light on the use of the granular kinetic theory under extreme conditions (shock formation) but bring new insight into the physics of shocks in general.

Velocity profiles of water flowing past solid glass surfaces using fluorescent nanoparticles and molecules as velocity probes

Measurements of the velocity profile of water flowing on a glass surface using fluorescent nanoparticles and single fluorescent molecules as velocity probes show that the no slip boundary condition holds down to at least 10 nm from the surface. For water flowing on a hydrophobic solid surface, silanized glass, the no slip boundary condition fails, and a slip length of 45 nm is measured. These velocity measurements are complemented with atomic force microscopy measurements of dissipation on a small sphere oscillating near the surface with results in agreement with the velocity profiles.

Thermal convection and emergence of isolated vortices in soap bubbles

A novel thermal convection cell consisting of half a soap bubble heated at the equator is introduced to study thermal convection and the movement of isolated vortices. The soap bubble, subject to stratification, develops thermal convection at its equator. A particular feature of this cell is the emergence of isolated vortices. These vortices resemble hurricanes or cyclones and similarities between our observed structures and these natural objects are found. This is brought forth through a study of the mean square displacement of these objects showing signs of superdiffusion.

Drag enhancement with polymers

Drag on a cylinder can be enhanced in the presence of polymers. This enhancement is directly related to the interaction of the polymers with the flow around the obstacle. The presence of the polymers modifies the flow in the vicinity of the cylinder giving rise to a band of higher shear, large molecular elongations and large velocity fluctuations. The measured drag on the cylinder is directly related to the modification of the flow field by the presence of the polymers.

Dynamics of impact cratering in shallow sand layers

When a solid sphere impacts a shallow layer of sand deposited on a solid surface, a crater can be obtained. The dynamics of the opening of the crater can be followed accurately. During this opening, the radius of the crater can be conveniently modeled by an exponential saturation with a well-defined time constant. The crater then closes up partially once the opening phase is over as the sand avalanches down the slope of the crater. We here present a detailed study of the full dynamics of the crater formation as well as the dynamics of the corrola formed during this process. A simple model accounts for most of our observations.

Where surface physics and fluid dynamics meet: Rupture of an amphiphile layer by fluid flow

We investigate the fluctuating pattern created by a jet of fluid impingent upon an amphiphile-covered surface. This microscopically thin layer is initially covered with 50 microm floating particles so that the layer can be visualized. A vertical jet of water located below the surface and directed upward drives a hole in this layer. The hole is particle-free and is surrounded by the particle-laden amphiphile region. The jet ruptures the amphiphile layer creating a particle-free region that is surrounded by the particle-covered surface. The aim of the experiment is to understand the (fluctuating) shape of the ramified interface between the particle-laden and particle-free regions.

Role of fluctuation-induced interactions in the axial segregation of granular materials

The movement of a few large diameter spheres immersed in a granular medium composed of smaller beads in a rotating cylinder is studied. We evidence attractions and repulsions between the large spheres depending on the rotation frequency. The large spheres also show relative position fluctuations which are Gaussian. A complete study of this problem sheds new light on the problem of size segregation in granular materials and points to the importance of fluctuation-induced interactions.

Conformation statistics of a deformable material line in two-dimensional turbulence

We have observed the fluctuations of the centerline position of a thin column of water injected into a turbulent soap film. As the turbulence intensity increases, the second order structure function of the centerline position increments undergoes a change between different power law scaling regimes. These scalings indicate that the centerline position makes a continuous transition from an analytic to a non-analytic function. Cusps and other singular configurations of the column occur at higher turbulent intensities. Since the column supports random wave patterns, we propose that this experiment could serve as a test bed for theories of wave turbulence in one dimension.

Experiments and direct numerical simulations of two-dimensional turbulence

Experiments and direct numerical simulations reveal the coexistence of two cascades in two-dimensional grid turbulence. Several features of this flow such as the energy density and the scalar spectra are found to be consistent with well known theoretical predictions. The energy transfer function displays the expected up-scale energy transfers. The vorticity correlation function is logarithmic and thus consistent with recently proposed models.

Batchelor scaling in fast-flowing soap films

The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40 years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.

Polymers suppress the inverse transfers of energy and the enstrophy flux fluctuations in two-dimensional turbulence

The addition of minute amounts of a flexible polymer to two-dimensional turbulence produced in fast-flowing soap films affects large scales and small scales differently. For large scales, the inverse transfers of energy are suppressed. For small scales, where mean quantities are barely affected, the enstrophy flux fluctuations are significantly reduced, making the flow less chaotic.

Dispersion in the enstrophy cascade of two-dimensional decaying grid turbulence

The use of vertically flowing soap films allows one to obtain decaying two-dimensional turbulence with an enstrophy cascade range. Here we use this property to study the dispersion of a fine column of slightly heated liquid entering the turbulent flow. The width of this column increases with time in an exponential manner consistent with theoretical predictions for the average dispersion of particle pairs despite the multiparticle nature of the dispersion studied. Other features such as Gaussian mean profiles of the temperature across the channel width are also evidenced.

Granular flow trapped on an incline: dynamics of the sandpile

Experimental results have been recently reported for the dynamics of two-dimensional sand fronts formed by the trapping of a flow running down an inclined plane. We explain the scaling law observed for the front profiles and give their analytic expression using a simple phenomonelogical model for interfacial shapes and interfacial flows of granular materials.

Self-similar dynamic quasi-two-dimensional sand fronts

We report on a study of advancing quasi-two-dimensional sand fronts on an inclined flat and thin strip confined between two vertical plates. These fronts form when a thin initial stream of sand running down the flat obstacle gets trapped at some distance from the injection point. Right after this trapping, the front starts to advance upstream and grow in time. The shapes at successive times are found to be self-similar in time. The stability conditions for the obtained fronts are also outlined. A simple model for interface dynamics gives reasonable predictions for the observed shapes.

Polymers in 2D turbulence: suppression of large scale fluctuations

Small quantities of a long chain molecule or polymer affect two-dimensional turbulence in unexpected ways. Their presence inhibits the transfers of energy to large scales causing their suppression in the energy density spectrum. This also leads to the change of the spectral properties of a passive scalar which turns out to be highly sensitive to the presence of energy transfers.

Thickness fluctuations in turbulent soap films

Rapidly flowing soap films provide a simple and attractive system to study two-dimensional hydrodynamics and turbulence. By measuring the rapid fluctuations of the thickness of the film in the turbulent regime, we find that the statistics of these fluctuations closely resemble those of a passive scalar field in a turbulent flow. The scalar spectra are well described by Kolmogorov-like scaling while the high-order moments show clear deviations from regular scaling just like dye or temperature fluctuations in 3D turbulent flows.

Fluctuation and dissipation in liquid-crystal electroconvection

In this experiment a steady-state current is maintained through a liquid-crystal thin film. When the applied voltage is increased through a threshold, a phase transition is observed to a convective state characterized by the chaotic motion of rolls. Above the threshold, an increase in power consumption is observed that is manifested by an increase in the mean conductivity. A sharp increase in the ratio of the power fluctuations to the mean power dissipated is observed above the transition. This ratio is compared to the predictions of the fluctuation theorem of Gallavotti and Cohen using an effective temperature associated with the rolls' chaotic motion.

Noncoalescing drops

A pure water drop coalesces almost immediately with a pure water surface. Minute amounts of surfactant can alter this process dramatically. When the drop is released towards the surface of the solution from a certain height smaller than a well defined critical height, the drop of surfactant solution either remains on the surface for a specific time or coalesces immediately. The statistics of the residence time are systematically measured along with the critical heights necessary for coalescence. It turns out that the surface elasticity controls coalescence in such a situation.

Dynamic sand dunes

When sand falling in the spacing between two plates goes past an obstacle, a dynamic dune with a parabolic shape and an inner triangular region of nonflowing or slowly creeping sand forms. The angle of the triangular zone increases with the height of the dune and saturates at a value determined by the geometry of the cell. The width of the dune, related to the radius of curvature at the tip, shows universal features versus its height rescaled by geometrical parameters. The velocity profile in the flowing part is determined and found to be nonlinear. The parabolic shape can be accounted for using a simple driven convection-diffusion equation for the interface.

Inhibition of the finite-time singularity during droplet fission of a polymeric fluid

When a drop of fluid detaches from a capillary, singular behavior ensues. We show that the addition of very small amounts of polymer inhibits this singularity in an abrupt way and gives rise, after a period of self-similar dynamics as for simple liquids, to long-lived cylindrical necks or filaments which thin exponentially in time. This abrupt change occurs when the elongation rate epsilon* becomes comparable to the inverse of the polymer relaxation time leading to a large elongational viscosity eta(E) of the dilute polymer solution.

Dynamic light scattering from lyotropic lamellar phases subjected to a flow field

Dynamic light scattering experiments on lyotropic lamellar phases of brine and surfactant subjected to a flow field have been realized. The obtained results reveal that the relaxation times measured depend strongly on the velocity of the flow. This dependence is indicative of an increase of the effective elasticity modulus K and a decrease of the effective compressibility modulus (-)B of the lamellar phase with the flow velocity. This leads to the conclusion that the shear can induce a suppression of the undulation fluctuations of the bilayers of the lamellar phase. Our results show also that the rigidity of the membranes decreases as the salt concentration of the sample increases.

Shear-induced first-order sponge-to-lamellar transition in a lyotropic surfactant system

We report a shear-induced sponge (L3) to lamellar (L(alpha)) transition in a surfactant system. Under a constant shear rate, after a delay time t(n) we observe random nucleation and subsequent growth of the L(alpha) phase, demonstrating that the shear-induced transition is first order. A simple argument for the energy of a two-dimensional nucleus accounts for the observed delay and its shear-rate dependence.

Observations of the collapse of dilute lyotropic lamellar phases under shear flow

Experimental evidence of the collapse of dilute lamellar phases due to shear flow is presented. Two systems are used: one composed of brine and an ionic surfactant, and another composed of water, a nonionic surfactant, and cosurfactant. We observe this transition for a range of lamellar spacings and brine salinity. The results are in reasonable agreement with recent theory in which the suppression of fluctuations by shear plays an important role.

Probability density functions of the enstrophy flux in two dimensional grid turbulence

Probability density functions of the enstrophy flux in two dimensional grid turbulence are found to be strongly non-Gaussian and can be mimicked by stretched exponential functions. Evidence of this behavior is found in experiments using turbulent soap films and numerical simulations. The enstrophy flux itself is found to be constant for a range of scales corresponding to the enstrophy cascade.

Coupling between flow and structure for a lamellar surfactant phase

The flow-structure relation of lamellar phases is studied using rheometry and cross-polarized microscopy under flow. The equilibrium phases show different defects. Low salinities lead to very viscous, "onion" phases, whereas at high salinity, a low viscosity plane lamellar phase is found. Under shear, the latter shows a sudden transition to a viscoelastic gel, with a texture and viscosity very similar to that of the onions. Gelation occurs after a certain delay time, increasing rapidly with salinity, by the nucleation of onions. This allows one to relate the delay time to the defect energy.

Numerical study of grid turbulence in two dimensions and comparison with experiments on turbulent soap films

Numerical simulations of two dimensional channel flow behind an array of cylinders are carried out for high Reynolds numbers. Results for the energy density and enstrophy spectra, as well as for velocity and vorticity differences, are presented. The results compare favorably with recent experiments carried out with turbulent soap films. Some marked deviations from expected behavior are found for the enstrophy spectrum and for moments of vorticity increments.

Delayed fracture of an inhomogeneous soft solid

The spontaneous fracture of polymer gels was studied. Contrary to crystalline solids, where fracture usually happens instantaneously at a well-defined breaking strength, the fracture of a polymer gel can occur with a delay. When a constant force was applied, the cracks nucleated and started to propagate after a delay that can be as long as 15 minutes, depending on the force. This phenomenon can be understood by calculating the activation energy for crack nucleation in arbitrary dimension and accounting for the inhomogeneity of the gel network in terms of its fractal dimension.