Phase boundaries in vertically vibrated granular materials

A boundary structure is observed in beds of vertically vibrated granular materials separating regions of opposite phase. This structure is investigated and it is identified as giving rise to both a global kink and hexagonal patterns. A global phase diagram of surface patterns on a vibrated bed is presented. c © 1998 Published by Elsevier Science B.V. In recent years, there has been a dramatic surge in interest in the behavior of granular materials. Of particularly high profile has been the compelling work on vertical vibration and pattern formation. In beds of small grains, convection, heaping and surface patterning have been reported [113]. Among the most detailed investigations of the surface pattern characteristics of such systems is a set of reports on surface geometries categorizing the dynamics of shallow layers of grains [416]. In this Letter, we report on a transitional structure in the phase change between these geometrical patterns. We examined the behavior of brass spheres of radius 0.1510.18 mm in a bed of 20 grains in depth. The grains were vertically vibrated in a chamber consisting of a horizontal aluminum platform stabilized by vertical stainless steel shafts supporting a cylindrical lucite wall of radius 45 mm and height 50 mm. The chamber was vertically vibrated using a standard laboratory vibrator driven by an amplified signal generator. The chamber and driver were placed in a vacuum chamber and the pressure was reduced to below to minimize gas-related effects [2]. Surface patterns were observed and recorded using both high-speed digital photography and strobed light video. The oscillation amplitude A was measured optically, from which the acceleration amplitude Γ = 4π2Af2g−1 was derived, where g, the acceleration of gravity is scaled to 1. Our results conform to those reported by several inFig. 1. Phase Diagram for 0.1510.18 mm brass spheres of layer depth 20. Regions of square, flat and oscillon behavior are entirely bounded by stripes. The system is hysteretic and the region boundaries depicted were constructed from data taken with decreasing Γ. As the zipper structure’s amplitude increases, hexagons bleb off before the pattern reverts to stripes. 0375-9601/98/$19.00 c © 1998 Published by Elsevier Science B.V. All rights reserved. PII S0375-9601(98)00227-8