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Rheology of periodically sheared suspensions undergoing reversible-irreversible transition

The rheology of non-colloidal suspensions under cyclic shear is studied numerically. The main findings are a strain amplitude ($γ_0$) dependent response in the shear stress and second normal stress difference ($N_2$). Specifically, we find a reduced viscosity, an enhanced intracycle shear thinning, the onset of a finite $N_2$ and its frequency doubling, all near a critical strain amplitude $γ_c$ that scales with the volume fraction $ϕ$ as $γ_c \sim ϕ^{-2}$. These rheological changes also signify a reversible-irreversible transition (RIT), dividing stroboscopic particle dynamics into a reversible absorbing phase (for $γ_0<γ_c$) and a persistently diffusing phase (for $γ_0>γ_c$). We explain the results based on two flow-induced mechanisms and elucidate their connection in the context of RIT through the underlying microstructure, which tends towards hyperuniformity near $γ_0=γ_c$. Overall, we expect this correspondence between rheology and emergent dynamics to hold in a wide range of settings where structural organizations are dominated by volume exclusions.