No abstract

Einstein's viscosity formula is only applicable for dilute suspensions in which hydrodynamic interactions or inertial effects are sufficiently negligible. Therefore, the contribution of hydrodynamic interactions or the effects of inertia on the rheology of suspensions should be investigated. In order to evaluate the inertial effects of microscopic particles on the macroscopic rheology of a suspension, pressure-driven flow simulations with various confinements and Reynolds numbers were performed by a two-way coupling scheme. The results showed that the relative viscosity of the suspension decreases with increase in the particle size even when the concentration of the suspension remains the same. The results also indicated that the confinement should be less than 0.02 when applying Einstein's viscosity formula. Moreover, the relative viscosity of the suspension under a high Reynolds number condition increases because of outward particle migration, and the non-Newtonian property of the suspension changes from thixotropy to dilatancy. Suspension is a potential fluid because its macroscopic rheological properties are altered owing to suspended particles' behavior, that is, its microstructure. It can be stated that inertia is one of the promising factors to control suspension rheology.

Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10−4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.

It is important to understand the rheology of suspensions because it has a wide range of relevance from biological to industrial fields. The rheology of suspensions is still unclear due to complexity of various factors. Among the factors that determine the rheological properties, we focused on the spatial arrangement of particles and solvent properties of the suspension. We investigated effects of the power-law fluidic properties of the solvent of suspension on the relative and intrinsic viscosities. Furthermore, we investigated the effect of Reynolds number on the rheology of the suspension. We performed a numerical simulation of pressure-driven suspension flows in 2D. The suspension had different solvents properties depends on the power-law model. The bulk flow was simulated by using the lattice Boltzmann method. The power-law model was used to represent the flow properties of the solvent. The particle shape was described on the Cartesian grid using the virtual flux method. The relative and intrinsic viscosities of the suspensions were discussed by property changes in the suspension rheology such as shear-thinning, Newtonian, and shear-thickening. The results showed that the higher power-law index of the solvent caused higher relative and intrinsic viscosities. Furthermore, Reynolds number had little influence on the relative and intrinsic viscosities of the suspension when the Reynolds number was under Re = 12.

Einstein's viscosity formula is sometimes strongly limited for viscosity estimation of suspensions; that is, it is only applicable for low-concentration suspensions in which hydrodynamic interactions are sufficiently negligible. In particular, hydrodynamic interactions between particles (cylinders in two dimensions) should be taken into consideration when finite-size particles are suspended. Therefore, change in the microstructure, i.e., spatial arrangement of particles in the flow field, is important for understanding mechanism of suspension rheology. In order to provide better practical applications for viscosity estimation instead of Einstein's formula, we investigated the influence of each cylinder's contribution on the total effective viscosity of a suspension with finite-size cylinders considering the microstructure, especially in terms of cylinder-wall and cylinder-cylinder distances. Two-dimensional pressure-driven flow simulations were performed using the regularized lattice Boltzmann method and a two-way coupling scheme. The rigid circular cylinders suspended in a Newtonian fluid were assumed to be neutrally buoyant and non-Brownian. As a result, we found that both distances between cylinders and cylinder-wall are significant for viscosity estimation. In addition, the effective viscosity can be estimated accurately when the confinement is sufficiently low (C ≈ 0.04). It can be stated that the microstructure of the suspension is one of the promising factors to estimate and control suspension rheology.