Matthias Schröter, Home

A static assembly of granules, for instance sand in a rigid container, responds differently to shear when packed loosely from when packed tightly.
An old magic trick is based on this qualitative difference: When a pot with a narrow neck is loosely filled with grains, a rod is easily inserted and withdrawn.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.
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.

Our measurements are performed with a home built granular penetrometer: a translation stage moves a stainless steel rod (diameter 6.3 mm and flat head) downwards into a granular sample with a speed of 10 mm/min. The force needed for penetration is measured with a load cell with a full range of 10 N. The sample consists of soda lime glass beads from Cataphote with a diameter of 265 ± 15 μm. The beads are contained in a water-fluidized bed where flow pulses of different flow rates allow us to prepare static sedimented beds with volume fraction Φ in the range 0.57-0.63.

Figure 1
The force on the rod penetrating the static sedimented bed increases monotonically with its depth. These curves are measured with a penetration speed of 10 mm/s; the total sample height is 110 mm (at Φ = 0.6).

Figure 2
The rate of change of force with volume fraction exhibits a well-defined transition, which occurs for Φ = 0.598 for a rod depth of 60 mm. The Φ values corresponding to the transition increase slowly with rod depth (cf. inset). The transition points were determined by the intersection of least-square fits for the volume fractions below and above the intersection, excluding points near the transition.

Figure 3
Change in the height of the bed relative to the original bed height for a rod inserted to a depth of 60 mm. The transition occurs at Φ = 0.597.

Conclusion

Pulses of fluidization are used to prepare static granular packings with well-defined particle volume fractions Φ in the range 0.57-0.63. We find a well-defined transition between two phases that differ in their resistance to shear as determined by slowly inserting a rod. Force measurements and volume response measurements both indicate that the transition occurs at Φ=0.60.

Publication

• Matthias Schröter, Sibylle Nägle, Charles Radin, and Harry L. Swinney
  Phase transition in a static granular system
  Europhysics Letters 78, 44004 (2007)
  [Journal URL], [pdf], [arxiv]

In collaboration with

Sibylle Nägle University of Texas at Austin

Charles Radin University of Texas at Austin

Harry L. Swinney University of Texas at Austin

Page maintained by Sibylle Nägle
Last modified: Tue Jun 12 02:56:57 CDT 2007