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

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, φ, but below the stress-dependent jamming fraction, we find a critical φc (σ, μ) where σ is a dimensionless shear stress and μ is the interparticle friction coefficient. For φ > φc , the proportion of particles in rigid clusters grows sharply, as frig ∼ |φ − φc |β with β = 1/8. The fluctuations in the fraction of particles in rigid clusters yield a susceptibility measure χrig ∼ |φ − φc|−γ with γ = 7/4. The system is thus found to exhibit criticality. The results are shown to depend on an effective field h(μ), which provides data collapse near φc for both frig and χrig. This behavior occurs over a range of stresses, with φc (σ, μ) increasing as the stress decreases.