  We show that the van der Waals-like phase separation instability of a driven
granular gas at zero gravity, previously investigated in two-dimensional
settings, persists in three dimensions. We consider a monodisperse granular gas
driven by a thermal wall of a three-dimensional rectangular container at zero
gravity. The basic steady state of this system, as described by granular
hydrodynamic equations, involves a denser and colder layer of granulate located
at the wall opposite to the driving wall. When the inelastic energy loss is
sufficiently high, the driven granular gas exhibits, in some range of average
densities, negative compressibility in the directions parallel to the driving
wall. When the lateral dimensions of the container are sufficiently large, the
negative compressibility causes spontaneous symmetry breaking of the basic
steady state and a phase separation instability. Event-driven molecular
dynamics simulations confirm and complement our theoretical predictions.
