Irreversibility and rate dependence in sheared adhesive suspensions

Recent experiments report that slowly-sheared noncolloidal particle suspensions can exhibit unexpected rate($\omega$)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that a weak interparticle attraction reproduces this behavior. At volume fractions $\varphi =20\sim 50$%, the complex viscosities in both experiments and simulations display power-law reductions in shear, with a $\varphi$-dependent exponent maximum at $\varphi =40$%, resulting from the interplay between hydrodynamic, collision and adhesive interactions. Furthermore, this rate dependence is accompanied by diverging particle diffusivities and pronounced cluster formations even at small oscillation amplitudes ${\gamma }_0$. Previous studies established that suspensions transition from reversible absorbing states to irreversible diffusing states when ${\gamma }_0$ exceeds a $\varphi$-dependent critical value ${\gamma }_{0,\varphi }^c$. Here, we show that a second transition to irreversibility occurs below an $\omega$-dependent critical amplitude, $\gamma_{0,\omega}^c \leq \gamma_{0,\phi}^c$, in the presence of weak attractions.