Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe

Previous experimental investigations have shown that when a narrow pipe is inserted into a granular bed and is vibrated vertically but the granular bed is kept still, the grains in the bed can enter the pipe and rise against gravity along the pipe and finally stabilized at a certain height. The growth velocity and final stable height of the grain column inside the pipe can be controlled by varying the vibration conditions. In this paper, we discuss those experimental findings. We establish a mathematic relation between the grain column height(h) and time(t), and by using the relation we discuss the change of the growth velocity( dh/ dt) and acceleration( d2h/ dt2) with t and h, respectively. We also analyze the mechanism of the rising motion of the grains during vibration. Furthermore, we derive a theoretical expression for describing the final stable height(h st), which shows that the main factors influencing the height are vibration strength(Γ), bulk density of grains,inner diameter of the pipe, and vibration frequency, and that h st increases nonlinearly in the presence of air and linearly in a vacuum environment with increasing Γ.