Discharge of a granular silo as a visco-plastic flow L. Staron∗ and P.-Y. Lagr´ee∗ Granular matter is a well-known example of thixotropic material, able to flow like a viscous fluid or resist shear stress like a solid, and evolving from one state to the other over a distance typically of a few grain diameters. The discharge of a silo is one of the situations where the thixotropic properties of granular matter are best illustrated: while a dilute flow creates a free fall arch in the vicinity of the aperture, higher regions undergo a slower shear, and region closer to the corners remains static (Figure 1). Unlike the clepsydra, the discharge of a granular silo implies a constant rate, dictated by the size of the aperture, but independent of the height of material stored. This phenomenology - known as the Berveloo law - is often understood as resulting from the friction forces mobilized at the walls of the silo, thereby decreasing the apparent weight of the material, and screening the bottom area from the pressure now partly sustained by the walls (the ”Janssen effect”). This explanation fails however in the case of wide systems for which walls are distant from several times the height of material stored. In this contribution, we simulate the continuum counterpart of the granular silo by implementing the visco-plastic µ(I)-rheology in a 2D Navier-Stokes solver (Gerris). We observe a constant discharge rate irrespective of the initial filling height, and we recover the Berverloo scaling relating discharge rate and aperture size. This result points at the existence of a yield stress, rather than at the mobilization of friction forces at walls, as controling the discharge of the granular silo. Moreover, comparison with Contact Dynamics simulations show the reliability of the µ(I)-rheology when modeling complex flow of granular matter. ∗ CNRS - Universit´ e Pierre et Marie Curie Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France. Figure 1: Velocity field in a numerical granular silo (left, Contact Dynamics) and its viscoplastic continuum counterpart (right, Gerris solver).
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