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

机译：在广泛的克努森数范围内预测微通道气体质量流量的解析解决方案

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摘要

To predict the gaseous mass flow rate of microchannels, conventional analytical solutions based on the Navier-nStokes equation or volume diffusion hydrodynamics (bivelocity hydrodynamics) associated with first-order ornsecond-order slip boundary condition are not very successful, especially in high-Knudsen-number flow. Annanalytical solution which agrees with experimental data to a Knudsen number of 50 is presented in this paper. Tonachieve this goal, a concept of effective volume diffusion is defined. Then, with a general slip boundary condition,nthe gaseous mass flow rate ofmicrochannel is derived by solving the momentum equation of this effective volumendiffusion hydrodynamics. Compared with six other analytical solutions and one group of numerical solutions ofnthe linearized Boltzmann equation, this solution is validated by three groups of experimental data. The resultsnnot only illustrate an improvement of this solution compared with other analytical solutions but also show thenimportance of the effective volume diffusion hydrodynamics for compressible microfluids.
机译：为了预测微通道的气体质量流速，基于Navier-nStokes方程或与一阶或二阶滑移边界条件相关的体积扩散流体动力学（容积动力学）的传统分析解决方案不是很成功，特别是在高克努森模型中数字流。本文提出了与实验数据一致的纳纳解析解，其努数数为50。为了达到这个目标，定义了有效体积扩散的概念。然后，在一般的滑移边界条件下，通过求解该有效体积扩散流体动力学的动量方程，导出微通道的气体质量流量。与线性化Boltzmann方程的其他六个解析解和一组数值解相比，该解由三组实验数据验证。结果不仅说明了该解决方案与其他分析解决方案相比的改进，而且还表明了可压缩微流体有效体积扩散流体力学的重要性。

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  • 来源
    《PHYSICAL REVIEW E》 |2013年第1期|1-7|共7页
  • 作者

    Qifeng Lv; Xiaoli Liu; Enzhi Wang; Sijing Wang;

  • 作者单位

    State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China;

    State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China;

    State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China;

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