Rheology of granular liquids in extensional flows: Beyond the $\mu (\mathcal{I})$-law

Abstract

The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of non monotonous evolution of the effective friction coefficient $\mu$ with the inertial number $\mathcal{I}$. By the reduction of the GITT equations to simple toy-models, we provide a generalization of the $\mu (\mathcal{I})$-law true for any type of flow deformation. Our analysis also includes a study of the Trouton ratio, which is shown to behave quite similarly to that of dense colloidal suspensions.

arXiv comment17 pages, 11 figures

References in corpus (28)

• On dense granular flows
• A constitutive law for dense granular flows
• Rheophysics of dense granular materials : Discrete simulation of plane shear flows
• Crucial role of side walls for granular surface flows: consequences for the rheology
• Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane
• Theory of nonlinear rheology and yielding of dense colloidal suspensions
• Unified study of glass and jamming rheology in soft particle systems
• Frictionless bead packs have macroscopic friction, but no dilatancy
• The physics of sediment transport initiation, cessation, and entrainment across aeolian and fluvial environments
• Glass Rheology: From mode-coupling theory to a dynamical yield criterion
• Schematic models for dynamic yielding of sheared colloidal glasses
• A mode coupling theory for Brownian particles in homogeneous steady shear flow
• Interparticle hydrogen bonding can elicit shear jamming in dense suspensions
• Disentangling glass and jamming physics in the rheology of soft materials
• Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
• Phase Diagram for Inertial Granular Flows
• Rheology of dense granular suspensions under extensional flow
• The influence of surface roughness on the rheology of immersed and dry frictional spheres
• Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows
• Dynamic shear jamming in dense granular suspensions under extension
• The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
• Complex fluids in the animal kingdom
• Rheology of inelastic hard spheres at finite density and shear rate
• Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and $\mu$-$J$ rheology
• Integration through transients approach to the $\mu (\mathcal{I})$ rheology
• Integration through transients for inelastic hard sphere fluids
• Unifying Suspension and Granular flows near Jamming
• Granular rheology: a tale of three time scales

Cited by in corpus (1)

• Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology