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The velocity boundary condition at solid walls in rarefied gas calculations

Lockerby, Duncan A. and Reese, Jason and Emerson, David and Barber, Robert W. (2004) The velocity boundary condition at solid walls in rarefied gas calculations. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 70 (1). 017303. ISSN 1063-651X

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Abstract

Maxwell's famous slip boundary condition is often misapplied in current rarefied gas flow calculations (e.g., in hypersonics, microfluidics). For simulations of gas flows over curved or moving surfaces, this means crucial physics can be lost. We give examples of such cases. We also propose a higher-order boundary condition based on Maxwell's general equation and the constitutive relations derived by Burnett. Unlike many other higher-order slip conditions these are applicable to any form of surface geometry. It is shown that these "Maxwell-Burnett" boundary conditions are in reasonable agreement with the limited experimental data available for Poiseuille flow and can also predict Sone's thermal-stress slip flow - a phenomenon which cannot be captured by conventional slip boundary conditions.