Anomalous density dependence of static friction in sand

Exploring the physics of sand drawings: The role of craters, furrows and piles

Few years ago an article addressing the physics behind aaabstract paintings was published by Herczyński et al. (Phys. Today 64, 31 (2011) issue No. 6). The authors aimed to understand how artists like Jackson Pollock manipulated paints to create pieces of art where the theory of fluid dynamics had a clear and perceivable role. Scaling laws were found to explain the plasticity observed in the artists's traces that we admire in worldwide museums. Because sand drawings are not only wonderful artistic expressions but also intangible cultural heritages of humanity, we wonder if they could be analyzed in a similar fashion. Our goal is to explore the physics behind the formation of such drawings. In order to do so, we carry out experimental studies on the formation of sand cavities, furrows and piles, which individually or interconnected, give rise to artistic patterns. Moreover, in order to manipulate such three observables, some control parameters are needed. Altogether, they conform into simple exponential and power laws that collapse when a scaling is performed.

Projectile interactions in granular impact cratering

We present evidence for the interactions between a ball and the container boundaries, as well as between two balls, that are mediated by the granular medium during impact cratering. The presence of the bottom boundary affects the final penetration depth only for low drop heights with shallow filling, in which case, surprisingly, the penetration becomes deeper. By contrast the presence of the sidewall causes less penetration and also an effective repulsion. Repulsion is also found for two balls dropped side by side.

Slow dynamics and aging of a confined granular flow

We present experimental results on slow flow properties of a granular assembly confined in a vertical column and driven upwards at a constant velocity V. The wall roughness is much lower than the typical grain size. For monodisperse assemblies this study evidences at low velocities (1<V<100 microm/s) a stiffening behavior, i.e., the stress necessary to obtain a steady-state velocity increases roughly logarithmically with velocity. On the other hand, at very low driving velocity (V<1 microm/s), we evidence a discontinuous and hysteretic transition to a stick-slip regime characterized by a strong divergence of the maximal blockage force when the velocity goes to zero. We show that all this phenomenology is strongly influenced by surrounding humidity. We also present an attempt to establish a link between the granular rheology and the solid friction forces between the wall and the grains. We base our discussions on a simple theoretical model and independent grain/wall tribology measurements. We also use finite element numerical simulations to compare experimental results with isotropic elasticity. A second system made of polydisperse assemblies of glass beads is investigated. We emphasize the onset of a new dynamical behavior, i.e., the large distribution of blockage forces evidenced in the stick-slip regime.

Shearing of loose granular materials: a statistical mesoscopic model

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the "density" of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a nontrivial patterning of the system, with high-density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band, which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is, however, metastable, and the system continues to evolve slowly in a manner reminiscent of glassy dynamics. Several quantities have been studied numerically which support this picture and elucidate the unusual system-size effects involved.

Rheology of a confined granular material

We study the rheology of a granular material slowly driven in a confined geometry. The motion is characterized by a steady sliding with a resistance force increasing with the driving velocity and the surrounding relative humidity. For lower driving velocities a transition to stick-slip motion occurs, exhibiting a blocking enhancement with decreasing velocity. We propose a model to explain this behavior pointing out the leading role of friction properties between the grains and the container's boundary.