Shear-thickening suspensions of non-Brownian polydisperse particles are simulated in two dimensions using a lubrication flow-discrete element method-based algorithm at high packing fractions ($\varphi$) and large nondimensional stresses ($\sigma$). Rigidity analysis of the stress-induced particle clusters is carried out using pebble game algorithm for polydisperse suspensions and compared with the statistically equivalent bidisperse systems. A critical value of the packing fraction, ${\varphi }_c$, close to the shear-jamming transition, ${\varphi }_J^{\mu }$, (${\varphi }_c<{\varphi }_J^{\mu }$) is obtained where rigid particle clusters begin to grow sharply. The growth is found to be characterized by a critical transition of an order parameter ($f_{\text{rig}}$), defined by the fraction of particles in rigid clusters, which scales as $f_{\text{rig}}\sim {(\varphi -{\varphi }_c)}^{\beta }$ for $\varphi >{\varphi }_c$, and by the susceptibility scaling, ${\chi }_{\text{rig}}\sim {|\varphi -{\varphi }_c|}^{-\gamma }$, with exponents having values consistent with the critical exponents in two-dimensional (2D) percolation transition. The variations of $f_{\text{rig}}$ and ${\chi }_{\text{rig}}$ in polydisperse suspensions are found to be identical to that of the statistically equivalent bidisperse suspensions. Finite-size-scaling analysis shows a divergence of correlation length near ${\varphi }_{c_{\infty }}$ following critical exponent $\nu \approx 1.33$, in agreement with the 2D percolation theory. Furthermore, ${\varphi }_c$ and ${\varphi }_J^{\mu }$ are found to vary nonmonotonically with polydispersity index and depend on the particle stiffness.

Close

PrevNext

View figure in article

• Critical phenomena
• Fluid-particle interactions
• Interparticle interactions
• Jamming
• Low Reynolds number flows
• Lubrication
• Order parameters
• Shear flows
• Suspensions
• Rheological properties
• Shear thickening
• Viscosity
• Ising model
• Langevin algorithm
• Percolation theory
• Scaling methods