Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

We investigate the transient dynamics of a sheared suspension neutrally buoyant particles under pressure-imposed conditions, subject to sudden change in shear rate or external pressure. Discrete Element Method simulations show that, depending on flow parameters (particle and system size, initial volume fraction), early stress response may strongly differ from prediction Suspension Balance Model based steady-state rheology. that two-phase model incorporating Reynolds-like dilatancy law Pailha & Pouliquen (2009), which prescribes dilation over strain scale $\gamma_0$, quantitatively captures dilation/compaction whole range investigated. Together with Darcy induced by pore pressure gradient during compaction, this implies is nonlocal, nonlocal length $\ell$ scales particle size diverges algebraically at jamming. In regions affected $\ell$, level fixed, not rheology, but fluid resulting rate. Our results extend validity rule, initially proposed for jammed suspensions, flowing below $\phi_\mathrm{c}$, thereby providing unified framework describe shear-induced migration. They pave way understanding more complex unsteady flows dense such as impacts, avalanches impulsive shear-thickening suspensions.