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, $\varphi$, but below the stress-dependent jamming fraction, we find a critical ${\varphi }_c(\sigma ,\mu )$ where $\sigma$ is a dimensionless shear stress and $\mu$ is the interparticle friction coefficient. For $\varphi >{\varphi }_c$, the proportion of particles in rigid clusters grows sharply, as $f_{\mathrm{rig}}\sim |\varphi -{\varphi }_c{|}^{\beta }$ with $\beta =1/8$. The fluctuations in the fraction of particles in rigid clusters yield a susceptibility measure ${\chi }_{\mathrm{rig}}\sim |\varphi -{\varphi }_c{|}^{-\gamma }$ 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 ${\varphi }_c$ for both $f_{\mathrm{rig}}$ and ${\chi }_{\mathrm{rig}}$. This behavior occurs over a range of stresses, with ${\varphi }_c(\sigma ,\mu )$ increasing as the stress decreases.

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Cited by in corpus (1)

• Boundary compliance selects heterogeneous dynamics in shear-thickening suspensions