Dynamic Jamming Point for Shear Thickening Suspensions

We report on rheometry measurements to characterize the critical behavior in two model shear thickening suspensions: cornstarch in water and glass spheres in oil. The slope of the shear thickening part of the viscosity curve is found to increase dramatically with packing fraction and diverge at a critical packing fraction ${\varphi }_c$. The magnitude of the viscosity and the yield stress are also found to have scalings that diverge at ${\varphi }_c$. We observe shear thickening as long as the yield stress is less than the stress at the viscosity maximum. Above this point the suspensions transition to purely shear thinning. Based on these data we present a dynamic jamming phase diagram for suspensions and show that a limiting case of shear thickening corresponds to a jammed state.

Figure 1

Shear stress $\tau$ vs shear rate $\dot{\gamma }$ for packing fractions $\varphi$, as indicated. (a) Glass spheres in mineral oil. (b) Cornstarch in water. Dashed lines: slope 1 indicating fixed viscosity.

Figure 2

Evolution of viscosity and yield stress with packing fraction $\varphi$ for glass spheres in mineral oil (a,c,e) and cornstarch in water (b,d,f). (a,b) Inverse logarithmic slope $ϵ$ of stress-shear rate traces in the shear thickening regime, defined by $\tau \propto {\dot{\gamma }}^{1/ϵ}$. Lower left inset: an example fit of viscosity vs stress on a log-log scale for $\varphi =0.562$. The open symbols represent the fit range. Upper right insets: micrographs of the particles. (c,d) Viscosity scale $\overline{\eta }$ defined as a geometric mean of the viscosity in the shear thickening region. Insets in (c,d): log-log plots of the same data relative to ${\varphi }_c$. (e,f) Yield stress ${\tau }_y$. Solid triangles: increasing stress measurements. Open triangles: decreasing stress measurements. Dotted lines: the plateau yield stress ${\tau }_{y,\max }$. Inset in (e): detailed view of the region close to ${\varphi }_c$. All panels: Solid lines are power law fits explained in the text; dashed lines are resulting values of ${\varphi }_c$.

Figure 3

Dynamic jamming phase diagram for shear thickening fluids. Data shown are for glass spheres in mineral oil. The solid line corresponds to the yield stress in Fig. 2e, while the dotted lines indicate transitions between shear thinning and thickening. Solid circle: dynamic jamming point at ${\varphi }_c$. Open circles: yield stress. Up-pointing triangles: onset of shear thickening. Down-pointing triangles: shear thickening maximum.