A Critical Review Of The Drag Force On A Sphere In The Transition Flow Regime

Improvements in micro-fabrication techniques are enabling Micro-Electro-Mechanical-Systems to be constructed with sub-micron feature sizes. At this scale, even at standard atmospheric conditions, the flow is in the transition regime. This paper considers the range 0.1 < Kn < 1, where non-equilibrium effects can be appreciable, and specifically illustrates problems involving non-planar surfaces by analyzing the drag force for low speed, incompressible flow past an unconfined microsphere. A critical comparison is made between experimental data, analytical solutions derived from kinetic theory, Grad’s thirteen-moment equations, and the Navier-Stokes equations with firstand secondorder treatment of the slip boundary. The results, even for this simple geometry, highlight major problems in predicting the drag in the transition flow regime for non-kinetic schemes.