We drive a sandpile sinusoidally in the vertical direction at approximately 10 Hz with an amplitude of approximately 1/3 cm. The cell itself is completely level -- within 0.5% verified by direct measurement. The granular material shown here is the ``rough sand'' which is 0.613 mm in diameter.
The equation of motion for the shaker is z=a sin(\omega t). We define two dimensionless parameters that help characterize the system, the dimensionless acceleration \Gamma and the dimensionless energy E, where \Gamma= a \omega2 g-1, and E = (a \omega)2 (g d)-1 = \Gamma (a/d).
(z=a sin(w t); G=a w2 g-1; and E=(a w)2 (g d)-1 = G (a/d), if your browser supports the ``face'' tag...)
A \Gamma=1.00 would correspond to the maximal downward acceleration of the platform is exactly equal to the downward acceleration of gravity; hence the sand particles are briefly in freefall. Granular convection begins at any \Gamma slightly greater than 1. At this point, the top layer of sand becomes slightly ``dilated'' during the freefall part of flight and are able to reorient themselves during the subsequent acceleration against gravity.
In addition, we rigidly mount a small CCD video camera to the platform
and shake the Plexiglas cell and Camera together. This allows the
collection of raw video without having to compensate for the vertical
motion of the cell.
If some of the sand particles are colored dark with a ``Sharpee'' magic marker, then those dark particles can be tracked and followed over many cycles (2500+ periods) in the shaker. The time of the streak photo is only limited by the available disk space and in general can be quite large.
The following is a 2 minute exposure at a \Gamma slightly greater than unity. As can clearly be seen, there is very little movement of the sand layer.
In the next photo, we show a very interesting 4-roll state where the sand travels up the pile in a thin layer just below the surface of the heap but either avalanches downwards over the peak or goes deeper into the pile in a convection roll that is time dependant. Again, this is a 2-minute exposure, but the driving frequency has been increased from the previous photograph.
In the last photo displayed here, the frequency has again been increased from that of the last photograph, but the 4-roll state has changed completely to a 2 roll state where the sand travels in a straight line from the bottom-center of the cell to the top of the sand heap.
The video was captured as fast as possible straight to the hard drive on a P90 with a Matrox Comet graphics board. This is a 5 minute exposure. Even at the maximum frame rate, the shaker is vibrating so quickly that it is hard to follow individual paths in the left convection roll, which is circulating quite quickly.
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