Contact Networks Enhance Shear Thickening in Attractive Colloid-Polymer Mixtures

Increased shear thinning arising due to strong attractive interactions between colloidal particles is thought to obscure shear thickening. Here, we demonstrate how moderate attractions, induced by adding a nonadsorbing polymer, can instead enhance shear thickening. We measure the rheology of colloidal suspensions at a constant particle volume fraction of $\varphi =0.40$ with dilute to weakly semidilute concentrations of three polyacrylamide depletants of different molecular weights. Suspensions containing large polymer exhibit increased shear thickening and positive first normal stress differences at high shear stress, and increased heterogeneous fluctuations in the boundary stress. These results are consistent with a friction-based model for shear thickening, suggesting that the presence of large, extended polymers induces the formation of near-spanning networks of interparticle contacts.

Figure 1

(a)–(c) Viscosity and (d)–(f) corrected $N_1$ as a function of shear stress for $\varphi =0.40$ suspensions with various free-volume concentrations of polyacrylamide $c/c^{*}$, normalized by the overlap concentration $c^{*}$. Polymers (a),(d) USP; (b),(e) ULP; (c),(f) DP. Insets: Micrographs of quiescent suspensions with $c/c^{*}=$ (d) 0.5 USP, (e) 0.7 ULP, and (f) 0.7 DP. Scale bars: $5\mu \mathrm{m}$.

Figure 2

Power-law (a) shear-thinning ($n$) and (b) shear-thickening ($\beta$) exponents as a function of normalized polyacrylamide (USP, ULP, DP) concentration in the free volume $c/c^{*}$ for $\varphi =0.40$ suspensions. Gray lines are guides for the eye.

Figure 3

(a) Relative viscosity as a function of stress, fit to Eq. (1) [5, 10] for representative suspensions without polymer, with normalized polyacrylamide concentration in the free volume $c/c^{*}=0.7$ ULP, and with $c/c^{*}=0.7$ DP. (b),(c) Fit parameters extracted from Eq. (1) as a function of $c/c^{*}$. Dashed lines are guides for the eye at (b) ${\varphi }_0=0.71$, ${\sigma }^{*}=100\mathrm{Pa}$, (c) $f_{\max }=1$. Samples in the shaded region ($f_{\max }>0.8$) exhibited $N_1>0$.

Figure 4

(a) Examples of boundary stress (in units of Pa) with weak and strong heterogeneity events. Shared scale bar: $100\mu \mathrm{m}$. (b) Average boundary stress as a function of measurement time while shearing at a rate of $100{\mathrm{s}}^{-1}$ (top row) and $500{\mathrm{s}}^{-1}$ (bottom row) for USP (first column), ULP (second column), and DP (third column) samples with $c/c^{*}=0.7$.