(movie)Granular Jets
When a marble or ball bearing is dropped on the ground, it will typically land with a thud. However, when the same object is dropped onto a bed of fine, loose sand there will be a remarkably different response: a broad splash of sand at impact and, after the marble has penetrated deeply into the bed, a tall jet of granular material that shoots up vertically. Such jets are among the most spectacular manifestations of liquid-like behavior in granular materials, curiously resembling similar phenomena in ordinary liquids. Yet they occur in the absence of any cohesion or surface tension. How are these jets formed and what keeps them so collimated?
(movie)
The original paper on granular jets by Amy Shen and Sigurdur Thoroddsen from the University of Illinois at Urbana-Champaign (now at Washington University and University of Singapore, respectively) reported the phenomenon and discussed the scaling of the jet height with experimental parameters such as velocity of the impacting sphere and size of the bed particles. Since then, Detlef Lohse and coworkers at the University of Twente have performed extensive high-speed video observations as well as computer simulations of granular jets, in particular focusing on the jets’ origin. They discovered that it is connected with the collapse of the void left behind the impacting sphere: driven by gravity, material rushes in radially from all sides and collides along the center; as a result, excess momentum is projected along the central, vertical axis which results in two, oppositely-directed jets. They also elucidated two conditions for large jets to occur, namely fine bed material and a sufficiently loose initial packing state of the bed. The Twente researchers used particles with diameters <100µm and packing densities where less than 50% of the bed volume was occupied by grains, a state they termed “dry quicksand”. For more information about their work click here.
These conditions suggest that interactions between grains and the surrounding
gas (usually air) is important. Experiments performed by our group in Chicago
show that the size of the jet is dramatically reduced at reduced pressure. Not
easily observable at ordinary atmospheric conditions, a striking two-stage structure
of the jet emerges when the air pressure is reduced (see the green figure, above,
and the set of panels, below), in which a thin, largely pressure-independent
jet is followed by a much larger second jet that strongly depends on pressure.
Under atmospheric conditions, the thin jet appears essentially subsumed by the
thick one, while below about 1/20 of an atmosphere only the thin jet remains.
To find out what goes on inside the bed during the early stages of jet formation
very fast imaging is required, given the high velocities of around 1m/s for
the impacting sphere.
Using the Advanced Radiation Source at Argonne National Laboratory we illuminated
the bed with the high-intensity synchrotron beam and, by video-recording the
transmitted signal at rates of 5000 frames per second, tracked the motion of
the sphere and the evolution of the void left behind it. Our results indicate
that gravity-driven void collapse can explain the thin jet but that the thick
jet is, in fact, driven upward by a bubble of compressed gas (see images below).
Pressure differences across a granular bed can produce forces that easily exceed
the bed weight. On the short time scales associated with the impact and subsequent
void closure, gas cannot efficiently diffuse through fine-grained bed material.
As gas gets trapped in the collapsing void, it builds up sufficient pressure
to propel the material that forms the large jet. It is likely that pressure
gradients also are responsible for keeping the jet collimated as it rises above
the bed. In this way, the interaction between interstitial gas and grains might
thus produce an effective surface tension. However, there are alternative possibilities
based on the clustering produced by inelastic collisions. Which of these effects
ultimately dominates will have to be seen.
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The image above is a collage of x-ray movie frames. Each vertical column corresponds to a particular time, starting with the first sphere entering the sand bed on the left and leaving behind a cylindrical void. Since the field of view for the x-ray experiments is only about 1.5cm tall, many individual runs were performed and images taken at different heights so they could be spliced together as shown here. Because the sphere's point of impact shifted slightly in horizontal direction from run to run the frames also shift laterally. The light blue arrow points to the region where the granular bed first pinches off the void. This pinching-off produces the thin jet (upper yellow arrow). Other granular material rushing onto the void just above the sphere also produces a thin jet (lower yellow arrow). More importantly, however, the void fills in from the bottom and this compresses the air trapped between the (moving) bottom of the void and the upper pinch-off region. This pressurized air pocket drives the thick jet which can be seen emerging at the top of the two image columns to the right (in fact, the air penetrates even into the thick jet a bit).
Movies
Jets at different ambient air pressures
Jets at Home
Create a small granular jet yourself.
For more info see
(Jan. 25, 2006; this page is still under construction).