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A critical review of the drag force on a sphere in the transition flow regime

Bailey, C.L. and Barber, Robert W. and Emerson, David and Lockerby, Duncan A. and Reese, Jason (2004) A critical review of the drag force on a sphere in the transition flow regime. In: Rarefied Gas Dynamics. AIP Conference Proceedings, 762 . American Institute of Physics, pp. 743-748. ISBN 0-7354-0247-7

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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 first- and second-order 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.