Velocity Slips And Flow Characteristics Of Micro/Nano-scale Gas Flows

As the development of Micro-Electro-Mechanical Systems (MEMS) and micro fabrication, micro flows have been receiving more and more attention. In micro/nano scale gas flow, the molecular mean free path and the characteristic length of the flow are comparable. And the non-equilibrium state of the gas comes into being near the wall. Meanwhile the rarefaction effect of the gas flow becomes important, although the gas flow itself is not in the state of rarefaction. Most MEMS devices operate in the slip and early transition regimes (10-3< Kn< 1). The Navier-Stokes (N-S) equation with present velocity slip boundary conditions, fails to describe the gas flow in this regime. On the other hand, the direct simulation Monte Carlo (DSMC) method, which is molecule based, converges slowly and requires lots of computational cost, especially for the low velocity flow. A new velocity slip boundary condition model for micro gas flow is con-structed from the linearized R13 moment equations for the first time. Furthermore, a new micro gas flow lubrication model (called moment lubrication model) is also established according to the lubrication theory and the R13 moment equations for the first time. Based on the new model, the characteristics of the micro/nano scale gas flow are investi-gated, with emphasis on the problems of oscillatory flow and micro gas flow lubrication. The main contents of this paper are as follows:Firstly, the Maxwell velocity slip boundary model and the unified formula of the velocity slip boundary conditions are given. Taken into account that the effect of Knud-sen layer is zero approximately beyond the Knudsen layer, a new velocity slip boundary condition model for micro gas flow is constructed from the linearized R13 moment e-quations for the first time. Different from other slip models, the slip coefficient of the new one not only relates with the wall accommodation coefficient, but also with the flow Knudsen number. In micro Poiseuille flow, the non-dimensional flow rate calculated from the new model is closer to the FK model from the linearized Boltzmann equation in the slip and the early transition flow regimes; Then the micro gas lubrication Reynold-s equation modified by the new slip boundary condition is established. The analysis shows that the modified Reynolds equation would predict the pressure distribution of the lubrication flow accurately, in accordance with the data of the DSMC simulation.Next the governing equation of the oscillatory Couette flow is given. And the solutions of Navier-Stokes equation with arbitrary slip boundary condition are obtained. Then calculations are performed as a function of the spatial Knudsen number and the temporal Knudsen number. When Kn> 0.5 and Kn,> 0.16, the results shows that our slip model is in excellent agreement with the DSMC data, while the other slip models fail to follow the DSMC data. And when Kn=0.9 and Kn,=1.014, our slip model is in good agreement with the DSMC data except at the oscillating wall, which is better than the results of the regularized 26 moment model and the regularized 13 moment model. The numerical results show that the Navier-Stokes equation with the new slip boundary condition can be extended to study the transition flow regime successfully.Finally, a new micro gas flow lubrication model (called moment lubrication model) is established according to the lubrication theory and the R13 moment equations for the first time. The moment lubrication model can analyze not only the pressure distribution, but also the wall shear stress, the velocity, the heat flux and other high order moment variables by considering the effect of the Knudsen layer. It is superior to the FK lubri-cation model widely accepted in the field of gas lubrication. In the slip flow and early transition flow regimes, the results from the moment lubrication model are in accordance with the DSMC data in the pressure distribution and wall shear stress, which shows its superiority to other micro gas lubrication models. Besides, the moment lubrication e-quation can be solved conveniently and its computing efficiency is much higher than the DSMC method. According to the moment lubrication model, the characteristic of the shear stress, heat flux and other high order moment variables in micro gas lubrication flow are further analyzed.