Shear Thinning of Noncolloidal Suspensions

Shear thinning—a reduction in suspension viscosity with increasing shear rates—is understood to arise in colloidal systems from a decrease in the relative contribution of entropic forces. The shear-thinning phenomenon has also been often reported in experiments with noncolloidal systems at high volume fractions. However its origin is an open theoretical question and the behavior is difficult to reproduce in numerical simulations where shear thickening is typically observed instead. In this letter we propose a non-Newtonian model of interparticle lubrication forces to explain shear thinning in noncolloidal suspensions. We show that hidden shear-thinning effects of the suspending medium, which occur at shear rates orders of magnitude larger than the range investigated experimentally, lead to significant shear thinning of the overall suspension at much smaller shear rates. At high particle volume fractions the local shear rates experienced by the fluid situated in the narrow gaps between particles are much larger than the averaged shear rate of the whole suspension. This allows the suspending medium to probe its high-shear non-Newtonian regime and it means that the matrix fluid rheology must be considered over a wide range of shear rates.

Figure 1

Snapshot of a simulation corresponding $\varphi =0.4$ and box size $L_z=H=32a$. Total number of solid particles (gray) was $N_c=3129$ and SPH fluid particles (blue) $N\approx 4.3\times 10^6$. For clarity, upper and lower walls have not been drawn. To rule out finite size effects simulations were conducted up to gap size $H=64a$.

Figure 2

Simulation of a suspension with Newtonian solvent of constant viscosity ${\eta }_0$: distribution of the local shear rates ${\dot{\gamma }}_{\text{loc}}^{*}$ vs gap length between the spheres surfaces and probability distribution of ${\dot{\gamma }}_{\text{loc}}^{*}$ (inset), for three different input shear rates ${\dot{\gamma }}_{\mathrm{in}}^{*}$ (vertical dashed line indicates ${\dot{\gamma }}_c^{*}=10{\dot{\gamma }}_{\mathrm{in}}^{*\max }$).

Figure 3

Rheology of the suspensions with non-Newtonian suspending medium for different ${\dot{\gamma }}_c^{*}$ (top) and different slopes of viscosity decay $m$ (bottom).

Figure 4

Power-law exponent $b$ extracted from the suspension viscosity ${\eta }_{\text{rel}}({\dot{\gamma }}_{\mathrm{in}}^{*})$ for a solvent fluid characterized by $m=0.35$ and ${\dot{\gamma }}_c^{*}/{\dot{\gamma }}_{\mathrm{in}}^{*\max }=10$. Simulations are compared with exponents extracted from experiments in the power-law regime at different concentrations $\varphi$ [21].