PARTICLE CLUSTERING IN GRANULAR FLOWS: HYDRODYNAMIC SINGULARITIES IN A BOX OF SAND

00:00 19-02-2008

An assembly of inelastically colliding hard spheres - the granular gas - is a simple model of flow of granular materials.  It provides  a  fascinating  example  of  a  complex  system  far from

equilibrium.   Granular  gases  exhibit  a  spontaneous  clustering

instability:  development  of  clusters  of  particles,  and  voids between them. A linear stability analysis of this system, employing a  hydrodynamic  description,  was  performed  in the nineties, but nonlinear theory of this instability was a major unresolved problem.

We simplified this problem  by  considering  a channel geometry, so that the coarse-grained flow  is  one-dimensional.  We  found  that, when described  by  idealized  hydrodynamic  equations,  the freely cooling granular  gas  exhibits  a finite-time density blowup. This "attempted"  singularity  is  usually  arrested only when the close packing  density  of  hard spheres is reached.  In one limit of the instability,  the  dynamics  is  describable  by  a  zero-viscosity Burgers equation  which  makes  this  system  a distant cousin of a structure forming expanding Universe.

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