Nonlinear rheology of colloidal suspensions probed by oscillatory shear

Abstract

The nonlinear stress and microstructural response of a colloidal hard sphere suspension undergoing medium and large amplitude oscillatory simple shear have been studied using Accelerated Stokesian dynamics. The goal is to understand how nonlinearity arises and to link the structural effects to the resulting suspension stress. The imposed shear is given by the time-dependent rate γ̇(t)=γ̇0eiαt. Most results are shown for a hard-sphere suspension at a particle volume fraction ϕ=0.4. These are freely flowing conditions far from either glassy or jammed conditions, but the concept of the particle cage from glass dynamics is used. The cage is defined here in a statistical manner as the surface of elevated nearest neighbor probability, a sphere at contact for equilibrium. The cage concept is used in interpreting the microstructural deformation: For sufficiently small strain amplitude γ0, the cage deforms negligibly due to flow and the suspension remains in the linear response regime, but this is found to require γ0<0.01 at ϕ=0.4, as shown by a spectral decomposition of the microstructure in time, which discriminates rigorously between linear and nonlinear deformation. At larger γ0, termed medium amplitude and large amplitude in other studies, the material response is nonlinear. To preface the large amplitude oscillatory shear analysis, we use linear viscoelasticity theory to compare stress fluctuations at equilibrium to results obtained at finite Péclet number Pe and small γ0, as well as available experimental data and theoretical predictions; Pe=6πηγ̇0a3/kT is the ratio of hydrodynamic to Brownian forces, where η is the viscosity of the suspending liquid, γ̇0 is the shear rate amplitude, a is the particle radius, k is the Boltzmann constant, and T is the absolute temperature. The shear stress σxy and the normal stress differences N1 and N2 are analyzed under oscillatory shear at amplitudes 0.01≤γ0≤3.6 for a range of Pe. (The frequency α is related to Pe through γ̇0=αγ0 and the nondimensional frequency is given by the Deborah number De=Pe/γ0=6πηαa3/kT.) Pipkin diagrams are shown for σxy, N1 and N2. When hydrodynamic forces dominate the flow of the suspension, the complex viscosity |η*| has a nonmonotonic dependence on γ0, and Fourier-transform rheology shows the nonlinearity of the stress response to be maximized at an intermediate strain amplitude that depends on Pe. The elastic and viscous behavior of the suspension, as determined by a Chebyshev polynomial decomposition, is distinctly different for small and large Pe. The influence of the microstructure on the normal stress differences is discussed, noting that N1 is significant only when angular distortion of the microstructure is present, whereas N2 is formed with an accumulation of pair correlation at contact even at low oscillation amplitude.