The smoothed profile method is extended to study the rheological behaviour of colloidal dispersions under shear flow by using the Lees-Edwards boundary conditions. We start with a reformulation of the smoothed profile method, a direct numerical simulation method for colloidal dispersions, so that it can be used with the Lees-Edwards boundary condition, under steady or oscillatory-shear flow. By this reformulation, all the resultant physical quantities, including local and total shear stresses, become available through direct calculation. Three simple rheological simulations are then performed for (1) a spherical particle, (2) a rigid bead chain and (3) a collision of two spherical particles under shear flow. Quantitative validity of these simulations is examined by comparing the viscosity with that obtained from theory and Stokesian dynamics calculations. Finally, we consider the shear-thinning behaviour of concentrated colloidal dispersions.

The purpose of the present study is to demonstrate the applicability of magnetic resonance imaging, especially T relaxation time mapping, for nondestructive monitoring of the dispersion state of nanoparticles (NPs) in concentrated suspensions. TiO 15-nm-diameter NPs, for use in sunscreen lotion products, were examined as a test NP. First, this study investigated whether T is sensitive to the NP concentration. In experiments with pulsed nuclear magnetic resonance on TiO NP suspensions with different organic solvents (ethanol, acetone, and decamethylcyclopentasiloxane), the T of each solvent varied in the suspensions according to the NP concentration. This study also confirmed that T mapping was effective for visualizing differences in NP concentration. Subsequently, gravitational sedimentation of the test suspensions was investigated. T mapping exhibited better detection sensitivity to sedimentation occurring in concentrated suspensions than visual observation, as it enabled the detection of changes in NP distributions that could not be visible to the naked eye. In addition, measurements of backscattered light enabled the full understanding of the dispersion stability of the TiO NPs in each solvent. Finally, the present study evaluated the centrifuge sedimentation of a commercial TiO NP suspension. T mapping clearly showed the complicated sedimentation behavior induced by the centrifugation treatment. The simulated fluid flow was consistent with the particle distribution in the centrifuged sample; thus, the sedimentation was believed to have developed in accordance with the vorticity generated by the centrifugation.