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Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.

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.