Gas Flow in Microchannel of Arbitrary Shape in Slip Flow Regime

Abstract

A theoretical analysis for laminar flow in the microchannels of arbitrary shape in slip flow regime is presented in this article. The momentum equations with the first-order slip, the second-order slip, and the thermal creep flow boundary conditions are solved by applying a computation-oriented method of the orthonormal function analysis for the fully developed laminar flow of the incompressible fluid in the microchannels. The dimensionless velocity profile and the friction factor are theoretically predicted for a microchannel of arbitrary shape. To justify the methodology, the friction factor of gas flowing in the rectangular microchannel is calculated and compared with the experimental data. The good agreement between analytic solutions and experimental data shows that within a definite extension of Knudsen number, the traditional Navier–Stokes equations with the slip boundary conditions can govern the gaseous slip flow mechanisms in microchannels, and the orthonormal function method is applicable to solve the momentum equation with the slip flow boundary condition in the microchannel of arbitrary shape. It is found from the theoretical predictions that the slip velocity of fluid on the microchannel wall increases as the Kn number increases, and the friction coefficient is substantially smaller for slip flow compared with the no-slip flow. The aspect ratio of a microchannel has a remarkable effect on the dimensionless drag coefficient at a fixed Kn number in the rectangular microchannels. The friction coefficient for the second-order slip boundary condition is greater than that for the first-order slip boundary condition, and the thermal creep flow on the microchannel wall tends to increase the friction coefficient in the microchannel.