Hydrodynamics of a vibrated granular monolayer

We investigate the long-standing puzzle of phase separation in a granular monolayer vibrated from below. Although this system is three dimensional, an interesting dynamics occurs mostly in the horizontal plane, perpendicular to the direction of vibration. Experiments [Olafsen and Urbach, Phys. Rev. Lett. 81, 4369 (1998)] demonstrated that for a high amplitude of vibration the system is in the gaslike phase, but when the amplitude becomes smaller than a certain threshold, a phase separation occurs: A solidlike dense condensate of particles forms in the center of the system, surrounded by particles in the gaslike phase. We explain theoretically the experimentally observed coexistence of dilute and dense phases, employing Navier-Stokes granular hydrodynamics. We show that the phase separation is associated with a negative compressibility of granular gas.