Oscillatory shear flows of dense suspensions at imposed pressure: Rheology and micro-structure

Oscillatory shear has been widely used to study the rheological properties of suspensions under unsteady shear. Furthermore, recent works have shown that oscillatory flows can improve the flowability of dense suspensions. While most studies have been done under constant volume we here study oscillatory shear flows of a two-dimensional suspensions using a normal pressure-controlled set-up. To characterise the rheology, we introduce both a complex macroscopic friction coefficient $\mu^{*}$, following the convention of the complex viscosity $\eta^{*}$, and a shear-rate averaged viscous number $J'$. The rheology and microstructure of dense suspensions are studied by systematically varying both the strain magnitude $\gamma_0$ and $J'$ using numerical simulations. We study both suspensions composed of frictional ($\mu_p=0.4$) or frictionless ($\mu_p=0$) particles and find that the critical values, as $J' \to 0$, of both the complex macroscopic friction and the number of contacts, both total and sliding, decrease with decreasing $\gamma_0$. For suspensions composed of frictional particles we also find that the critical (i.e.~the shear jamming) packing fraction $\phi_c$ increase with decreasing $\gamma_0$. In both cases, frictional and frictionless, we find that the rheological response approaching the shear jamming turns from a viscous to an elastic response as $\gamma_0$ is lowered below $\sim0.33$.