Lattice Boltzmann study of three-dimensional gas microchannel flows

Abstract

The compressibility and rarefaction of three-dimensional (3D) pressure-driven gas microchannel flow is studied by the lattice Boltzmann equation method. The method employs a modified particle distribution function and a Knudsen-number-relaxation-time relation without use of any ad hoc treatment at the wall for the slip velocity. The effects of the aspect ratio of the channel width to height, Ar, and the outlet Knudsen number, Kn(0), on pressure nonlinearity, slip velocity and mass flow rate are investigated. As Ar increases, the slip velocity decreases. As a consequence, the nonlinearity of pressure increases. Their distributions, as expected, get closer to some two-dimensional (2D) limit lines. With Ar being greater than 1, one of the most interesting phenomena is the variation of the slip velocity along the wall due to variation in shear rate. As Kno decreases, the differences between slip velocities Us-z at the bottom and top walls and Us-y at the side walls decrease. The mass flow rate is also calculated and compared with 2D analytical solution. The results show that the mass flow rate through the gas microchannel decreases with decreasing Ar. On the other hand, as Ar increases, the computed mass flow rate gets closer to 2D analytical solution.