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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 became active research topics, like debris flows, sand storms, transport of volcanic ash, coal combustion, drug delivery and steel making. Thus, the motion of a neutrally buoyant elliptical particle in a double-lid-driven square cavity is studied with the lattice Boltzmann method, where the effects of the initial position, Reynolds number and aspect ratio are studied. The square cavity is divided into two parts by the two primary vortexes, and the motion of the elliptical particle is determined by the interaction of the two primary vortexes. The limit cycle is sensitive to the initial position of the elliptical particle, namely, placing the elliptical particle at different positions initially, the motion of the elliptical particle exhibits different modes. Especially, the elliptical particle is apt to cross the horizontal centerline of the square cavity at moderate Reynolds numbers. The effect of the Reynolds number on the motion of the elliptical particle is significant, with the increase of the Reynolds number, the effects of the two primary vortexes on the motion of the elliptical particle are different, which affects the trajectory of the elliptical particle fundamentally. With the increase of the aspect ratio, the elliptical particle becomes flatter, the hydrodynamic force and torque acting on the elliptical particle become unbalanced and the elliptical particle no longer moves along the 8-like limit cycle. [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]

To understand, predict and control the motion of the solid particles, the motion of a neutrally buoyant circular particle with thermal convection in a square cavity is studied with the lattice Boltzmann method, where the effects of the initial position of the circular particle, Rayleigh number and particle size are investigated. Under the effect of thermal convection, the obvious feature of the motion of the circular particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the circular particle, confinement of the boundaries of the square cavity and centrifugal force. Interestingly, the limit cycle is insensitive to the initial position of the circular particle. The effect of the Rayleigh number on the motion of the circular particle is obvious, with the increase of the Rayleigh number, the limit cycle expands toward the boundaries of the square cavity first, then shrinks and migrates toward the bottom left corner, which is caused by the combined effects of the centrifugal force and vortex behavior. The effect of the particle size on the motion of the circular particle is significant, with the increase of the particle size, the inertia of the circular particle becomes larger, which is more difficultly dragged by the fluid, thus, the limit cycle shrinks toward the bottom left corner of the square cavity. [ABSTRACT FROM AUTHOR]