Deformation and flow of a two-dimensional foam under continuous shear

We investigate the flow properties of a two-dimensional aqueous foam submitted to a quasistatic shear in a Couette geometry. A strong localization of the flow (shear banding) at the edge of the moving wall is evidenced, characterized by an exponential decay of the average tangential velocity. Moreover, the analysis of the rapid velocity fluctuations reveals self-similar dynamical structures consisting of clusters of bubbles rolling as rigid bodies. To relate the instantaneous (elastic) and time-averaged (plastic) components of the strain, we develop a stochastic model where irreversible rearrangements are activated by local stress fluctuations originating from the rubbing of the wall. This model gives a complete description of our observations and is also consistent with data obtained on granular shear bands by other groups.Comment: 5 pages, 2 figure

Texture-induced modulations of friction force: the fingerprint effect

Dry solid friction is often accompanied by force modulations originating from stick-slip instabilities. Here a distinct, quasi-static mechanism is evidenced leading to quasi-periodic force oscillations during sliding contact between an elastomer block, whose surface is patterned with parallel grooves, and finely abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the period of the grooves. A mechanical model is proposed that provides a quantitative prediction for the amplitude of the force modulations as a function of the normal load, the period of the grooves and the roughness characteristics of the substrate. The model's main ingredient is the non-linearity of the friction law. Since such non-linearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and might in particular have important consequences in human (or humanoid) active digital touch.Comment: 4 page

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

Experimental evidence of non-Amontons behaviour at a multicontact interface

We report on normal stress field measurements at the multicontact interface between a rough elastomeric film and a smooth glass sphere under normal load, using an original MEMS-based stress sensing device. These measurements are compared to Finite Elements Method calculations with boundary conditions obeying locally Amontons' rigid-plastic-like friction law with a uniform friction coefficient. In dry contact conditions, significant deviations are observed which decrease with increasing load. In lubricated conditions, the measured profile recovers almost perfectly the predicted profile. These results are interpreted as a consequence of the finite compliance of the multicontact interface, a mechanism which is not taken into account in Amontons' law

An elasto-visco-plastic model for immortal foams or emulsions

A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.Comment: 69 pages, 29 figure

A study of the static yield stress in a binary Lennard-Jones glass

The stress-strain relations and the yield behavior of model glass (a 80:20 binary Lennard-Jones mixture) is studied by means of MD simulations. First, a thorough analysis of the static yield stress is presented via simulations under imposed stress. Furthermore, using steady shear simulations, the effect of physical aging, shear rate and temperature on the stress-strain relation is investigated. In particular, we find that the stress at the yield point (the ``peak''-value of the stress-strain curve) exhibits a logarithmic dependence both on the imposed shear rate and on the ``age'' of the system in qualitative agreement with experiments on amorphous polymers and on metallic glasses. In addition to the very observation of the yield stress which is an important feature seen in experiments on complex systems like pastes, dense colloidal suspensions and foams, further links between our model and soft glassy materials are found. An example are hysteresis loops in the system response to a varying imposed stress. Finally, we measure the static yield stress for our model and study its dependence on temperature. We find that for temperatures far below the mode coupling critical temperature of the model ($Tc = 0.435$), \sigmay decreases slowly upon heating followed by a stronger decrease as \Tc is approached. We discuss the reliability of results on the static yield stress and give a criterion for its validity in terms of the time scales relevant to the problem.Comment: 14 pages, 18 figure

Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations

The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N=40,000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale \xi is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em non-affine} part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table

Theory on quench-induced pattern formation: Application to the isotropic to smectic-A phase transitions

During catastrophic processes of environmental variations of a thermodynamic system, such as rapid temperature decreasing, many novel and complex patterns often form. To understand such phenomena, a general mechanism is proposed based on the competition between heat transfer and conversion of heat to other energy forms. We apply it to the smectic-A filament growth process during quench-induced isotropic to smectic-A phase transition. Analytical forms for the buckling patterns are derived and we find good agreement with experimental observation [Phys. Rev. {\bf E55} (1997) 1655]. The present work strongly indicates that rapid cooling will lead to structural transitions in the smectic-A filament at the molecular level to optimize heat conversion. The force associated with this pattern formation process is estimated to be in the order of $10^{-1}$ piconewton.Comment: 9 pages in RevTex form, with 3 postscript figures. Accepted by PR

Sensorimotor computation underlying phototaxis in zebrafish

Animals continuously gather sensory cues to move towards favourable environments. Efficient goal-directed navigation requires sensory perception and motor commands to be intertwined in a feedback loop, yet the neural substrate underlying this sensorimotor task in the vertebrate brain remains elusive. Here, we combine virtual-reality behavioural assays, volumetric calcium imaging, optogenetic stimulation and circuit modelling to reveal the neural mechanisms through which a zebrafish performs phototaxis, i.e. actively orients towards a light source. Key to this process is a self-oscillating hindbrain population (HBO) that acts as a pacemaker for ocular saccades and controls the orientation of successive swim-bouts. It further integrates visual stimuli in a state-dependent manner, i.e. its response to visual inputs varies with the motor context, a mechanism that manifests itself in the phase-locked entrainment of the HBO by periodic stimuli. A rate model is developed that reproduces our observations and demonstrates how this sensorimotor processing eventually biases the animal trajectory towards bright regions

Evaporation of liquid nitrogen droplets in superheated immiscible liquids

Liquid nitrogen or other cryogenic liquids have the potential to replace or augment current energy sources in cooling and power applications. This can be done by the rapid evaporation and expansion processes that occur when liquid nitrogen is injected into hotter fluids in mechanical expander systems. In this study, the evaporation process of single liquid nitrogen droplets when submerged into n-propanol, methanol, n-hexane, and n-pentane maintained at 294 K has been investigated experimentally and numerically. The evaporation process is quantified by tracking the growth rate of the resulting nitrogen vapour bubble that has an interface with the bulk liquid. The experimental data suggest that the bubble volume growth is proportional to the time and the bubble growth rate is mainly determined by the initial droplet size. A comparison between the four different bulk liquids indicates that the evaporation rate in n-pentane is the highest, possibly due to its low surface tension. A scaling law based on the pure diffusion-controlled evaporation of droplet in open air environment has been successfully implemented to scale the experimental data. The deviation between the scaling law predictions and the experimental data for 2-propanol, methanol and n-hexane vary between 4% and 30% and the deviation for n-pentane was between 24% and 65%. The more detailed bubble growth rates have been modelled by a heuristic one-dimensional, spherically symmetric quasi-steady-state confined model, which can predict the growth trend well but consistently underestimate the growth rate. A fixed effective thermal conductivity is then introduced to account for the complex dynamics of the droplet inside the bubble and the subsequent convective processes in the surrounding vapour, which leads to a satisfactory quantitative prediction of the growth rate