Simulation of Low Knudsen Number Isothermal Flow Past a Confined Spherical Particle in a Micro-Pipe

Low Knudsen number isothermal slip flow past a confined spherical particle has been investigated using a specially adapted Navier-Stokes solver. Knudsen numbers covering the continuum and slip-flow regimes (Kn ≤ 10⁻¹) are considered while the Reynolds number is varied between 10⁻³ ≤ Re ≤ 0.5. In addition, blockage effects are studied by varying the ratio between the diameter of the pipe (H) and the diameter of the particle (D). A particularly important aspect of the present study is the proper formulation of the slip-velocity boundary condition over the curved surface of the particle. This is achieved by recasting Maxwell’s conventional velocity-slip equation as a function of the wall shear stress in order to account correctly for the curvature. The results show that blockage effects are extremely important in the continuum regime and cause amplification in the hydrodynamic drag on the particle. However, blockage phenomena are shown to be less important as the Knudsen number is increased. At the upper limit of the slip-flow regime, Kn ≈ 10⁻¹, blockage amplification effects are reduced by almost 50% for a pipesphere geometry of H/D = 2.