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, ηr, as a function of the reduced solid volume fraction, f=fm, with fm
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, ηr, as a function of the reduced solid volume fraction, f=fm, with fm 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, Iv, 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 fb ¼ 0:1 to 0.6 and considered three different Coulomb friction coefficients: μc ¼ 0, 0.2, and 0.39. We find that ηr scales well with f=fm, with fm obtained from fitting the Maron–Pierce correlation. We also find that μ scales well with Iv. Furthermore, we find a monotonic relation between f=fm and Iv, which depends only weakly on μc. Since ηr ¼ μ=Iv, 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=fm or Iv, remain explicitly dependent on μc in a manner that is not yet fully understood.
