Shear-induced diffusion and rheology of noncolloidal suspensions: Time scales and particle displacements

Abstract

The shear-induced self-diffusion and rheology of concentrated suspensions of noncolloidal hard spheres have been studied experimentally. The combined results provide an interesting physical picture. The projection of the trajectories of individual particles on the vorticity (z)–velocity (x) plane were determined through particle tracking. The particle trajectories turned out to be very useful for gaining qualitative insight into the microscopic particle motion. However, the technique is less suitable to obtain quantitative information. For a quantitative analysis of the particle displacements we measured the evolution of the ensemble averaged displacements as a function of time. The statistical analysis revealed two diffusion regimes, where 〈ΔzΔz〉∼γ̇Δt. For large strain values (γ̇Δt>1) long-time self-diffusion was observed. The associated diffusion coefficient D̂∞ is in excellent agreement with literature data on shear-induced self-diffusion. On very short times (γ̇Δt≪1) a novel diffusive regime was discovered, characterized by a diffusion coefficient D̂0, which is significantly smaller than D̂∞ and grows monotonically with φ. D̂0 is detected on time scales on which the particle configuration is not changed significantly and thus it must represent the fluctuating motion of particles in the “cage” formed by their nearest neighbors. Finally, the rheology was studied with steady shear and oscillatory rheometry. The dynamic measurements in a controlled stress rheometer revealed that the viscoelastic response of the suspension is determined mainly by the amplitude of deformation. At small strain amplitudes γ0<1, the response is linear and a dynamic viscosity η′ is found, which is in excellent agreement with the high frequency limit η∞′ as reported in literature for colloidal hard sphere suspensions. Around γ0=1 the “cage” around a particle is deformed and a shear-induced microstructure is built. This leads to O(a) displacements of the particles and the viscoelastic response becomes strongly nonharmonic. Although the effect persists at large amplitudes, it becomes relatively small for γ0≫1. The microstructure is rearranged immediately after flow reversal and remains unchanged for the larger part of the period of oscillation. As a result a pseudolinear viscoelastic regime is found with a viscosity close to steady shear viscosity. Experiments show a correlation between the time scales controlling the D̂0/D̂∞ diffusive behavior and the ones controlling the shear-induced changes in particle configuration as probed by the rheological measurements.