Effect of hoisting tube shape on particle climbing

By inserting a vibrating tube in granular silo, particles can climb along the tube, named as “particle climbing”. In this study, a hopper is assembled at the bottom of a straight tube that forms in a tapered-tip tube. The particle climbing in both the straight and tapered-tip tubes are studied. Particles can climb only when the vibration strength is large enough (Γ > Γa) or some particles are initially filled in the straight tube. By contrast, the climbing in the tapered-tip tube is easier because of the strengthened force chain in the assembled hopper. In addition, the particles can directly climb even when Γ < Γa or without initial filling. In the tapered-tip tube, both the climbing velocity and the equilibrium height increase with the increasing of the vibration strength. As the tube diameter increases, the particles also can climb much higher. However, the climbing in the tapered-tip tube is insensitive to the inserting depth and the slope of the assembled hopper at the tube bottom.