E. DeGiuli
Phase diagram for inertial granular flows
DeGiuli, E.; McElwaine, J.N.; Wyart, M.
Abstract
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.
Citation
DeGiuli, E., McElwaine, J., & Wyart, M. (2016). Phase diagram for inertial granular flows. Physical Review E, 94(1), Article 012904. https://doi.org/10.1103/physreve.94.012904
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 21, 2016 |
Online Publication Date | Jul 12, 2016 |
Publication Date | Jul 12, 2016 |
Deposit Date | Oct 21, 2016 |
Publicly Available Date | Jan 26, 2017 |
Journal | Physical review . E, Statistical, nonlinear, and soft matter physics |
Print ISSN | 2470-0045 |
Electronic ISSN | 2470-0053 |
Publisher | American Physical Society |
Peer Reviewed | Peer Reviewed |
Volume | 94 |
Issue | 1 |
Article Number | 012904 |
DOI | https://doi.org/10.1103/physreve.94.012904 |
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Copyright 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.
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