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We present a numerical study of noncolloidal spherical and rigid particlessuspended in Newtonian, shear thinning and shear thickening fluids employing anImmersed Boundary Method. We consider a linear Couette configuration to explorea wide range of solid volume fractions ($0.1\le \Phi \le 0.4$) and particleReynolds Numbers ($0.1\le Re_p \le 10$). We report the distribution of solidand fluid phase velocity and solid volume fraction and show that close to theboundaries inertial effects result in a significant slip velocity between thesolid and fluid phase. The local solid volume fraction profiles indicateparticle layering close to the walls, which increases with the nominal $\Phi$.This feature is associated with the confinement effects. We calculate theprobability density function of local strain rates and compare their mean valuewith the values estimated from the homogenization theory of \cite{Chateau08},indicating a reasonable agreement in the Stokesian regimes. Both the mean valueand standard deviation of the local strain rates increase primarily with thesolid volume fraction and secondarily with the $Re_p$. The wide spectrum of thelocal shear rate and its dependency on $\Phi$ and $Re_p$ points to thedeficiencies of the mean value of the local shear rates in estimating therheology of these noncolloidal complex suspensions. Finally, we show that inthe presence of inertia, the effective viscosity of these noncolloidalsuspensions deviates from that of Stokesian suspensions. We discuss how inertiaaffects the microstructure and provide a scaling argument to give a closure forthe suspension shear stress for both Newtonian and power-law suspending fluids.The stress closure is valid for moderate particle Reynolds numbers, $O(Re_p)\sim 10$.

Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids