ABSTRACT
Dense granular systems, unlike granular gases, exhibit long-lived and relatively long-range structure in the form of force chains. These chains are a significant source of the rigidity of dense systems, and are presumably a key part of the jamming process. For a jammed system to deform/unjam, or for a particle within a jammed system to move, the force structure/chains must adjust appropriately. Hence, the motion of a particle within a deforming system that is close to the jamming point can provide important information. In this work we describe experiments (Geng & Behringer 2004; Geng & Behringer 2005) to determine the diffusivity, D, and mobility, B, in a dense deforming granular system. These experiments are novel in that they combine measurements of both these quantities, and at the same time are able to provide information on the forces at the grain scale. Theoretical motivation for this work can be found in studies by Makse & Kurchan (2002), who carried out molecular dynamics simulations on sheared systems to determine D and B, and by Radjai & Roux (2002) who used contact dynamics to characterize diffusion in a uniformly sheared system. Makse and Kurchan explored the idea of a generalized granular temperature, Teff = D/B, and found that this Teff was identical for particles of different sizes. Radjai and Roux found super-diffusive behavior, i.e. particle variances grew faster than linearly with time. There have also been a number of previous studies of diffusion and mobility in granular systems, and much of this work is reviewed in Utter & Behringer (2004) (see also elsewhere in this volume). In particular, experiments by Albert et al. (1999) characterized the impedance to a rod that was pushed through a granular sample, and theoretical studies by Khang et al. (2001) to describe the phenomena observed in the Albert et al. experiments. We note several important regimes in which
to characterize diffusion and mobility, and we draw contrasts between the granular and fluid cases. Measurements of D and B typically involve following a tracer through a sea of surrounding particles. Situations that may occur include: a dilated sea of particles (DIL) – the tracer easily moves past the surrounding particles; or a dense packing (DEN) – the tracer must escape from surrounding cages of particles to move. The tracer may be subject to a constant velocity condition (CV), or a constant force (CF); it may be large (L) relatively to the other particles, or of comparable size (C). For gases and liquids (away from the glassy regime) the distinction between CV and CF is irrelevant for Stokes-like flow. Also for these materials, L almost always applies. For granular systems, it is crucial to distinguish DEN from DIL, and if DEN applies, as it does in the present experiments, it is important to distinguish CV from CF. In the present experiments, we use tracer sizes that fall in the C regime, whereas Albert et al. operated in the L limit.
