Pierre Jop

A constitutive law for dense granular flows

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

Initiation of granular surface flows in a narrow channel

We experimentally investigate how a long granular pile confined in a narrow channel destabilizes when it is inclined above the angle of repose. A uniform flow then develops, which is localized at the free surface. It first accelerates before reaching a steady uniform regime. During this process, an apparent erosion is observed and the thickness of the flowing layer increases. We precisely study the evolution of the vertical velocity profile in this transient regime. The measurements are compared with the prediction of a viscoplastic model [Jop et al., Nature 441, 727 (2006)].

Hydrodynamic modeling of granular flows in a modified Couette cell.

We present simulations of granular flows in a modified Couette cell, using a continuum model recently proposed for dense granular flows. Based on a friction coefficient, which depends on an inertial number, the model captures the positions of the wide shear bands. We show that a smooth transition in velocity-profile shape occurs when the height of the granular material is increased, leading to a differential rotation of the central part close to the surface. The numerical predictions are in qualitative agreement with previous experimental results. The model provides predictions for the increase of the shear band width when the rotation rate is increased.

Work and dissipation fluctuations near the stochastic resonance of a colloidal particle

We study experimentally the fluctuations of the injected and dissipated energy in a system of a colloidal particle trapped in a double well potential periodically modulated by an external perturbation. The work done by the external force and the dissipated energy are measured close to the stochastic resonance where the injected power is maximum. We show that the steady state fluctuation theorem holds in this system.The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fréedericksz transition, which is a second-order transition driven by an electric field. We show that, near the critical value of the field, the spatially averaged order parameter has a generalized Gumbel distribution instead of a Gaussian one. The latter is recovered away from the critical point. The relevance of slow modes is pointed out. The parameter of the generalized Gumbel distribution is related to the effective number of degrees of freedom.

Experimental study of out-of-equilibrium fluctuations in a colloidal suspension of Laponite using optical traps

This work is devoted to the study of displacement fluctuations of micron-sized particles in an aging colloidal glass. We address the issue of the validity of the fluctuation dissipation theorem (FDT) and the time evolution of viscoelastic properties during aging of aqueous suspensions of a clay (Laponite RG) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using emph{simultaneously} passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of micro-sized brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that both microrheology techniques lead to compatible results even at low frequencies and no violation of FDT is observed. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.

Probability density functions of work and heat near the stochastic resonance of a colloidal particle

We study experimentally and theoretically the probability density functions of the injected and dissipated energy in a system of a colloidal particle trapped in a double-well potential periodically modulated by an external perturbation. The work done by the external force and the dissipated energy are measured close to the stochastic resonance where the injected power is maximum. We show a good agreement between the probability density functions exactly computed from a Langevin dynamics and the measured ones. The probability density function of the work done on the particle satisfies the fluctuation theorem.

Effective temperature in a colloidal glass

We study the Brownian motion of particles trapped by optical tweezers inside a colloidal glass (Laponite) during the sol-gel transition. We use two methods based on passive rheology to extract the effective temperature from the fluctuations of the Brownian particles. All of them give a temperature that, within experimental errors, is equal to the heat bath temperature. Several interesting features concerning the statistical properties and the long-time correlations of the particles are observed during the transition.

Accretion Dynamics on Wet Granular Materials

Wet granular aggregates are common precursors of construction materials, food, and health care products. The physical mechanisms involved in the mixing of dry grains with a wet substrate are not well understood and difficult to control. Here, we study experimentally the accretion of dry grains on a wet granular substrate by measuring the growth dynamics of the wet aggregate. We show that this aggregate is fully saturated and its cohesion is ensured by the capillary depression at the air-liquid interface. The growth dynamics is controlled by the liquid fraction at the surface of the aggregate and exhibits two regimes. In the viscous regime, the growth dynamics is limited by the capillary-driven flow of liquid through the granular packing to the surface of the aggregate. In the capture regime, the capture probability depends on the availability of the liquid at the saturated interface, which is controlled by the hydrostatic depression in the material. We propose a model that rationalizes our observations and captures both dynamics based on the evolution of the capture probability with the hydrostatic depression.