No abstract

Migration of a particle in a confined shear flow of Giesekus fluids is investigated numerically with the method of direct forcing/fictitious domain. We focus on the migration direction for the particle with initial lateral position y0 and determination of critical point yc of a particle moving towards the center line or wall. The effect of viscosity ratio μr, shear-thinning parameter α, Weissenberg number Wi, and blocking rate β on the value yc is analyzed. The results showed that when μr ≤ 0.5, the particle will migrate towards the wall regardless of the value of y0. When μr > 0.5, yc increases with increasing μr, and some particles will migrate towards the center line with the increase in μr. The particle is more likely to migrate towards the center line at small values of Wi and α but at large values of μr. The impact of Wi and β on the particle migration direction is more obvious. The particle will migrate towards the wall for β = 0.3 and is more likely to migrate towards the wall with increasing β. α and Wi have little influence on the pressure distribution in the case of the same β and μr. The particle near the wall will migrate faster because large positive pressure and negative pressure appear around the particle.

The contraction/expansion laminar flow containing rodlike particles in power-law fluid is studied numerically when the particles are in a dilute phase. The fluid velocity vector and streamline of flow are given at the finite Reynolds number (Re) region. The effects of Re, power index n and particle aspect ratio β on the spatial and orientation distributions of particles are analyzed. The results showed that for the shear-thickening fluid, particles are dispersed in the whole area in the contraction flow, while more particles are gathered near the two walls in the expansion flow. The spatial distribution of particles with small β is more regular. Β has a significant, n has a moderate, but Re has a small impact on the spatial distribution of particles in the contraction and expansion flow. In the case of large Re, most particles are oriented in the flow direction. The particles near the wall show obvious orientation along the flow direction. In shear-thickening fluid, when the flow changes from contraction to expansion, the orientation distribution of particles becomes more dispersed; while in shear-thinning fluid, the opposite is true. More particles orient to the flow direction in expansion flow than that in contraction flow. The particles with a large β tend to align with the flow direction more obviously. Re, n and β have great influence on the orientation distribution of particles in the contraction and expansion flow. Whether the particles initially located at the inlet can bypass the cylinder depends on the transverse position and initial orientation of the particles at the inlet. The number of particles with θ0 = 90° bypassing the cylinder is the largest, followed by θ0 = 45° and θ0 = 0°. The conclusions obtained in this paper have reference value for practical engineering applications.