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[SCG74-12] Scaling of convective velocity in intermittently vibrated granular packing
Keywords:granular convection, scaling, regolith
In the experiment, a two-dimensional chamber filled with bi-disperse disks (diameter: = 10 or 15 mm) is vertically mounted on an electromagnetic vibrator. Then the chamber is subject to 1,000 successive tappings (each tapping event consists of a single period of sinusoidal oscillation). The interval between these tappings is fixed at 2 s. We define the tapping strength Γ as Γ= A(2πf)2/g, where A is vibration amplitude, f is its frequency, and g is gravitational acceleration (i. e. Γ means the ratio of maximum tapping acceleration and gravitational acceleration). Γ is systematically varied as Γ= 2.5, 5, 10, 20, and f is also varied in the range of f = 50, 100, 200 Hz.
In the analysis, we calculated particle velocities using by the particle tracking velocimetry method. In addition, we calculated vorticity field from each particle velocity so that we quantitatively evaluated the occurrence of convective motion in the intermittently tapped granular packing. When the particles form convective motion, we first normalize the mean particle’s velocity v as v* = v/(gd)1/2, where (gd)1/2 is the characteristic velocity created by gravity and particle size. We then constructed the scaling relationship between v* and the dimensionless parameter S = (2πAf)2/gd (Here, S denotes the balance between the squared tapping-velocity and the squared characteristic velocity created by gravity).
As a result, we found a scaling relationship between v* and S for the intermittently tapped granular packing: v* ~ S0.56 (Fig.1). This result indicates that v is roughly scaled by S1/2 which is almost identical to the scaling obtained with a steady vibration. Therefore, we conclude the intermittency of oscillation doesn’t affect the velocity of granular convection.
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