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

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 φb = 0.2 and 0.6, and the Coulomb friction coefficient is either μc = 0 or 0.5. The main objectives are to unravel the influence of (1) φb and μc 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 φb/ R, where 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/φm, where φm is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number Iv in the core region, where the macroscopic friction coefficientμdrops 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/φmp as function of Iv, where φmp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond φm at high φb and maximum core concentrations below φm at lower φb.