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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 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]

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]

The interaction between a particle cluster and a single particle during sedimentation is studied with the lattice Boltzmann method, where the effects of the initial distance and particle number on the motion and distribution of the particle cluster are investigated. Compared to the case without the single particle, the motion and distribution of the particle cluster are affected significantly due to the effect of the single particle. Due to the interaction between the particle cluster and the single particle, the particle-particle interaction becomes stronger; compared to the case without the single particle, the velocity fluctuation of the particle cluster is much more intensive. Besides, the particle cluster is scattered by the single particle, and the distribution of the particle cluster becomes more inhomogeneous. [ABSTRACT FROM AUTHOR]

A two-dimensional study of mass transfer from a circular composite particle settling in a vertical channel is conducted with the lattice Boltzmann method. The particle is composed of two materials, one insoluble while the other soluble in the ambient fluid. In the problem, mass transfer, particle motion and fluid flow are closely coupled, where the concentration at the particle surface and particle properties vary with mass transfer. It is observed that mass transfer follows a Schmidt number independent scaling law of [ t / ( t ν Sc ) ] - 1.5 ( t is the physical time, t ν is the momentum diffusion time scale and Sc is the Schmidt number), which is quite different from the pure diffusion of a stationary particle, ∼ ( t / t α ) - 0.5 ( t α is the mass diffusion time scale). An analysis of the concentration and flow pattern around the particle suggests that the scaling law for a settling particle is related to both diffusion distance and convection distance, while it is only relevant to the diffusion distance in the case of a stationary particle. For a settling particle, mass transfer is enhanced by two mechanisms due to convection, i.e., the concentration around the particle surface transported to the downstream of the particle by the fluid flow and the interface of mass transfer stretched with the particle motion, which are absent in the case of a stationary particle. Thus, the rate of mass transfer in the case of a settling particle is much higher than that for a stationary particle. [ABSTRACT FROM AUTHOR]

The flow in the square cavity with internal obstacles exists widely; thus, investigating the effect of the existence of the obstacles on the flow and the motion of the solid particles is important. To understand, predict, and control the motion of the solid particles, the motion of a neutrally buoyant circular particle in a lid-driven square cavity with an internal circular obstacle is studied with the lattice Boltzmann method, where the effects of the obstacle size, obstacle location, initial position of the circular particle, and Reynolds number are investigated. Under the effect of the obstacle, the flow and the motion of the particle are quite different. Especially, under some cases, no limit cycle is observed, and the particle is captured by the secondary vortex at the lower layer of the square cavity, which is insensitive to the initial position of the circular particle. The effect of the Reynolds number on the motion of the particle is significant, with the increase in the Reynolds number, and the motion of the particle is different obviously. At low Reynolds numbers, the motion of the particle is confined by the primary vortex, which moves along the limit cycle at the upper layer of the square cavity. With the increase in the Reynolds number, the effect of the inertia of the particle becomes stronger, and the particle moves from the primary vortex to the secondary vortex until it is captured by the secondary vortex. At relatively high Reynolds numbers, the primary vortex develops, and the particle is confined by the primary vortex again, forming another limit cycle. [ABSTRACT FROM AUTHOR]