Herein, we used the fictitious domain method to numerically investigate the lateral migration and rotation of an oblate spheroidal particle in a square duct filled with Oldroyd-B fluids. We adopted Reynolds numbers ranging from 25 to 100 and Weissenberg numbers from 0.01 to 0.50. At low to moderate Weissenberg numbers (Wi ≤ 0.50), viscous forces remain dominant in particle motion. Additionally, we considered the effects of initial lateral position, orientation, and blocking ratio on particle dynamics. The results indicate that for flow in square channels with finite fluid inertia, as Wi increases, the elastic effects gradually strengthen, causing the equilibrium position of the particles to shift from near the centerline of the channel toward the diagonal. Notably, under significant fluid elasticity conditions, additional equilibrium positions emerge in the corners of the channel. When released with their x0–y0 plane (containing the two longest axes of the oblate spheroid) parallel to the x–y plane (duct cross section) of the flow field, particles exhibited three distinct motion modes: tumbling, rolling, and kayaking. Tumbling was influenced by fluid inertia and corner attraction, which exhibited transitions to rolling or kayaking. The study also emphasized that the initial orientation of the particles impacted their sustained tumbling under low inertial flows. In addition, the blockage ratio (the ratio of the equivalent diameter of the particle to the duct height) mainly affected the equilibrium positions, and particles with a blockage ratio β ≤ 0.125 were readily attracted to the corners.
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