Phase Diagram for Inertial Granular Flows

Abstract

Flows of hard granular materials depend strongly on the interparticle friction coefficient ${\mu }_p$ and on the inertial number $\mathcal{I}$, 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 $10^{-4}\lesssim \mathcal{I}\lesssim 10^{-1}$: \textit{ frictionless, frictional sliding, } and {\it rolling}. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as ${\mu }_p$ increases from zero at constant $\mathcal{I}$. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display non-monotonic behavior with ${\mu }_p$, 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 $\mathcal{I}\ge 10^{-2.5}$ that the growth of the macroscopic friction $\mu (\mathcal{I})$ with $\mathcal{I}$ is induced by an increase of collisional dissipation. This implies in that range that $\mu (\mathcal{I})-\mu (0)\sim {\mathcal{I}}^{1-2b}$, where $b\approx 0.2$ is an exponent that characterizes both the dimensionless velocity fluctuations $\mathcal{L}\sim {\mathcal{I}}^{-b}$ and the density of sliding contacts $\chi \sim {\mathcal{I}}^b$.

6 pages + 6 pages SI

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• Flow-Arrest Transitions in Frictional Granular Matter
• Flow and rheology of frictional elongated grains
• Viscometric flow of dense granular materials under controlled pressure and shear stress
• A gravity-independent powder-based additive manufacturing process tailored for space applications
• Effect of particle collisions in dense suspension flows
• Flow and Arrest in Stressed Granular Materials
• Integration through transients approach to the $\mu (\mathcal{I})$ rheology
• Inertial Force Transmission in Dense Granular Flows
• Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology
• Rheology of granular liquids in extensional flows: Beyond the $\mu (\mathcal{I})$-law
• Comment on: `What Determines the Static Force Chains in Stressed Granular Media?'
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• Unifying Suspension and Granular flows near Jamming
• Shear flow of frictional spheroids: Comparison between elongated and flattened particles
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