0 Granular fingers in Hele - Shaw experiments

Granular materials constitute an intermediate state of matter between fluids and solids[1]. Over the past decade, a large series of experimental assays on granular systems, concentrated in the quantitative studies of compaction, mixing, segregation and patterns formed by vibration, have been done[2-9]. They uncovered numerous mechanisms (percolation, convection, ordered settling, arching, etc.) for segregation of dissimilar grains; remarkable standing-wave patterns (stripes, hexagons, disordered waves, cluster of localized solitary excitations, etc.) in vibrating layers of granular materials and highly inhomogeneous and localized stresses chains in nearly static granular media. Nevertheless, in contrast to viscous fingering in fluids, a widely studied pattern-forming phenomena[9], grain-grain displacement seems to be an unexplored area in granular physics. Here we investigate the pattern formation when a grain is displaced by another type of grain in a radial Hele-Shaw cell. We show that several morphologies can occur, ranging from rounded to fingered patterns, interconnected by a continuous crossover. Fourier analyses shows that, in contrast to the rounded patterns, the fingered shapes present mode selection. The experiments were carried out in a radial Hele-Shaw cell made of two parallel square glass plates, each with a thickness of 0.5 cm and lengths of 90 cm (bottom plate) and 80 cm (top plate). The top plate had a hole of 0.5 cm in diameter in its centre for the injection of grains. Initially, a dense uniform circular monolayer of styrofoam spheres was formed on the cell's bottom plate, always covering the same area. After that, the cell was closed with the top plate, over which weights were placed to prevent upward movement, and another kind of grain was injected through its hole. In all experiments steel spheres with a diameter of 3.94 ± 0.03 mm were manually injected, whereas three types of styrofoam initial monolayers were used: type A, with an average diameter of 2.3 ± 0.1 mm and low polydispersion; type B, composed of spheres with diameters in the range of 0.5 to 4.0 mm and average diameter of 2.9 ± 0.6 mm; and type C, with an average diameter of 3.5 ± 0.3 mm and low polydispersion. After 1