Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static sedimented states with well-defined particle volume fractions φ in the range 0.57–0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. Force measurements and bed height measurements both indicate that the transition occurs at φ= 0.60 for a range of speeds of the rod. Copyright c © EPLA, 2007 A static assembly of granules, for instance sand in a rigid container, responds differently to shear when packed loosely from when packed tightly [1]. It is natural to enquire whether these two states are smoothly connected as volume fraction varies, or, as with assemblies of particles in thermal equilibrium, are such states sharply separated by one or more phase transitions. We use recent advances in controlling the preparation of granular assemblies to show that the latter holds. An old magic trick is based on the qualitative difference in the resistance to shear of loosely packed and tightly packed particles: When a pot with a narrow neck is loosely filled with grains, a rod is easily inserted and withdrawn. The rod is then inserted and the grains are shaken or otherwise agitated to a denser state, whereupon the whole apparatus can be lifted by the rod and spun about the performer’s head [2,3]. The existence of distinct phases in granular matter has been widely discussed, but a sharp distinction between the two phases has remained elusive [4–6], the distinction being hampered by the difficulty in preparing a welldefined initial state [6]. The effort to overcome this was advanced significantly by Nowak et al. [7], who used a mechanical tapping protocol to obtain well-defined volume fractions φ in the range 0.628–0.658. Recently, Schröter et al. [8] showed that a protocol based on expanding the granular medium by pulses of fluid from below could be used to prepare a column of grains with φ defined to within (a)E-mail: [email protected] (b)E-mail: [email protected] 0.1%. Using this technique, we prepare granular samples in the range 0.571 < φ < 0.633. Experiment. – We measure the response of a granular sample to the insertion of a rod using an apparatus similar to that in [9–11]. Those previous studies focused on the influence of geometrical factors such as the size of particles, rod, and vessel, and on how the penetration force increased when the rod approached the bottom boundary. Those experiments were performed at a single volume fraction, φ= 0.59 [9,10]. Our measurements are performed with a home-built granular penetrometer: a translation stage (driven by a stepper motor with a step size 2.5μm) moves a stainless steel rod (diameter 6.3mm and flat head) downwards into a granular sample. The force needed for penetration is measured with a load cell with a full range of 10N (Honeywell, Model 31). The sample consists of soda lime glass beads from Cataphote with a diameter of 265± 15μm and a density of 2.484± 0.002 g/cm (measured with a Micromeritics gas pycnometer AccuPhys 1330). The beads are contained in a water-fluidized bed where flow pulses of different flow rates allow us to select a volume fraction φ for the static sedimented bed [8]. (If air rather than water is used to fluidize a bed, it is difficult to obtain low enough volume fraction to see the transition [12].) The beads are fluidized inside a square bore glass tube (39.9× 39.9mm). The ratio of inner tube size to rod diameter is 6.3, larger than the value five that [9] found to be sufficient so that the influence of the vessel walls was negligible. Flow pulses are generated