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

The equilibrium position yep/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 & LE; & beta; & LE; 2, fluid power-law index 0.4 & LE; n & LE; 1, Reynolds number 20 & LE; Re & LE; 60, and blockage ratio 0.15 & LE; k & LE; 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, yep/H, and the larger the value of & beta;, the closer the value of yep/H is to the centerline. Therefore, the value of yep/H can be controlled by changing & beta; 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 yep/H when n, Re and k are fixed, but the values of yep/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 yep/H is to the centerline. The value of & beta; has no effect on the value of yep/H. In the flow far downstream from the obstacle, the flow distance required for the particle to reach yep/H increases with increasing & beta; and n but decreases with decreasing Re and k.