A cross-scale slip model for eccentric Taylor–Couette flow with inhomogeneous Knudsen number

In slip and transition flow regions, the slip boundary determines the accuracy of the flow field calculations. However, the applicability of existing slip models is limited when there is an inhomogeneous distribution of the Knudsen number and large regional gradient pressure, which occurs naturally in the core components of rotating machinery, including aerodynamic gas bearings and floating ring seals. Considering eccentric micro-scale Couette–Poiseuille flow, a partial slip revised by limit shear stress (PSR-τs) approach was developed. A corrected limit shear stress based on the local Kn, pressure, and density gradient was proposed for the inner physical mechanism. This facilitated the coupling of the solutions of the shear stress and pressure field via multiple iterations. For both the characteristic of the flow field and the distribution of the slip velocity, the PSR-τs results exhibited better agreement with the direct simulation of Monte Carlo (DSMC) (0.1 < Kn < 1), the Frenkel–Kontorova model (0.001 < Kn < 0.1) and experimental measurements (0.0001 < Kn < 0.001) compared to previously reported slip methods including first-order slip velocity, second-order slip velocity and Wu slip. Furthermore, to analyze the difference among the different slip methods, a comparison of the flow field characteristic between PSR-τs and several slip methods was performed for Couette–Poiseuille flow under different conditions. The slip velocity model does not consider the effect of either a large pressure gradient or diffusion owing to the density gradient for strong rarefaction. Therefore, it applies to Couette–Poiseuille flow with small eccentricity when Kn varies from 10−4 to 0.1. In contrast, the PSR-τs can be utilized to investigate Couette–Poiseuille flow across a broader range of Kn. An increase in Kn reduced the influence of the pressure gradient on the shear stress, which improved the uniformity of the velocity distribution. This phenomenon was caused by partial-slip boundaries. The findings of this study are significant because they provide a comprehensive framework for investigating the physical mechanism in multiscale flow problems and can potentially be utilized for simulation studies involving industrial applications.