  The microstructure and rheological properties of suspensions of neutrally
buoyant hard spherical particles in Newtonian fluid under conditions of finite
inertia are studied using the lattice-Boltzmann method (LBM), which is based on
a discrete Boltzmann model for the fluid and Newtonian dynamics for the
particles. The suspensions are subjected to simple-shear flow and the
properties are studied as a function of Reynolds number and volume fraction,
$\phi$. The inertia is characterized by the particle-scale shear flow Reynolds
number $Re = \frac{\rho \dot{\gamma}a^{2}}{\mu}$, where $a$ is the particle
radius, $\dot{\gamma}$ is the shear rate and $\rho$ and $\mu$ are the density
and viscosity of the fluid, respectively. The influences of inertia and of the
volume fraction are studied for $0.005\leqslant Re \leqslant 5$ and
$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied
using the pair distribution function $g(\boldsymbol{r})$. Different stress
mechanisms, including those due to surface tractions (stresslet), acceleration,
and the Reynolds stress due to velocity fluctuations are computed and their
influence on the first and second normal stress differences, the particle
pressure and the viscosity of the suspensions are detailed. The probability
density functions of particle force and torque are also presented.
