The formation of polygon-shaped patterns in vibrated, cylindrical granular beds

摘要

In this work particle image velocimetry (PIV) was employed to probe the motion of particles within a quasi-2D vibrated bed of circular cross-section. We have observed a polygon-shaped pattern for Γ = A(2πf)~2/g greater than 10. It has been argued that the polygon pattern formed in 2D cylindrical beds is related to the arching structure encountered in square-shaped vibrated beds [G. Lu, J. R. Third, M. H. K?hl, and C. R. Müller. 2012. On the occurrence of polygon-shaped patterns in vibrated cylindrical granular beds. The European Physical Journal E 35, 90.]. However, using PIV a significant difference in the velocity profiles in the polygon and the arching patterns was observed. We found that in the arching structure the velocity profile around a node was highly symmetric, whereas this was not the case for the polygon structure. Using cylindrical beds of different diameters filled with a constant number of particles, we could confirm that the spatially varying filling height of cylindrical beds is the main cause of the asymmetric velocity profiles within such systems.