Behaviors of spherical intruder in 3-D vertically vibrating granular system with vertical longitudinal air pressure wave

We investigated the behavior of a spherical intruder in a 3-D vertically vibrating small granular system. Vibration was represented as z=Asin(2πft). The surface formation and the rising time of the intruder, trise, were proven to be influenced by both vibration and system parameters. We focused on the effects of vibration frequency: f, dimensionless accelerator: Γ=(4π2Af2)/g and air pressure inside the container at equilibrium state: p, on trise. A parameter y=(Γ2/f2)p was defined to describe the activation extent of small particle convection. Surface formation of the pile is more tilted, whereas trise lowers, at higher y. When Γ alone was increased, trise decreased and fluctuated, and large trise deviations from the average values were also observed. When Γ or p alone was increased, or when f alone was decreased, trise decreased. A vertical longitudinal air pressure wave was produced inside the pile. Mathematical model was set up to describe intruder behavior. Three forces were considered along the z-axis. The pushing-up force had the most influence on trise. Fluctuations and deviations in the trise–Γ relationship were caused by the air pressure gradient force, and the dynamical resistance force increased trise.