A square particle suspended in a Poiseuille flow is investigated by using the lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration of Segré-Silberberg effect is observed for the square particle, accompanied by the nonuniform rotation and regular wave. To compare with the circular particle, its circumscribed and inscribed squares are used in the simulations. Because the circumscribed square takes up a greater difference between the upper and lower flow rates, it reaches the equilibrium position earlier than the inscribed one. The trajectories of the latter are much closer to those of circle; this indicates that the circle and its inscribed square have a similar hydrodynamic radius in a Poiseuille flow. The equilibrium positions of the square particles change with Reynolds number and show a shape of saddle, whereas those of the circular particles are virtually not affected by Reynolds number. The regular wave and nonuniform rotation are owing to the interactions of the square shape and the parabolic velocity distribution of Poiseuille flow, and high Reynolds number makes the square rotating faster and decrease its oscillating amplitude. A series of contours illustrate the dynamic flow fields when the square particle has successive postures in a half rotating period. This study is beneficial to understand the motion of anisotropic particles and the dendrite growth in dynamic environment.
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