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).
