The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region

Abstract

We carry out a numerical study to investigate the dynamics of non-Brownian hard-sphere suspensions near the liquid and crystal coexistence region in small to large amplitude oscillatory shear flow. The first normal stress difference (N₁) and related rheological functions are carefully analyzed, focusing on the strain stiffening phenomenon, which occurs in the large strain amplitude region. Under oscillatory shear, we observe several unique behaviors of N₁. A negative nonzero mean value of N₁ (N_1,0) is observed for the applied strain amplitudes. The change of the sign, from negative to positive, at the maximum value of N₁ (N_1,max) is observed at a specific point, which is not consistent with the critical strain amplitude (γ_0,c) at which the modulus begins to deviate from linear viscoelasticity. The behavior of N₁ in the oscillatory shear flow is different from that of N₁ in steady shear flow, that is, the characteristics of N₁ in strain stiffening and shear thickening are quite distinguished from each other. We also perform structural analysis to confirm the relationship between the rheological properties and microstructure of the suspension. A strong correlation is observed between the global bond order parameter (Ψ₆) and the distortions in both nonlinear shear and normal stresses. The most noticeable characteristic is captured through the maximum of the global bond order parameter (Ψ_6,max). The strain amplitude at the slope change of Ψ_6,max corresponds to the point where a unique behavior of N₁ is observed, i.e. the change of the sign in N_1,max, but a strong correlation is not captured at γ_0,c. This demonstrates that the normal stress responds to particle ordering more sensitively than other rheological functions based on shear stress like dynamic moduli. As far as we are concerned, the behavior of N₁ has rarely been fully explored and related with the strain stiffening of non-Brownian suspensions so far. Therefore, this study has significance as the first report to strictly analyze strain stiffening along with the first normal stress difference N₁.