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, ϕ, but below the stress-dependent jamming fraction, we find a critical ϕ_{c}(σ,μ) where σ is a dimensionless shear stress and μ is the interparticle friction coefficient. For ϕ>ϕ_{c}, the proportion of particles in rigid clusters grows sharply, as f_{rig}∼|ϕ−ϕ_{c}|^{β} with β=1/8. The fluctuations in the fraction of particles in rigid clusters yield a susceptibility measure χ_{rig}∼|ϕ−ϕ_{c}|^{−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 ϕ_{c} for both f_{rig} and χ_{rig}. This behavior occurs over a range of stresses, with ϕ_{c}(σ,μ) increasing as the stress decreases.