Dry granular flows: Rheological measurements of the μ (I) -rheology

Granular materials do not always flow homogeneously like fluids when submitted to external stress, but often form rigid regions that are separated by narrow shear bands where the material yields and flows. This shear localization impacts their apparent rheology, which makes it difficult to infer a constitutive behavior from conventional rheometric measurements. Moreover, they present a dilatant behavior, which makes their study in classical fixed-volume geometries difficult. These features led numerous groups to perform extensive studies with inclined plane flows, which were of crucial importance for the development and the validation of the μ (I)-rheology. Our aim is to develop a method to characterize granular materials with rheometrical tools. Using rheometry measurements in an annular shear cell, dense granular flows of 0.5mm spherical and monodisperse beads are studied. A focus is placed on the comparison between the present results and the μ (I)-rheology. From steady state measurements of the torque and the gap under imposed shear rate γ and normal force F_N, we define an inertial number I. We show that, at low I (small γ and/or large F_N), the flow goes to a quasistatic limit, and the response in terms of dimensionless stress or internal friction coefficient - μ - and solid concentration - profiles is independent of the inertial number. Upon increasing I (large γ and/or small F_N), dilation occurs and decreases while μ increases. The observed variations are in good agreement with previous observations of the literature [Jop et al., Nature 441, 727-730 (2006) and Hatano, Phys. Rev. E 75, 060301 (R) (2007)]. These results show that the constitutive equations μ (I) and (I) of granular materials can be measured with a rheometer.