Irreversibility and rate dependence in sheared adhesive suspensions

Recent experiments report that slowly sheared noncolloidal particle suspensions unexpectedly exhibit rate$\left(\omega \right)$-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that van der Waals attraction gives rise to this behavior. At volume fractions $\varphi =20\text{–}50$%, 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 after repeated oscillations. Previous studies established that suspensions transition from reversible absorbing states to irreversible diffusing states when the oscillation amplitude 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, ${\gamma }_{0,\omega }^c\le {\gamma }_{0,\varphi }^c$, in the presence of weak attractions.

Figure 1

Experiment at $\varphi =40\%$: (a) Relative viscosity (${\eta }_R$) and first normal stress difference ($N_1$, inset) vs shear rate in SS. (b),(c) Evolution of the dynamic viscosity (${\eta }_R^{\prime }$) and its elastic counterpart (${\eta }_R^{″}$) vs the total accumulated strain at ${\gamma }_0=1\%$ (b) and 10% (c) in OS. The angular frequencies are indicated in the figure.

Figure 2

Suspension viscosities in OS and SS (inset). Dashed lines are least squares fits to data for Sr $<100$; numbers indicate the slopes.

Figure 3

Shear stress components of representative OS and SS cases at $\varphi =40\%$; see Fig. 2 for the annotation.

Figure 4

Microstructure statistics in OS. (a) Relative particle diffusivities at $\varphi =$ 40% and 50% (not distinguished). The dashed line is a fit of $D_x/D_x^{\infty }$. (b) Mean fraction of active (colliding) particles on linear and logarithmic (inset) scales. The dashed line is a power-law fit with slope $\beta =-0.40$. (c) Power-law distribution of cluster size, $P\left(n\right)\sim n^{-3.33}$ (solid line). (d) A snapshot of the particle suspension at $\varphi =$ 40%. Different cluster groups are indicated by colors.

Figure 5

Phase diagrams for irreversibility in sheared adhesive suspensions. (a) Critical strain amplitudes due to collisions (left) or attractions (right). $\omega$ is normalized by ${\tau }_a\equiv 6{\eta }_0{\epsilon }^{2}a/A$. (b) Projection of the irreversibility map on the $(\varphi ,\omega {\tau }_a)$ plane. (c) Volume of the reversible absorbing states in the $(\varphi ,\omega {\tau }_a,{\gamma }_0)$ space.