Abstract
Non-equilibrium effects exist extensively in microfluidic flows, and the accurate simulation of the Knudsen layer behind them is rather challenging for the linear Newton–Fourier model. In this paper, a high-order reduced model (nonlinear coupled constitutive relations) from Eu’s generalized hydrodynamic equations is applied for the investigation of the micro-Couette flows of diatomic nitrogen and monatomic argon as well as Maxwell and hard-sphere molecules using the MacCormack scheme. In order to simulate the confined flows accurately, a set of enhanced wall boundary conditions based on this model are derived with respect to the degree of non-equilibrium. Both the 1st-order Maxwell–Smoluchowski model and the Langmuir slip model are also investigated. For a large range of Knudsen numbers, the results show that the enhanced boundary conditions make a significant improvement in the prediction of flow profiles, especially the temperature profile. The reason behind that is analyzed in detail. The numerical predictions obtained from the high-order model in conjunction with the enhanced boundary conditions are also compared with DSMC, regularized 13 moment equations, Burnett-type equations as well as Navier–Stokes solutions, which highlight its excellent capability in describing the underlying mechanism of the Knudsen layer in the Couette flow.
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Acknowledgements
This research was fund by the National Natural Science Foundation of China (Grant Nos. 11502232, 51575487 and 11572284), the National Basic Research Program of China (Grant No. 2014CB340201) and the Fundamental Research Funds for the Central Universities. The first author of this paper (Zhongzheng Jiang) was supported by the China Scholarship Council (Grant No. 201706320214). Meanwhile, the authors would also like to acknowledge the discussion from Prof. Dr. Manuel Torrilhon and the resources of the Mathematics Division in the Center for Computational Engineering Science at RWTH Aachen University.
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Jiang, Z., Chen, W. & Zhao, W. Numerical analysis of the micro-Couette flow using a non-Newton–Fourier model with enhanced wall boundary conditions. Microfluid Nanofluid 22, 10 (2018). https://doi.org/10.1007/s10404-017-2028-y
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DOI: https://doi.org/10.1007/s10404-017-2028-y