Experimental evidence of viscous-inertial transition in non-colloidal granular suspensions

Dense granular suspensions can exhibit different regimes depending on the boundary conditions and stress distribution. In general, the flow is mainly controlled by the ratio of the shear rate and the particle pressure, which could be partially well described by a frictional approach for a dilatant granular media. However, as the shear rate increases and the fluid viscosity decreases, the flow can transit from a viscous to an inertial regime. In absence of constitutive equations, dimensional analysis does not give the crucial information to determine this transition, and except for some numerical works, there is not substantial experimental evidence of this phenomenon. 

In the present work, we present an experimental evidence of the viscous-inertial transition for suspension of non-colloidal rigid particles. A specially  designed pressure-and-volume imposed rheometer is used to explore the dense regime. By varying systematically the interstitial fluid, the shear rate, and packing fraction, we show that the transition takes place at a specific Stokes number, which is independent of the packing fraction. The algebraic power law for the viscosity divergence is also shown to be independent of the regime