A rheological signature of frictional interactions in shear thickening suspensions

We elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces to colloidal shear thickening by measuring both the viscosity $\eta$ and first normal stress difference $N_1$ in suspensions of silica spheres over a wide range of volume fractions. The first normal stress difference reveals a transition not apparent in the viscosity alone, from $N_1<0$ at moderate volume fractions $\phi \leq 0.52$ to $N_1 > 0$ at larger values of $\phi$. While the $N_1 <0$ behavior is consistent with hydrodynamic models, the $N_1 >0$ behavior (dilation) is instead a characteristic of frictional `granular' suspensions. Fitting our viscosity profiles $\eta(\sigma, \phi)$ to a model for friction-driven shear thickening, we capture the shear thickening for $\phi \geq 0.52$ but must adjust the adjust the maximum fraction of frictional contacts to fit at lower volume fractions. Our results bring together two contrasting theories for shear thickening; they show that friction drives shear thickening in concentrated colloidal suspensions, but also highlight the need to include hydrodynamic effects to fully describe the rheology at moderate concentrations.