Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

Abstract

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.