Granular Jets as a Classical Analog of RHIC Collisions
By Xiang Cheng, Heinrich Jaeger and Sidney Nagel
After a cylindrical stream of non-cohesive granular particles hits a target, a thin sheet of particles emerges in the plane normal to the initial direction of the jet. Although particulate in nature, the granular jet behaves like a liquid with zero surface tension if the density of collisions is high enough . For jets with an elongated cross-section, the resulting spray is collimated and emerges from the long side of the collision region. This appears to be a classical analog of the elliptic anisotropic flow observed at RHIC for the quark-gluon plasma.
In our experiment, we fill a tube with mono-disperse spherical glass beads of diameter, d, ranging between 50µm and 2.1mm. The granular column is accelerated by pressurized gas to an impact velocity U0 before hitting a circular aluminum target. (Fig.1(a)). The diameter of the jet, set by the tube diameter, was DJet = 0.73cm. We varied the ratio of the target diameter, DTar, to DJet, between 0.2 and 10 and varied U0 between 1m/s and 16m/s.
With 100µm glass beads at U0 = 10m/s, the granular jet deforms after hitting the target into a quasi-2D granular cone pointing in the downstream direction enclosing the target (Fig.1(b)-(d)). The opening angle of the cone increases with increasing DTar/ DJet; when DTar/ DJet > 2.0 the opening angle is 900 so that the jet forms a sheet (Fig.1(b), (c)). The opening angle of the jet as a function DTar/ DJet coincides with the results for normal liquids in the zero surface tension limit.
By increasing the diameter, d, of glass beads but fixing the jet diameter, DJet, the ejected sheets and cones become less well defined as the granular nature of the jet becomes more apparent (Fig.2). With 2.1mm particles (about 4 particles in the cross-section of the beam), one can see the typical firework pattern of particulate behavior (Fig.2(c)).
The target of our experiment reverses the momentum of any particle hitting it and therefore severs as a mirror for the incoming beam. Hence, the impact of the beam on a target can be thought of as the head-on collision of two beams. The reaction zone of the beam with its reflection is located in front of the target. For beams with circular cross-section, this region is cylindrically symmetric. In making the comparison with the collision of heavy ions, this geometry would correspond to a head-on collision.
In order to simulate the non-central collision of two ions at RHIC, we need an elongated reaction zone rather that a circular one. To produce such a geometry, we direct the beam through a slot with rectangular shape before it hits the target. This results in a rectangular reaction zone. In our experiment, the aspect ratio of the beam is about 2. With small particles, we found that the resulting granular sheet is highly anisotropic in the plane; two strong back-to-back jets shoot outward from the long side of the rectangle with fewer particles emerging from the short side (Fig.3(a)). Furthermore, when using bigger particles so that there are fewer collisions in the interaction zone, the anisotropy is less pronounced. As shown in Fig.3(b), with 1mm particles (about 6 particles along the long axis of the beam cross-section) the emerging particles fly out isotropically.
Our experiments demonstrate that hydrodynamic behavior can emerge from the normal kinetics of classical particles with a high density of rapid collisions. For our dense jets where the liquid behavior is most pronounced, the mean free path in the interaction region is very short – much smaller than the diameter of the particles themselves. The counterpart of this behavior can be found in disparate fields of physics, such as the strongly-interacting cold fermions in AMO physics and the quark-gluon plasma in RHIC physics. Our experiments also raise an interesting question: does one really need the concept of equilibrium for a system to show hydrodynamic behavior? In our granular experiment, there is no clear evidence that the collisions between particles in front of target generate a fully equilibrium state. Some degrees of freedom in the system may reach equilibrium in the time scale of the experiment while others may not. How much equilibration is necessary to produce the hydrodynamic features of the observed phenomena? A further interesting step would be to estimate the effective viscosity and entropy of our granular beam after impact to see to what extent it is also a perfect fluid.
Acknowledgement: This work is supported by NSF through its MRSEC program and by the W.M. Keck Foundation.
 X. Cheng, G. Varas, D. Citron, H.M. Jaeger, & S.R. Nagel, Phys. Rev. Lett. 99, 188001 (2007). (arXiv:0706.2027)