Numerical simulation of low Reynolds number slip flow past a confined microsphere

Rapid progress in Micro-Electro-Mechanical Systems (MEMS) technology has led to the development of an increasing number of miniaturised flow devices which involve the manipulation of gases. However, an emerging research issue is the realisation that non-continuum and surface phenomena become increasingly important as devices are reduced in scale. This study investigates the important problem of low Reynolds number rarefied gas flow past a confined microsphere within a circular pipe and focuses on the estimation of the hydrodynamic drag forces on a stationary sphere. Knudsen numbers covering the continuum and slip-flow regimes (0 less than or equal to Kn less than or equal to 10(-1)) are studied whilst the Reynolds number is varied between 10(-2) less than or equal to Re less than or equal to 1. In addition, blockage effects are investigated by varying the ratio between the diameter of the pipe, H, and the diameter of the sphere, D. The results indicate that blockage effects are extremely important in the continuum regime and cause an amplification in the hydrodynamic drag. 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 approximate to 10(-1)), blockage amplification effects are found to be reduced by almost 50% for a pipe-sphere geometry of H/D = 2.