Jamming, Yielding, and Rheology of Weakly Vibrated Granular Media

We establish that the rheological curve of dry granular media is nonmonotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the nonmonotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the nonmonotonic flow curve governs the yielding behavior of granular media. Finally, we show that nonmonotonic flow curves can be seen in at least two different flow geometries and for several granular materials.

Figure 1

Hypothetical flow curves for granular media, relating strain rate $\dot{\gamma }$ and stress $\sigma$. (a) Monotonic flow curve with a different static (${\sigma }_s$) and dynamic (${\sigma }_d$) yield stress. (b) Nonmonotonic flow curve—the region with negative slope signals “forbidden” strain rates in stress-controlled experiments. (c) A typical flow curve observed in our experiments for finite vibration strengths.

Figure 2

Flow curves $T(\Omega )$ for $\Gamma =0,0.1,\dots ,1$ as indicated. We normalize $T$ by the dynamic yield torque $T_d$. Inset: vibrated split-bottom rheological setup.

Figure 3

(a) Finite $\Gamma$ hysteresis loops for $\Gamma =0.1$, 0.3, 0.5. (b) Several hysteresis loops at $\Gamma =0.5$, with the rheological data from $\Gamma =0.5$ from Fig. 2 overplotted in black.

Figure 4

(a) Typical examples of $\Omega (T)$ curves during a torque ramp. The dashed line indicates the threshold rotation rate ${\Omega }_{\mathrm{Th}}=0.016\mathrm{rps}$ that defines a yield event. ◇ indicates a microyielding event, □ a global failure event. (b) The probability distribution function of microyielding (gray) and global yielding (black). Gray bars indicate the onset value for the rheological instability $T_{\min }$, and the dynamic yield stress $T_d$. (c) Flow curve for $\Gamma =0$.

Figure 5

Rheological curves for a range of materials as indicated, where a vane (see sketch) directly coupled to an Anton Paar MCR501 rheometer was placed just above the bottom. All torques are normalized by their mean value and (with the exception of the bottom curve) shifted upwards for clarity.