Steady State of Motion of Two Particles in Poiseuille Flow of Power-Law Fluid

Abstract

The steady state of motion of two particles in Poiseuille flow of power-law fluid is numerically studied using the lattice Boltzmann method in the range of Reynolds number 20 ≤ Re ≤ 60, diameter ratio of two particles 0.125 ≤ β ≤ 2.4, and power-law index of the fluid 0.4 ≤ n ≤ 1.2. Some results are validated by comparing with other available results. The effects of Re, β, and n on the steady state of motion of two particles are discussed. The results show that, for two particles of the same diameter, the particle spacing l in the steady state is independent of n. In shear-thinning fluid, l increases rapidly at first and then slowly, finally approaching a constant for different Re. In shear-thickening fluid, although l tends to be stable in the end, the values of l after stabilization are different. For two particles of different sizes, l does not always reach a stable state, and whether it reaches a stable state depends on n. When the small particle is downstream, l increases rapidly at first and then slowly in shear-thickening fluid, but increases rapidly at first and then decreases slowly, finally approaching a constant in a shear-thinning fluid. In shear-thinning fluid, the larger n is, the smaller l is. In shear-thickening fluid, β has no effect on l in steady-state. When the large particle is downstream, l increases rapidly at first and then slowly in shear-thinning fluid but increases rapidly at first and then decreases in a shear-thickening fluid. The effect of n on l in the steady state is obvious. In shear-thinning fluid, l increases rapidly at first and then slowly, the larger Re is, the smaller l is. In shear- thickening fluid, l will reach a stable state.