The rheophysics of two athermal systems: dry granular media and non-Brownian suspensions

The steady-state, pressure-controlled simple shear flow constitutes a paradigm for the study of flows of dense athermal systems such as dry grains or non-Brownian suspensions. The introduction of two dimensionless numbers called inertial and viscous was an important step. In an attempt to provide a common rheophysical framework to both systems, we relate their flow properties in the dense regime close to jamming transition to two basic constitutive laws or equations of state : both the free volume and the ratio of shear stress to particle pressure (in excess of a static friction coefficient) vary as power laws, with systemdependent exponents, of a Deborah number. The first law is derived from the Boltzmann equation expressed in the approximation of relaxation. The second law is deduced from the expression of the probability for a particle to belong to a transient cluster of particles in contact. Mots clefs : systemes athermiques, rheophysique. 21 eme Congres Francais de Mecanique Bordeaux, 26 au 30 aout 2013