The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra

Abstract

The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constant friction), we simulate the continuum counterpart of the granular silo. Doing so, we obtain a constant flow rate during the discharge and recover the Beverloo scaling independently of the initial filling height of the silo. We show that lowering the value of the coefficient of friction leads to a transition toward a different behavior, similar to that of a viscous fluid, and where the filling height becomes active in the discharge process. The pressure field shows that large enough values of the coefficient of friction ($\simeq$ 0.3) allow for a low-pressure cavity to form above the outlet, and can thus explain the Beverloo scaling. In conclusion, the difference between the discharge of a hourglass and a clepsydra seems to reside in the existence or not of a plastic yield stress.

arXiv comment6 pages, 6 figures

References in corpus (5)

• A constitutive law for dense granular flows
• Jamming during the discharge of granular matter from a silo
• Experiments on Corn Pressure in Silo Cells -- Translation and Comment of Janssen's Paper from 1895
• Granular discharge and clogging for tilted hoppers
• Rheology of a confined granular material

Cited by in corpus (19)

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• Small Solar System Bodies as granular media
• 2D granular flows with the $\mu (I)$ rheology and side walls friction: a well balanced multilayer discretization
• Granular discharge rate for submerged hoppers
• Flow in an hourglass: particle friction and stiffness matter
• Modeling silo clogging with nonlocal granular rheology
• Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations
• Differential equation for the flow rate of discharging silos based on energy balance
• Forced flow of granular media: Breakdown of the Beverloo scaling
• Velocity scaling in the region of orifice influence in silo draining under gravity
• Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow
• A weakly non-hydrostatic shallow model for dry granular flows
• External pressure dependence of Granular Orifice Flow: transition to Beverloo flow
• Velocity profiles in forced silo discharges
• A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule
• A note on Stokes' problem in dense granular media using the $\mu (I)$--rheology
• Unjamming strongly compressed particle rafts