Computing the near-wall region in gas micro- and nanofluidics: Critical Knudsen layer phenomena

In order to capture critical near-wall phenomena in gas micro- and nanoflows within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen layer) can be described. Its advantage over higher order hydrodynamic models for gas micro- and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (provided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a micro-sphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn less than or similar to 0.1 and acceptable results up to Kn approximate to 0.25. This is much better than the traditional NSF model with non-scaled constitutive relations.