Equilibrium Position of a Particle in a Microchannel Flow of Newtonian and Power-Law Fluids with an Obstacle

The equilibrium position y ep / H of a particle in a microchannel flow of Newtonian and power-law fluids with an obstacle is numerically studied using the lattice Boltzmann method in the range of the ratio of an obstacle to particle diameter 0.5 ≤ β ≤ 2, fluid power-law index 0.4 ≤ n ≤ 1, Reynolds number 20 ≤ Re ≤ 60, and blockage ratio 0.15 ≤ k ≤ 0.3. Some results are validated by comparing them with the available results. The results showed that, when a particle migrates around an obstacle in the flow behind and near the obstacle, the particle with a different initial, y / H, migrates downstream in a different lateral position, y ep / H , and the larger the value of β , the closer the value of y ep / H is to the centerline. Therefore, the value of y ep / H can be controlled by changing β in the wake zone of the obstacle. However, in the flow far downstream from the obstacle, the particle with a different initial y / H tends to have the same y ep / H when n , Re and k are fixed , but the values of y ep / H are different for different n , Re and k ; i.e., the larger the values of n , Re and k , the closer the value of y ep / H is to the centerline. The value of β has no effect on the value of y ep / H . In the flow far downstream from the obstacle, the flow distance required for the particle to reach y ep / H increases with increasing β and n but decreases with decreasing Re and k .