Shear-induced clustering of Brownian colloids in associative polymer networks at moderate Péclet number

We investigate shear-induced clustering and its impact on fluid rheology in polymer-colloid mixtures at moderate colloid volume fraction. By employing a thermoresponsive system that forms associative polymer-colloid networks, we present experiments of rheology and flow-induced microstructure on colloid-polymer mixtures in which the relative magnitudes of the time scales associated with relaxation of viscoelasticity and suspension microstructure are widely and controllably varied. In doing so, we explore several limits of relative magnitude of the relevant dimensionless shear rates, the Weissenberg number Wi and the Péclet number Pe. In all of these limits, we find that the fluid exhibits two distinct regimes of shear thinning at relatively low and high shear rates, in which the rheology collapses by scaling with Wi and Pe, respectively. Using three-dimensionally-resolved flow small-angle neutron scattering measurements, we observe clustering of the suspension above a critical shear rate corresponding to $\mathrm{Pe}\sim 0.1$ over a wide range of fluid conditions, having anisotropy with projected orientation along both the vorticity and compressional axes of shear. The degree of anisotropy is shown to scale with Pe. From this we formulate an empirical model for the shear stress and viscosity, in which the viscoelastic network stress is augmented by an asymptotic shear thickening contribution due to hydrodynamic clustering. Overall, our results elucidate the significant role of hydrodynamic interactions in contributing to shear-induced clustering of Brownian suspensions in viscoelastic liquids.

Figure 1

(a) Schematic diagram of the Couette shear cell for the 2D flow-SANS scattering. Also shown are 2D scattering projections for the (b) flow-vorticity (1-3) plane and (c) flow-gradient (1-2) plane.

Figure 2

TTS master curves and characteristic time scales. Nanoemulsions contain ${\varphi }_o=0.33$ PDMS droplets with PEG and $C_s=120\mathrm{mM}$ SDS, with (a) and (b) $\langle a\rangle =34.6\mathrm{nm}$ and ${\varphi }_p=0.33$, (c) and (d) $\langle a\rangle =31.7\mathrm{nm}$ and ${\varphi }_p=0.36$, and (e) and (f) $\langle a\rangle =35.4\mathrm{nm}$ and ${\varphi }_p=0.40$. The reference temperature is 15 °C. (See SM [35] for the horizontal and vertical shifting factors.)

Figure 3

Steady shear rheology for several nanoemulsions at the indicated temperatures. Nanoemulsions contain ${\varphi }_o=0.33$ PDMS droplets with PEG and $C_s=120\mathrm{mM}$ SDS, with (a) $\langle a\rangle =34.6\mathrm{nm}$ and ${\varphi }_p=0.33$, (b) $\langle a\rangle =31.7\mathrm{nm}$ and ${\varphi }_p=0.36$, and (c) $\langle a\rangle =35.4\mathrm{nm}$ and ${\varphi }_p=0.40$. Dashed lines represent the Carreau-Yasuda model fitting at low shear rates and solid lines represent the fitting result proposed by the perturbation model (4).

Figure 4

Scaled steady shear rheology. (a)–(c) Weissenberg number scaling. (d)–(f) Péclet number scaling. Nanoemulsions contain ${\varphi }_o=0.33$ PDMS droplets with PEG and $C_s=120\mathrm{mM}$ SDS. (a) and (d) $\langle a\rangle =34.6\mathrm{nm}$ and ${\varphi }_p=0.33$. (b) and (e) $\langle a\rangle =31.7\mathrm{nm}$ and ${\varphi }_p=0.36$. (c) and (f) $\langle a\rangle =35.4\mathrm{nm}$ and ${\varphi }_p=0.40$.

Figure 5

2D flow-SANS scattering patterns showing heat plots of absolute intensity (a) before and (b) after subtracting the intensity at zero shear rate in both 1-3 (flow-vorticity) and 1-2 (flow-gradient) planes at the Péclet numbers indicated. Data are for the nanoemulsion containing ${\varphi }_o=0.33$ PDMS droplets $(\langle a\rangle =34.6\mathrm{nm})$ with ${\varphi }_p=0.33$ PEG and $C_s=120\mathrm{mM}$ SDS. Scale tick labels represent values of $q_x$ and $q_y$ in $\mathrm{n}{\mathrm{m}}^{–1}$ and the color intensity scales represent the absolute scattering intensity in $\mathrm{c}{\mathrm{m}}^{–1}$.

Figure 6

Anisotropy factors as a function of (a) shear rate and (b) Pe with power-law scaling. The power-law exponent is 0.34 ± 0.026. Legend represents scattering plane, average radius of droplets, concentration of polymer, and temperatures. Open symbols represent values that represent unresolvable anisotropy.

Figure 7

Temperature dependence of the Carreau-Yasuda power-law slope for the samples indicated, obtained by fits to shear rates in the low-Wi regime.

Figure 8

${\sigma }_{\mathrm{total}}\left(\dot{\gamma }\right)/{\sigma }_{\mathrm{viscoelastic}}\left(\dot{\gamma }\right)-1$ as a function of Pe for the nanoemulsions containing (a) ${\varphi }_p=0.33$, (b) ${\varphi }_p=0.36$, and (c) ${\varphi }_p=0.40$.