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Understanding, predicting and controlling the motion of the solid particles in the square cavity with obstacles are important. This work performs a lattice Boltzmann study on the motion of a neutrally buoyant circular particle in a lid-driven square cavity with a semicircular obstacle, where the effects of Reynolds numbers and initial positions of the circular particle on the motion of the circular particle are investigated. The motion of the circular particle is affected significantly by the semicircular obstacle, which is quite different from the case without obstacles. With the increase of the Reynolds number, the motion of the circular particle is divided into three stages. At low Reynolds numbers (5 0 0 ≤ Re ≤ 8 0 0), similar to the case without obstacles, no matter where the initial position of the circular particle is, the limit cycle of the circular particle is the same. Beyond a critical Reynolds number (between 800 and 900), the limit cycle of the circular particle is dependent on the initial position of the circular particle obviously, which is attributed to the opposing centrifugal and wall-repulsion forces. [ABSTRACT FROM AUTHOR]

The solid particles with different sizes exist widely, like cell separation, food processing, water treatment, thus, investigating the motion of the solid particles with different sizes is important. This study investigates the motion of a pair of neutrally buoyant circular particles with different sizes in a lid-driven square cavity using the lattice Boltzmann method. The motion of the circular particles with different sizes and that of the circular particles with identical sizes are quite different. The steady trajectories of the circular particles with identical sizes are identical, which is not affected by the Reynolds number. Differently, the circular particles with different sizes orbit along different steady trajectories, namely, the steady trajectory of the small particle is closer to the walls of the square cavity, while that of the large particle shrinks toward the center of the square cavity, which may provide us a possible method to separate them. However, it is not always effective, if the Reynolds number is low, the velocity difference between the circular particles with different sizes is small, which may fail to separate them completely. [ABSTRACT FROM AUTHOR]

The motion of a neutrally buoyant circular particle in a parallel double-lid-driven square cavity is studied with the lattice Boltzmann method. To understand, predict and control the motion of the circular particle, the effects of the initial position and particle size are studied. If the circular particle is placed at the centerline of the square cavity, at the steady state, it is confined at the bottom left corner, otherwise, the circular particle is stabilized at the 8-like trajectory, which is created by both the inertia of the circular particle and the confinement of the boundaries of the square cavity. The effect of the particle size on the motion of the circular particle is obvious, with the increase of the particle size, the confinement of the boundaries of the square cavity becomes stronger, and the 8-like trajectory shrinks toward the center. Furthermore, if the particle size is large enough, the centrifugal motion of the circular particle becomes weaker, and the circular particle cannot cross the centerline of the square cavity. [ABSTRACT FROM AUTHOR]