Rigid clusters in shear-thickening suspensions: a nonequilibrium critical transition

Abstract

The onset and growth of rigid clusters in a two-dimensional (2D) suspension in shear flow are studied by numerical simulations. The suspension exhibits the lubricated-to-frictional rheology transition, but the key results here are for stresses above the levels that cause extreme shear-thickening. At large solid fraction, $\phi$, but below the stress-dependent jamming fraction, we find a critical $\phi_{c}(\sigma,\mu)$ where $\sigma$ is a dimensionless shear stress and $\mu$ is the interparticle friction coefficient. For $\phi>\phi_c$, the proportion of particles in rigid clusters grows sharply, as $f_{\rm rig} \sim |\phi-\phi_{c}|^{\beta}$ with $\beta=1/8$. The fluctuations in the fraction of particles in rigid clusters yield a susceptibility measure $\chi_{\rm rig} \sim |\phi-\phi_{c}|^{-\gamma}$ with $\gamma = 7/4$. The system is thus found to exhibit criticality. The results are shown to depend on an effective field $h(\mu)$, which provides data collapse near $\phi_c$ for both $f_{\rm rig}$ and $\chi_{\rm rig}$. This behavior occurs over a range of stresses, with $\phi_c(\sigma,\mu)$ increasing as the stress decreases.