  We investigate shear-induced crystallization in a very dense flow of
mono-disperse inelastic hard spheres. We consider a steady plane Couette flow
under constant pressure and neglect gravity. We assume that the granular
density is greater than the melting point of the equilibrium phase diagram of
elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive
relations all of which (except the shear viscosity) diverge at the crystal
packing density, while the shear viscosity diverges at a smaller density. The
phase diagram of the steady flow is described by three parameters: an effective
Mach number, a scaled energy loss parameter, and an integer number m: the
number of half-oscillations in a mechanical analogy that appears in this
problem. In a steady shear flow the viscous heating is balanced by energy
dissipation via inelastic collisions. This balance can have different forms,
producing either a uniform shear flow or a variety of more complicated,
nonlinear density, velocity and temperature profiles. In particular, the model
predicts a variety of multi-layer two-phase steady shear flows with sharp
interphase boundaries. Such a flow may include a few zero-shear (solid-like)
layers, each of which moving as a whole, separated by fluid-like regions. As we
are dealing with a hard sphere model, the granulate is fluidized within the
"solid" layers: the granular temperature is non-zero there, and there is energy
flow through the boundaries of the "solid" layers. A linear stability analysis
of the uniform steady shear flow is performed, and a plausible bifurcation
diagram of the system, for a fixed m, is suggested. The problem of selection of
m remains open.
