Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules

Cercignani C.; Lorenzani S.

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Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules

机译：基于玻尔兹曼方程的硬球分子二阶滑移系数的变分推导

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The objective of the present paper is to provide an analytic expression for the first- and second-order velocity slip coefficients. Therefore, gas flow rates in microchannels have been rigorously evaluated in the near-continuum limit by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator. The diffuse-specular reflection condition of Maxwell's type has been considered in order to take into account the influence of the accommodation coefficient on the slip parameters. The polynomial form of the Knudsen number obtained for the Poiseuille mass flow rate and the values of the velocity slip coefficients, found on the basis of our variational solution of the linearized Boltzmann equation for hard-sphere molecules, are analyzed in the frame of potential applications of classical continuum numerical tools in simulations of microscale flows.

机译：本文的目的是提供一阶和二阶速度滑移系数的解析表达式。因此，已经通过变分技术在接近连续极限的范围内严格评估了微通道中的气体流速，该变分技术适用于基于真实线性化碰撞算子的Boltzmann方程的积分微分形式。为了考虑调节系数对滑移参数的影响，考虑了麦克斯韦类型的漫反射反射条件。在潜在应用的框架内，分析了根据Poiseuille质量流量获得的Knudsen数的多项式形式以及基于我们对硬球分子线性化的Boltzmann方程的变分解而得出的速度滑移系数的值。连续流数值工具在微观流模拟中的应用。

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《Physics of fluids》 |2010年第6期|共8页
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Cercignani C.; Lorenzani S.;
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正文语种 eng
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1. Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules [J] . Cercignani C., Lorenzani S. Physics of fluids . 2010,第6期

机译：基于玻尔兹曼方程的硬球分子二阶滑移系数的变分推导
2. Response to "Comment on 'Velocity slip coefficients based on the hard-sphere Boltzmann equation'" [Phys Fluids 24, 079101 (2012)] [J] . Gibelli L. Physics of fluids . 2012,第7期

机译：对“关于'基于硬球玻尔兹曼方程的速度滑移系数'的评论”的回应[Phys Fluids 24，079101（2012）]
3. Velocity slip coefficients based on the hard-sphere Boltzmann equation [J] . Gibelli L. Physics of fluids . 2012,第2期

机译：基于硬球玻尔兹曼方程的速度滑移系数
4. Diffusion Slip for a Binary Mixture of Hard-Sphere Molecular Gases: Numerical Analysis Based on the Linearized Boltzmann Equation [C] . Shigeru Takata International Symposium on Rarefied Gas Dynamics . 2001

机译：硬球分子气体的二元混合物的扩散滑移：基于线性化Boltzmann方程的数值分析
5. A variational derivation of P(N) equations and boundary conditions in planar and three-dimensional geometries [D] . Rulko, Robert Pawel 1991

机译：平面和三维几何中P（N）方程和边界条件的变分推导
6. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients [O] . Vyacheslav M. Boyko, Roman O. Popovych, Nataliya M. Shapoval -1

机译：常系数二阶线性常微分方程组的Lie对称性
7. Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results [O] . Nhu Ngoc Nguyen, Irina Graur, Pierre Perrier, 2020

机译：基于硬球分子的Boltzmann方程的热滑系数的变分衍生，与实验结果相比
8. Derivation of the Boltzmann Distribution Law with Illustrations from a Hard-Sphere Model Computer Program. [R] . conant,donald r. 1972

机译：用Hard-sphere模型计算机程序插图推导Boltzmann分布律。

Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules

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