Analytical solution of low Reynolds number slip flow past a sphere
Analytical solution of low Reynolds number slip flow past a sphere
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球体低雷诺数滑流的解析解
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Emerson
中科院分区：
文献类型：
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作者：
R. Barber;Emerson
导出了用于预测流经无约束球体的低雷诺数稀薄气流的解析解。在斯托克斯对穿过球体的蠕动流的原始分析中，实施了连续介质流假设，并在表面上利用了无滑移边界条件。然而，当球体的尺寸接近气体分子的平均自由程时，斯托克斯的连续介质假设就会失效，因此解释稀疏效应就很重要。在目前的工作中，Stokes 的解决方案已扩展用于滑流流态，该流态对 Knudsen 数有效，0.1 Kn ≤ 。球体上的总阻力等于连续流的斯托克斯解乘以稀疏系数，稀疏系数取决于克努森数。将滑流技术应用于微球终端速度的估计表明，稀疏效应增加了预测的沉降速度。通过将解析解与密立根具有里程碑意义的油滴实验中获得的实验终端速度进行比较，证实了这一结果。还进行了一项额外的验证研究，将解析阻力公式与有限体积纳维-斯托克斯求解器的数值预测进行比较。
An analytical solution is derived for predicting low Reynolds number rarefied gas flow past an unconfined sphere. In Stokes’ original analysis of creeping flow past a sphere, a continuum flow hypothesis was implemented and no-slip boundary conditions were utilised on the surface. However, when the size of the sphere approaches the mean free path of the gas molecules, Stokes’ continuum hypothesis breaks down and it is then important to account for rarefaction effects. In the present work, Stokes’ solution has been extended for use in the slip-flow regime which is valid for Knudsen numbers, 0.1 Kn ≤ . The total drag on the sphere is shown to be equivalent to Stokes’ solution for continuum flows multiplied by a rarefaction coefficient which is dependent upon the Knudsen number. Applying the slip-flow technique to the estimation of the terminal velocity of a microsphere shows that rarefaction effects increase the predicted settling speed. This result is confirmed by comparing the analytical solution with the experimental terminal velocities obtained in Millikan’s landmark oil drop experiment. An additional validation study has also been conducted which compares the analytical drag formulae against numerical predictions from a finite-volume Navier-Stokes solver.