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Granular Streams

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Freely Falling Granular Streams

The movies below show how dry, freely-flowing granular material falling out of a hopper or funnel can behave like a liquid: it necks down and eventually breaks up to form clusters just like liquid droplets in a stream of water falling from a faucet. Closer inspection reveals a liquid unlike any other [1,2]. Tracking the streams with a free-falling high-speed video camera and measuring grain-grain interactions with AFM, we demonstrate that droplet formation is driven by minute, nanoNewton cohesive forces between nanoscale surface asperities, resulting in an effective surface tension ~100,000x smaller than in molecular liquids. The neck shapes resemble those predicted [3] for liquid nanojets in this regime, but the break-up scaling mimics simple inviscid liquids while the drop size selection rule is unique to granular streams.

In 3D molecular dynamics simulations of these granular streams we can show that the cluster and droplet formation is indeed due to the tiny cohesive forces and not merely a consequence of dissipation due to inelastic collisions between repulsive grains. In fact, the freely falling granular streams are uniquely capable of separating out the roles of cohesion and inelastic dissipation: under gravitational stretching all transient clusters formed in the absence of cohesion will eventually drift apart and only clusters held together by (even minute) cohesion will stay together. Details about these processes and a first "phase diagram" of the types of structures formed (sprays, clusters and droplets) by varying the coefficient of restitution and the strength of cohesion can be found in [4].

The two b/w movies on the left are from our experiments (100 micron spherical glass beads). The two color movies in the middle are simulations with d=100 micron spheres falling out of a D = 2.0mm aperture. Left: Coefficient of restitution e = 0.40 and cohesive strength Fcoh = 100 nN (cohesion sufficient to cluster). Right: e = 0.88 and Fcoh = 1 nN (cohesion too low to cluster). The movies follow the grains in the co-moving frame, mimicking the falling cmaera of the experiments. Grains are color coded according to their rms velocity difference with neighboring grains within a distance of 1.5d. Isolated grains are shown in pink. Note in the more cohesive stream how the "granular temperature" first increases in the neck regions (shear!) and then suddently drops once the droplets break off and freeze (blue-ish). Contrast this with the less cohesive stream, where inelasticity leads to collimation but particles simply drift apart (by the way, this happens no matter how small e, see Fig. 4 in [4]). The final movie (b/w; e = 0.40, Fcoh = 100 nN) tracks the evolution of a single droplet, starting with grains still inside the hopper, as they fall through the aperture (can you tell when?), and eventually form the droplet. Only the grains belonging to this one droplet are shown. Each grain is indicated by its center and a circle delineating its diameter. The movie is not a vertical slice through the system but a 2D projection of the 3D "spherical cap" inside the hopper that evolves into the droplet.

The initial granular stream experiments were started in our lab by Matthias Möbius (now at Trinity College, Dublin). John Royer (now at NYU) modified the system and installed the free-fall camera. The current, further improved set-up (<1nN force sensitivity, turbo-pumped for better vacuum) was built by Scott Waitukaitis. The simulations were initiated by Helge Grütjen and then finished in a team effort with Scott and John. Alison Koser worked as a summer REU student on the project, and Loreto Oyarte Galvez was working with us for 10 weeks as an exchange student from Chile. Dan Evans, Qiti Guo and Eliot Kapit contributed key elements to the early phases of the experiments.

[1] High-Speed Tracking of Rupture and Clustering in Freely Falling Granular Streams, J. Royer, D. Evans, L. Gálvez, Q. Guo, E. Kapit, M. Möbius, S. Waitukaitis, and H. Jaeger, Nature 459, 1110 (2009). pdf

[2] John R. Royer, Loreto Oyarte, Matthias E. Möbius, and Heinrich M. Jaeger, “Rupture and clustering in granular streams”, Chaos 19, 1 (2009).

[3] M. Moseler and U. Landman, Science 289, 1165 (2000).

[4] Scott R. Waitukaitis, Helge Grütjen, John R. Royer, and Heinrich M. Jaeger, ”Droplet and cluster formation in granular streams”, Phys. Rev. E 83, 051302 (2011). pdf


Here you can download less compressed versions of the left movie (30Mb) and the right movie (2.6Mb).

In addition, here are even less compressed movies of streams of 50 micron grains and 100 micron grains.

Note: All these videos require the QuickTime Player. Please download the player from here if needed.

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