Analytical solution to predicting gaseous mass flow rates of microchannels in a wide range of Knudsen numbers

Abstract

To predict the gaseous mass flow rate of microchannels, conventional analytical solutions based on the Navier-Stokes equation or volume diffusion hydrodynamics (bivelocity hydrodynamics) associated with first-order or second-order slip boundary condition are not very successful, especially in high-Knudsen-number flow. An analytical solution which agrees with experimental data to a Knudsen number of 50 is presented in this paper. To achieve this goal, a concept of effective volume diffusion is defined. Then, with a general slip boundary condition, the gaseous mass flow rate of microchannel is derived by solving the momentum equation of this effective volume diffusion hydrodynamics. Compared with six other analytical solutions and one group of numerical solutions of the linearized Boltzmann equation, this solution is validated by three groups of experimental data. The results not only illustrate an improvement of this solution compared with other analytical solutions but also show the importance of the effective volume diffusion hydrodynamics for compressible microfluids.