Gaseous slip flow of a rectangular microchannel with non-uniform slip boundary conditions

This article presents analytical expressions of velocity and mass flow rate in terms of Fourier series for gaseous slip flows in long, straight, and uniform rectangular microchannels in the case of different first-order slip boundary conditions on each wall of the microchannels. The derived velocity expressions were in good agreement with those presented by Ebert and Sparrow (J Basic Eng 87:1018, 1965), when the slip boundary conditions on each wall of the microchannels were identical. The computed first-order dimensionless mass flow rate was also in very good agreement with the dimensionless mass flow rate for the planar channel reported by Arkilic et al. (J Microelectromec Syst 6:167, 1997) as the channel aspect ratio approached zero. Using the derived first-order dimensionless mass flow expression and the previously reported mass flow data, we found the unknown tangential momentum accommodation coefficient (TMAC) of nitrogen on a glass surface in a rectangular microchannel made by anodic bonding. The effects of the channel aspect ratio and Knudsen number on the velocity fields were discussed. The uncertainty level of the estimation of TMAC from mass flow rate measurements was also discussed, along with the effects of the channel aspect ratio and Knudsen number on the uncertainty level.