Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ϕ with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.

International audienceWe measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen & Guazzeli (J. Fluid Mech., 2011, doi:10.1017/ jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small. 1. Introduction Despite several decades of active research, the rheology of suspensions is not fully deciphered even in the simplest case of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. When suspensions are subjected to simple shear flow at very low Reynolds numbers (see figure 1), the linearity of the Stokes equations implies a linear relation between the shear stress τ = Σ xy and the shear rate ˙ γ and therefore a quasi-Newtonian rheological relation τ = η s ˙ γ. The effective suspension viscosity is given by η s (φ) = η f × f (φ) where η f is the viscosity of the pure Newtonian fluid and f (φ) is a sole function of the volume fraction φ which diverges when approaching maximum packing fraction (see e.g. Stickel & Powell 2005). However, this quasi-Newtonian relation does not fully describe the suspension rheology as differences in normal stresses develop, i.e. normal stresses are no longer isotropic, in the non-dilute limit. As the suspension is incompressible, the pressure itself (i.e. the trace of the bulk suspension stress Σ) is of no rheological interest, and the two relevant quantities are the first and second normal-stress differences defined as N 1 = Σ yy − Σ xx and N 2 = Σ yy − Σ zz respectively (see e.g. Bird, Armstrong