title: Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.
abstract: We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Israel.
authors.forename: Itamar
authors.initials: I
authors.lastname: Kolvin
authors.forename: Eli
authors.initials: E
authors.lastname: Livne
authors.forename: Baruch
authors.initials: B
authors.lastname: Meerson