Rheology and microstructure of non-Brownian suspensions under shear flow investigated by the lattice Boltzmann method

Abstract

Particle suspensions are used extensively in many industrial applications such as manufacturing of batteries, electronic components, solar cells, printed electronics, and so on. The rheological properties of the suspensions are changed during the process, which affects the quality of the final products. Therefore, understanding their rheology is essential to manufacturing. It is strongly correlated with its microstructue, and numerical simulation is highly desirable to explore their relations. In this study, we investigated the rheology and microstructure of non-Brownian suspensions in both steady and oscillatory shear flow. To describe the suspension system, the Lattice Boltzmann method (LBM) coupled with the smoothed profile method (SPM) was adopted. First, the rheology of non-Brownian suspensions under steady shear flow was studied. The effect of particle volume fraction and particle Reynolds number on the rheology of the suspension was investigated, and the correlation of local quantities such as local shear stress and local particle volume fraction was analyzed. Previous studies focused only on the bulk rheology of complex fluids because the local rheology was not accessible due to the technical limitations. On the other hand, we adopted the novel algorithm, called the method of planes (MOP) to correlate non-Newtonian fluid behavior with the structural evolution of concentrated suspensions. At low particle Reynolds number, an increase in the relative shear viscosity was observed with an increase in the particle volume fraction, and the results corresponded well with the Krieger-Dougherty equation. Shear thickening was successfully captured with highly concentrated suspensions at high particle Reynolds number. By analyzing the microstructure, we observed that large clusters were formed at high particle Reynolds number, and they were aligned to the compressive axis with shear thickening. Both the local rheology and the local structure of the suspensions were analyzed, and we found that the linear correlation between the local particle stress and local particle volume fraction was dramatically reduced during shear thickening. These results prove that the local structure of the suspensions affect both local and bulk rheology during shear thickening. Secondly, nonlinear rheological responses of concentrated hard-sphere suspensions under oscillatory shear flow were investigated. It is known that the concentrated suspensions show a peculiar nonlinear behavior under large amplitude oscillatory shear (LAOS) flow, so-called strain stiffening, in which the complex viscosity or dynamic moduli begin to increase at critical strain amplitude. Although this phenomenon has been widely observed in experiments, its mechanism has never been explored in a systematic way. To clarify this mechanism, numerical simulation was performed by LBM coupled with SPM. Dynamic moduli of the suspensions were investigated for varying strain amplitudes at a fixed angular frequency, and the strain stiffening was clearly observed at high strain amplitudes. With strain stiffening, the shear stress began to show distorted waveform near the critical strain amplitude, and this behavior was quantified by the Fourier transform (FT) and the stress decomposition. Microstructure of the suspensions was also investigated to find the origin of strain stiffening. The bond order parameter was applied to quantify the structural change of the suspensions, and it was found that the distortion in shear stress and the increase of dynamic moduli are strongly correlated with the ordering of particles during the oscillatory shear flow. Our results clearly demonstrate how the ordering of particles affects nonlinear rheological behavior of non-Brownian suspensions in large amplitude oscillatory shear flow.