[论文解读] Studies On Falling Ball Viscometry

Amit Vikram Singh, Lavanjay Sharma+1 more|arXiv (Cornell University)|Feb 7, 2012

Rheology and Fluid Dynamics Studies参考文献 29被引用 4

一句话总结

本文提出了一种基于落球黏度计测量液体黏度的校正方法，该方法将适用范围从低雷诺数的‘蠕动流’区域扩展至更广范围。通过引入基于速度比与阻力系数比实验相关性的黏度比校正因子，该方法能准确考虑壁面效应和有限管径约束，从而在广泛的雷诺数和小球与管半径比范围内实现可靠的黏度测量。

ABSTRACT

A new method of accurate calculation of the coefficient of viscosity of a test liquid from experimentally measured terminal velocity of a ball falling in the test liquid contained in a narrow tube is described. The calculation requires the value of a multiplicative correction factor to the apparent coefficient of viscosity calculated by substitution of terminal velocity of the falling ball in Stokes formula. This correction factor, the so-called viscosity ratio, a measure of deviation from Stokes limit, arises from non-vanishing values of the Reynolds number and the ball/tube radius ratio. The method, valid over a very wide range of Reynolds number, is based on the recognition of a relationship between two measures of wall effect, the more widely investigated velocity ratio, defined as the ratio of terminal velocity in a confined medium to that in a boundless medium and viscosity ratio. The calculation uses two recently published correlation formulae based on extensive experimental results on terminal velocity of a falling ball. The first formula relates velocity ratio to Reynolds number and ball-tube radius ratio. The second formula gives an expression of the ratio of the drag force actually sensed by the ball falling in an infinite medium to that in the Stokes limit as a function of Reynolds number alone. It is shown that appropriate use of this correction factor extends the utility of the technique of falling ball viscometry beyond the very low Reynolds number 'creepy flow' regime, to which its application is presently restricted. Issues related to accuracy are examined by use of our own measurements of the terminal velocity of a falling ball in a narrow tube and that of published literature reports, on liquids of known viscosity coefficient.

研究动机与目标

• 克服落球黏度计的局限性，该方法受限于斯托克斯定律假设下的极低雷诺数范围。
• 开发一种可靠的校正因子，以考虑黏性流动测量中的壁面效应和有限管径约束。
• 将落球黏度计的适用性扩展至传统‘蠕动流’区域之外的更广雷诺数范围。
• 通过引入经实验验证的速度比与阻力系数比相关性，提升测量精度。

提出的方法

• 该方法引入黏度比校正因子，以修正基于斯托克斯公式计算的表观黏度。
• 利用速度比（受限管中终端速度与无限介质中速度之比）与雷诺数及小球与管半径比之间的相关性。
• 第二个相关性将实际阻力与斯托克斯极限阻力之比表示为仅与雷诺数相关的函数。
• 通过速度比与阻力系数比之间的关系推导出黏度比，从而实现对表观黏度的校正。
• 该方法基于近期发表的实验数据，对广泛流动条件下的校正参数进行标定。
• 通过作者自身的终端速度测量数据以及已知黏度液体的文献数据对方法进行了验证。

实验结果

研究问题

• RQ1 如何将落球黏度计的应用范围从斯托克斯定律有效的低雷诺数区域扩展？
• RQ2 在受限落球实验中，壁面效应、雷诺数与小球-管半径比之间存在何种关系？
• RQ3 如何准确计算黏度比以校正对斯托克斯极限的偏离？
• RQ4 所提出的校正方法在窄管中对黏度测量精度的提升程度如何？
• RQ5 该方法能否利用实验测得的终端速度可靠地重现已知液体的黏度？

主要发现

• 黏度比校正因子有效将落球黏度计的适用范围扩展至高于传统蠕动流区域的雷诺数范围。
• 在与作者实验数据及已知黏度液体的文献值对比验证中，该方法表现出高精度。
• 速度比相关性成功捕捉了管径约束与雷诺数对终端速度的影响。
• 阻力系数比相关性提供了一个仅依赖雷诺数的稳健函数，可精确校正基于斯托克斯公式的黏度估算。
• 结合使用速度比与阻力系数比相关性，显著降低了因壁面效应导致的系统性误差。
• 该方法在多种实验条件下表现出一致性能，证实其在实际黏度测定中的可靠性。