Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy
arXiv:2110.02342 · doi:10.1017/jfm.2022.741
Abstract
We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles under pressure-imposed conditions, subject to a sudden change in shear rate or external pressure. Discrete Element Method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may strongly differ from the prediction of the Suspension Balance Model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (2009), which prescribes the dilation rate of the suspension over a strain scale , quantitatively captures the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is nonlocal, with a nonlocal length scale which scales with the particle size and diverges algebraically at jamming. In regions affected by , the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below , thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.
arXiv comment24 pages, 9 figures
References in corpus (20)
- Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions
- Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions
- Discontinuous shear thickening without inertia in dense non-Brownian suspensions
- Reynolds Pressure and Relaxation in a Sheared Granular System
- High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming
- Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
- Non-monotonic flow curves of shear thickening suspensions
- The physics of dense suspensions
- Dynamic vorticity banding in discontinuously shear thickening suspensions
- Drop impact of shear thickening liquids
- Unifying impacts in granular matter from quicksand to cornstarch
- Constitutive relations for shear fronts in shear-thickening suspensions
- Splashing onset in dense suspension droplets
- Shear Reversal in Dense Suspensions: The Challenge to Fabric Evolution Models from Simulation Data
- Fully developed and transient concentration profiles of particulate suspensions sheared in a cylindrical Couette
- From splashing to bouncing: the influence of viscosity on the impact of suspension droplets on a solid surface
- X Radiography of Viscous Resuspension
- Viscous resuspension of non-Brownian particles: determination of the concentration profiles and particle normal stresses
- Deformation upon impact of a concentrated suspension drop
- Viscous-like forces control the impact response of shear-thickening dense suspensions