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Phase diagram for inertial granular flows.

DeGiuli, E. and McElwaine, J. N. and Wyart, M. (2016) 'Phase diagram for inertial granular flows.', Physical review E., 94 (1). 012904.


Flows of hard granular materials depend strongly on the interparticle friction coefficient μp and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10−4≲I≲10−1: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as μp increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with μp, corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I≥10−2.5 that the growth of the macroscopic friction μ(I) with I is induced by an increase of collisional dissipation. This implies in that range that μ(I)−μ(0)∼I1−2b, where b≈0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L∼I−b and the density of sliding contacts χ∼Ib.

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Publisher statement:Reprinted with permission from the American Physical Society: Physical Review E 94, 012904 © (2016) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Date accepted:21 June 2016
Date deposited:26 January 2017
Date of first online publication:12 July 2016
Date first made open access:26 January 2017

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