First-Order Wall-Slip-Induced Departure from Inverse-Cubic Scaling of Levitation-Pressure RMS in a Push–Pull Levitation Stage

Abstract

This study clarifies how rarefaction-induced wall slip in a thin gas film affects the established inverse-cubic scaling law for the spatial nonuniformity of levitation pressure in a push–pull levitation stage. The levitation force in this stage is generated by the combined action of blowing and suction. The continuum-based stress description is retained, and only the wall boundary condition is changed from the no-slip condition to a first-order slip condition. Three-dimensional incompressible unsteady Stokes simulations in a thin-gap unit-cell model are combined with a lubrication-theory scaling analysis. The effects of levitation height, blowing-velocity distribution, port-radius ratio, and computational-domain width are examined systematically. The results show that wall slip has only a minor influence at relatively large levitation heights. As the levitation height decreases, however, rarefaction-induced slip increases the flow-rate conductance. Consequently, the intensity of the spatial variation in levitation pressure is systematically reduced below that predicted by the no-slip inverse-cubic scaling law. This departure is well described by a correction relation derived from the lubrication approximation and remains robust against changes in the prescribed blowing-velocity distribution and geometric conditions. These findings provide an incompressible baseline for predicting levitation-pressure nonuniformity within the nominal gap-based Knudsen-number range examined here.