Eulerian–Lagrangian simulations of shear thinning and shear thickening in suspensions of repulsive particles

Suspensions of neutrally buoyant, non-Brownian, repulsive particles dispersed in Newtonian fluids give rise to complex rheology, shear thinning at low shear rates and shear thickening at high shear rates. Despite extensive study, important aspects of their rheology remain in part unclear, including (i) the role of the drag force in the onset of shear thickening; (ii) the relation between the range of the repulsive force and the rate of shear thinning; and (iii) the value and shear rate dependence of the exponent describing their viscosity divergence. To address these questions, we study the rheology of these suspensions under simple shear flow via a comprehensive numerical Eulerian–Lagrangian model that resolves both the solid and liquid phases, thereby eliminating the need to prescribe the fluid velocity field. This approach allows us to test the assumption of ideal simple shear flow, where the phasic velocity profiles are linear and the shear rate is spatially uniform—an assumption that becomes increasingly inaccurate as the system approaches the jamming transition. Using a simple force balance and accounting for the drag-force hindrance function in the nondimensionalization of the shear rate, we retrieve the onset of shear thickening at the expected order of magnitude of dimensionless shear rate and obtain an expression for the interparticle equilibrium distance that fits the numerical results accurately. Treating the repulsive particles as apparent particles consisting of a rigid core and a soft shell, whose thickness is related to the interparticle equilibrium distance, we describe the suspension rheology by means of a modified Krieger–Dougherty equation, relating its parameters to the shear rate and the repulsive force range.