Origin of Two Distinct Stress Relaxation Regimes in Shear Jammed Dense Suspensions

Many dense particulate suspensions show a stress induced transformation from a liquidlike state to a solidlike shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly nonexponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and normal stress measurements confirm that such stress discontinuity originates from the localized plastic events, whereas system spanning dilation controls the slower relaxation process. We also find an intriguing correlation between the nature of transient relaxation and the steady-state shear jamming phase diagram obtained from the Wyart-Cates model.

Figure 1

(a) Shear stress $\sigma$ as a function of time $t$ (symbols) under different applied step strains $\gamma$ (thin lines). Solid lines are the fits to the power-law cutoff by a stretched exponential function (main text). The arrow indicates peak stress (${\sigma }_p$) for $\gamma =130\%$. (b) Plots of $\sigma$ vs $t$ for $\gamma \ge 100\%$ showing a self similarity. Power-law decay with slope 0.5 is also indicated. Solid lines show typical stretched exponential fits after the discontinuous stress drop. The fast ${\tau }_f$ (yellow shade) and slow ${\tau }_s$ (brown shade) relaxation timescales are marked. (c) Evolution of first normal stress difference $N_1$ corresponding to the data shown in panel (b). In all cases $\varphi =58\%$ and solvent viscosity ${\eta }_l=80\mathrm{mPa}$.s.

Figure 2

Intensity $I$ as a function of time $t$ (gray lines) for different regions with (a) and without (e) PCs with the average behaviors (thick red lines) are also indicated. Here, the starting time for each graph corresponds to an absolute time $t=t_0$ as mentioned in Fig. 1. Relaxation time for PC (${\tau }_p$) and dilation (${\tau }_d$) are marked with vertical dash lines in (a). Inset: distribution of ${\tau }_p$ and ${\tau }_d$ ($N=130$). (b) and (c) Consecutive images of the sample boundary, during the fast relaxation, and the corresponding difference image is shown in (d). (f) and (g) Consecutive images of the sample boundary, during slow relaxation, and the corresponding difference image shown in (h). (i) Elastic modulus ($G^{\prime }$) vs strain amplitude (${\gamma }_0$). Dashed lines represent the slope in different ${\gamma }_0$ regimes with the corresponding boundary images shown in panels (j), (k), and (l). $\varphi =61\%$ and ${\eta }_l=80\mathrm{mPa}.\mathrm{s}$ in all cases.

Figure 3

(a) Dependance of fast (${\tau }_p$ and ${\tau }_f$) and slow (${\tau }_d$ and ${\tau }_s$) timescales as a function of volume fraction $\varphi$. ${\tau }_i=1/\dot{{\gamma }_c}$ obtained from the steady-state measurements. Inset: ${\tau }_f$ and ${\tau }_s$ as a function of ${\eta }_l$. Error bars indicate standard deviation over three independent measurements. Gray dashed lines are guides to the eye. (b) State diagram in $\sigma \text{−}\varphi$ parameter plane. Thick green line indicates SSSJ onset. In the pink shaded region discontinuous stress relaxation (red triangles) and PCs (yellow dots) are observed, whereas, in the green region (with dark-green triangles), a continuous relaxation (power-law cutoff by a stretched exponential) is found. Below the SSSJ regime (purple region with blue triangles) initial power-law relaxation behavior disappears. Gray shaded region indicates isotropic jamming. In all cases symbols are the peak stress ${\sigma }_p$ obtained from the transient relaxation experiments.