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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]

Understanding, predicting and controlling the motion of the solid particles in a confined cavity is significant. The motion of a neutrally buoyant circular particle in a lid-driven square cavity is studied with the lattice Boltzmann method, where the effects of the initial position, particle size and Reynolds number are investigated. The obvious characteristic of the motion of the circular particle is the existence of the limit cycle, which is the competitive result of the inertia, wall-repulsion force and vortex behavior. The limit cycle is insensitive to the initial position of the circular particle, namely, no matter where the circular particle is placed initially, the limit cycle is the same. With the increase of the particle size, the wall-repulsion force becomes stronger, which is dominant over the centrifugal force, and the limit cycle shrinks toward the center of the square cavity. With the increase of the Reynolds number, a new secondary vortex develops at the top left corner of the square cavity, and the limit cycle is pushed toward the bottom right corner of the square cavity. [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 the solid particles in the enclosed cavity is important, to investigate the interaction between the motion of the solid particles and the fluid flow, the motion of a neutrally buoyant elliptical particle in a lid-driven square cavity is studied with the lattice Boltzmann method. To understand, predict and control the motion of the elliptical particle, the effects of the aspect ratio, initial orientation, initial position, particle size and Reynolds number are studied. The obvious characteristic of the motion of the elliptical particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the elliptical particle, confinement of the boundaries of the square cavity and vortex behavior. Compared with the circular particle, with the increase of the aspect ratio, the roundness of the limit cycle decreases, namely, the limit cycle becomes flatter. Especially, the limit cycle is insensitive to the initial orientation and position, namely, the limit cycle is the same no matter where the elliptical particle is placed initially. With the increase of the particle size, the confinement of the boundaries becomes stronger, and the limit cycle is squeezed toward the center of the square cavity. Finally, with the increase of the Reynolds number, the vortex at the top left corner develops, and the limit cycle is pushed toward the bottom right corner of the square cavity. • A global limit cycle for the motion of the elliptic particle is observed. • The limit cycle is insensitive to the initial position of the elliptic particle. • The limit cycle shrinks toward the center of the square cavity with the increase of the particle size. • The limit cycle migrates toward the bottom right corner of the square cavity with the increase of Re. [ABSTRACT FROM AUTHOR]