Stress Controlled Rheology of Dense Suspensions Using Transient Flows

Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we can track how a dense suspension approaches its shear-jammed state dynamically and quantitatively map out the onset stress for solidification in a state diagram.

Figure 1

(a) Relation between shear stress $\mathrm{\Sigma }$ and shear rate $\dot{\gamma }$ for a suspension in the SJ regime. Steady-state rheology was performed with parallel-plates geometry schematically illustrated in (b), and the transient flow in a wide-gap geometry is shown in (c). Red arrows indicate the motions of the solid boundaries.

Figure 2

Front profiles in the comoving frame for a suspension with $\varphi =0.53$. (a) Velocity profile $v(x-x_f)$. (b) Shear stress $\mathrm{\Sigma }$ (magenta squares) and shear rate $\dot{\gamma }$ (blue circles) profiles. (c) Local viscosity $\eta =\mathrm{\Sigma }/\dot{\gamma }$.

Figure 3

$\mathrm{\Sigma }-\dot{\gamma }$ flow curves for a suspension with $\varphi =0.53$, driven at different boundary speeds $U_0$. The solid black curve shows the prediction of the Wyart-Cates model. The dashed black line shows $\mathrm{\Sigma }={\eta }_N\dot{\gamma }$. The dashed-dotted black line is $\mathrm{\Sigma }\propto {\dot{\gamma }}^{1.7}$.

Figure 4

(a) Normalized front propagation speed $k/k_p$ as a function of shear stress ${\mathrm{\Sigma }}_{\infty }$ for different packing fractions $\varphi$. (b) Predictions of the generalized Wyart-Cates model [Eq. (5)].

Figure 5

State diagram. Squares are the onset stress of DST obtained from standard rheology with parallel plates (black) [34] and wide-gap Couette cell (open) [13]. Solid circles show the SJ regime mapped out by our experiments with transient flows [${\mathrm{\Sigma }}_{\infty }(\varphi )$]. Open circles are the onset stress of SJ from Peters et al. [13]. The red region shows the DST regime and the green curve shows ${\mathrm{\Sigma }}_{\mathrm{SJ}}$ [Eq. (6)] predicted by the Wyart-Cates model [22].