Brazil nut effect and excluded volume attraction in vibrofluidized granular mixtures

Depletion forces in athermally sheared mixtures of frictionless disks and rods in two dimensions

We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this clustering increases, leading to an increase in the average rate of rotation of the rods, and a decrease in the magnitude of their nematic ordering.

Clustering-Induced Attraction in Granular Mixtures of Rods and Spheres

Depletion-induced aggregation of rods enhanced by clustering is observed to produce a novel model of attractive pairs of rods separated by a line of spheres in a quasi-2D, vertically-shaken, granular gas of rods and spheres. We show that the stability of these peculiar granular aggregates increases as a function of shaking intensity. Velocity distributions of spheres inside and outside of a pair of rods trapping a line of spheres show a clear suppression of the momentum acquired by the trapped spheres. The condensed phase formed between the rods is caused by a clustering instability of the trapped spheres, enhanced by a vertical guidance produced by the confining rods. The liberated area corresponding to direct excluded-volume pairs and indirect depletion-aggregated pairs is measured as a function of time. The stability of rod pairs mediated by spheres reveals an attraction comparable in strength to the one purely induced by depletion forces.

Depletion force in a bidisperse granular layer

We demonstrate the effect of the depletion force in experiments and simulations of vertically vibrated mixtures of large and small steel spheres. The system exhibits size segregation and a large increase in the pair correlation function of the large spheres for short distances that can be accurately described using a combination of the depletion potential derived for equilibrium colloidal systems and a Boltzmann factor. The Boltzmann factor defines an effective temperature for the system, which we compare to other measures of temperature.

Mechanisms in the size segregation of a binary granular mixture

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

Fluctuation-induced casimir forces in granular fluids

We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.