Results from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between ϕ_b=0.2 and 0.6, and the Coulomb friction coefficient is either μ_c=0 or 0.5. The main objectives are to unravel the influence of (1) ϕ_b and μ_c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing ϕ_b/Φ_R, where Φ_R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration ϕ¯/ϕ_m, where ϕ_m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number I_v in the core region, where the macroscopic friction coefficient μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for ϕ¯/ϕ_mp as function of I_v, where ϕ_mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond ϕ_m at high ϕ_b and maximum core concentrations below ϕ_m at lower ϕ_b.

In the literature, two different frameworks exist for describing the rheology of solid/liquid suspensions: (1) the “viscous” framework in terms of the relative suspension viscosity, η_r, as a function of the reduced solid volume fraction, f=f_m, with f_m the maximum flowable packing fraction, and (2) the “frictional” framework in terms of a macroscopic friction coefficient, μ, as a function of the viscous number, I_v, defined as the ratio of the viscous shear to the wall-normal particle stress. Our goal is to compare the two different frameworks, focusing on the effect of friction between particles. We have conducted a particle-resolved direct numerical simulation study of a dense non-Brownian suspension of neutrally buoyant spheres in slow plane Couette flow. We varied the bulk solid volume fraction from f_b ¼ 0:1 to 0.6 and considered three different Coulomb friction coefficients: μ_c ¼ 0, 0.2, and 0.39. We find that η_r scales well with f=f_m, with f_m obtained from fitting the Maron–Pierce correlation. We also find that μ scales well with I_v. Furthermore, we find a monotonic relation between f=f_m and I_v, which depends only weakly on μ_c. Since η_r ¼ μ=I_v, we thus find that the two frameworks are largely equivalent and that both account implicitly for Coulomb friction. However, we find that the normal particle stress differences, N₁ and N₂, when normalized with the total shear stress and plotted against either f=f_m or I_v, remain explicitly dependent on μ_c in a manner that is not yet fully understood.