Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe
Liu Yua)†, Zhao Jun-Hongb)
       
Grain column height ( h ), the growth velocity of the height v (d h /d t ), and acceleration a (d2 h /d t 2) as a function of t and h , respectively. Γ = 3.3, f = 12 Hz. (a) h , v , and a as functions of t . (b) v and a as functions of h . The dotted line represents h , the solid lines and square dots represent v and a , respectively.