Flow-Switched Bistability in a Colloidal Gel with Non-Brownian Grains

We show that mixing a colloidal gel with larger, non-Brownian grains generates novel flow-switched bistability. Using a combination of confocal microscopy and rheology, we find that prolonged moderate shear results in liquefaction by collapsing the gel into disjoint globules, whereas fast shear gives rise to a yield-stress gel with granular inclusions upon flow cessation. We map out the state diagram of this new “mechanorheological material” with varying granular content and demonstrate that its behavior is also found in separate mixture using different particles and solvents.

Figure 1

(a)–(d) Flow-switched transition between solid and liquid states in a binary mixture with ${\varphi }_S=0.13$ and ${\varphi }_L=0.3$ (see also Supplemental Material, Video S1 [15]). After slow roller mixing, the sample flows freely when the vial is tilted (a) and remains in this liquidlike state when left undisturbed for a week (c). After brief vortex shaking (b), the sample transitions into a solid that can support itself when inverted. This solid state likewise persists when left at rest (d). (e) A schematic transition diagram, using the yield stress after shear cessation to distinguish solid (red) and liquid (blue) states. Horizontal dashed lines denote unstable states, where sustained shear drives a transition to the stable state (solid lines) after a large accumulated strain.

Figure 2

(a) Flow curves $\sigma (\dot{\gamma })$ for a sample with ${\varphi }_S=0.1$ and ${\varphi }_L=0.2$ measured at fixed rate using two protocols. Ramp-down (blue square): the shear rate is ramped down, at each point taking the steady-state stress after shearing for 300 s. Step-down (red circle): the sample first rejuvenated at ${\dot{\gamma }}_{\mathrm{rej}}=1000{\mathrm{s}}^{-1}$ for 100 s between each shear rate, and the transient stress is measured for 30 s. Full line: Herschel-Bulkley fit $\sigma ={\sigma }_y+k{\dot{\gamma }}^n$, giving ${\sigma }_y=2.6\mathrm{Pa}$, $k=1.8\mathrm{Pa}{\mathrm{s}}^n$, and $n=0.7$. Gray: flow curves for the same protocols applied to a colloidal gel with $\varphi ={\varphi }_S=0.1$. (b) Strain $\gamma$ versus time $t$ for a creep test performed on the binary sample in (a). After preshear at ${\sigma }_{\mathrm{pre}}=100\mathrm{Pa}$ (blue cross, imposing 1 Pa after preshear at ${\sigma }_{\mathrm{pre}}=5\mathrm{Pa}$), we impose stepwise increasing shear stress $\sigma$ and measure the evolution of strain $\gamma$.

Figure 3

(a) Yield stress measured via creep tests after variable preshear stress ${\sigma }_{\mathrm{pre}}$ for a sample with ${\varphi }_S=0.1$ and ${\varphi }_L=0.2$. Before applying ${\sigma }_{\mathrm{pre}}$, the sample was either initially in a solid state (diamond symbol, obtained by shearing for 100 s at $1000{\mathrm{s}}^{-1}$) or a liquid state (red circle, obtained by shearing for $\approx 20\min$ at $5{\mathrm{s}}^{-1}$). Error bars reflect the finite stress step in the creep tests. (b) Confocal images in the flow-vorticity ($x\text{−}y$) plane at a height $z=30\mu \mathrm{m}$, separately showing the small (red) and large (green) particles. The sample was sheared at ${\sigma }_{\mathrm{pre}}$ (given above each image) for sufficiently long. Top and bottom images in the left-hand panel correspond to samples that started initially as the sample on the right and in the middle panel, respectively. (c),(d) Volume renderings constructed by thresholding the red small-particle channel from 3D confocal stacks. These stacks run from $z=0\mu \mathrm{m}$ to $z=60\mu \mathrm{m}$ and correspond to the same ${\sigma }_{\mathrm{pre}}=10\mathrm{Pa}$ (c) and ${\sigma }_{\mathrm{pre}}=100\mathrm{Pa}$ (d) samples shown in (b).

Figure 4

State transition dynamics. Confocal snapshots at $z=30\mu \mathrm{m}$ showing the shear-driven phase separation at $\sigma =5\mathrm{Pa}$ (a) and high-shear homogenization at $\sigma =50\mathrm{Pa}$ (b), both for ${\varphi }_S=0.1$ and ${\varphi }_L=0.2$. See also Supplemental Material, Videos S2 and S3 [15].

Figure 5

(a) State diagram in ${\varphi }_L–\sigma$ space for fixed ${\varphi }_S=0.1$. For each point, the sample is first high-shear rejuvenated by applying fixed stress ${\sigma }_{\mathrm{rej}}=100\mathrm{Pa}$ for 100 s, then a stress $\sigma$ is applied until reaching a steady state (typically $\gtrsim 10\min$ for PS region and $\gtrsim 100\mathrm{s}$ for H region). The PS (blue square) and H (red circle) states are identified by imaging the 3D microstructure after shear is ceased. We do not obtain steady flow (red cross, blue cross) below the yield stress of the high-shear rejuvenated state, in agreement with ${\sigma }_y^H$ (star) estimated from Herschel-Bulkley fits to flow curves measured by step-down protocol (see Sec. VI of Ref. [15]). Samples with bistability in the low-stress regime (gray star) are highlighted in pink. (b),(c) Mean blob size measured from 3D confocal stacks, varying both $\sigma$ (b) and ${\varphi }_L$ (c) within the PS region of the state diagram. Error bars denote standard deviation from blobs within the imaging volume.

Figure 6

(a)–(d) Images of the fumed-silica-based binary suspension (${\varphi }_S=0.02$ and ${\varphi }_L=0.3$) in a glass vial, showing a similar liquid-solid transition under alternating high-shear vortex mixing and gentle roller mixing as in Fig. 1. See also Supplemental Material, Video S4 [15]. (c),(d) Cryogenic SEM images showing the solid (c) and liquid (d) states at the same composition, prepared by $\sigma =250\mathrm{Pa}$ and $\sigma =10\mathrm{Pa}$ in a rheometer, respectively. Note that individual fumed silica particles cannot be resolved, only the larger blobs of the smaller particles in the liquid state. (e) Flow curves obtained using the same two protocols as in Fig. 2. A Herschel-Bulkley fit (solid red line) to the data from step-down protocol gives ${\sigma }_y=5.2\mathrm{Pa}$, $k=3.5\mathrm{Pa}{\mathrm{s}}^n$, and $n=0.7$.