The velocity boundary condition at solid walls in rarefied gas simulations

Maxwell’s original slip boundary condition is widely misapplied in current rarefied gas flow calculations (e.g. in hypersonics, microfluidics). If its commonly-accepted form is applied in simulations of gas flows over curved or moving surfaces, crucial physics can be lost. We give examples of such cases. We also propose a new higher-order boundary condition which is based on Maxwell’s original equation and the constitutive relations derived by Burnett. Unlike other higher-order models this is generally applicable to three-dimensional moving surfaces. It is shown that these ‘MaxwellBurnett’ boundary conditions give much closer agreement with experimental data for Poiseuille flow than existing higher-order models and can also predict Sone’s thermal-stress slip flow — a phenomenon which cannot be captured by conventional slip boundary conditions.