  This work investigates phase separation of a monodisperse gas of
inelastically colliding hard disks confined in a two-dimensional annulus, the
inner circle of which represents a "thermal wall". When described by granular
hydrodynamic equations, the basic steady state of this system is an azimuthally
symmetric state of increased particle density at the exterior circle of the
annulus. When the inelastic energy loss is sufficiently large, hydrodynamics
predicts spontaneous symmetry breaking of the annular state, analogous to the
van der Waals-like phase separation phenomenon previously found in a driven
granular gas in rectangular geometry. At a fixed aspect ratio of the annulus,
the phase separation involves a "spinodal interval" of particle area fractions,
where the gas has negative compressibility in the azimuthal direction. The heat
conduction in the azimuthal direction tends to suppress the instability, as
corroborated by a marginal stability analysis of the basic steady state with
respect to small perturbations. To test and complement our theoretical
predictions we performed event-driven molecular dynamics (MD) simulations of
this system. We clearly identify the transition to phase separated states in
the MD simulations, despite large fluctuations present, by measuring the
probability distribution of the amplitude of the fundamental Fourier mode of
the azimuthal spectrum of the particle density. We find that the instability
region, predicted from hydrodynamics, is always located within the phase
separation region observed in the MD simulations. This implies the presence of
a binodal (coexistence) region, where the annular state is metastable. The
phase separation persists when the driving and elastic walls are interchanged,
and also when the elastic wall is replaced by weakly inelastic one.
