力学与实践 ›› 2011, Vol. 33 ›› Issue (6): 18-22.DOI: 10.6052/1000-0879-lxysj2011-211

• 应用研究 • 上一篇    下一篇

幂律流体在单根弯曲毛细管中的毛细上升

王世芳1,郁伯铭2   

  1. 1. 华中科技大学
    2. 华中科技大学物理学院
  • 收稿日期:2011-05-23 修回日期:2011-07-09 出版日期:2011-12-15 发布日期:2011-12-23
  • 通讯作者: 郁伯铭
  • 基金资助:
    国家自然科学基金

CAPILLARY RISE OF A POWER LAW LIQUID IN A SINGLE TORTUOUS CAPILLARY

Shifang Wang1,Baiming Yv2   

  1. 1. Huazhong University of Science and Technology
    2.
  • Received:2011-05-23 Revised:2011-07-09 Online:2011-12-15 Published:2011-12-23
  • Contact: Baiming Yv

摘要: 基于分形理论和数值模拟的方法, 给出了幂律流体在单根弯曲毛细管的上升高 度和上升累积质量随时间的变化关系曲线. 研究结果表明: 在上升初期阶段, 重力因素可以 忽略; 但随着时间增加, 重力因素的影响越来越大; 幂律流体上升的最大高度只与毛细管直 径$\lambda$、幂律流体密度$\rho $有关, 与毛细管弯曲程度$\tau _0 $和幂指数$n$无关; 幂指数$n$越小, 上升初期上升速度越快; 迂曲度分形维数$D_T $越大, 平衡时吸入的幂律流体质量也越大.

关键词: 幂律流体,渗析高度,迂曲度分形维数, Lucas—Washburn方程

Abstract: Based on the fractal theory and the numerical simulation method, the curres of the height of imbibition and the mass of imbibition against time are obtained for a power law liquid in a single tortuous capillary. The results show that the effect of the gravity may be neglected at the initial stage of capillary rise and the effect of the gravity becomes important as time goes on. The maximum equilibrium height of imbibition for a power law liquid in a single tortuous capillary is found to be a function of the capillary diameter $\lambda $ and the density $\rho $ of the power law liquid, and independent of the tortuousity of a single tortuous capillary and the power exponent $n$. Meanwhile, the rise velocity increases with the decrease of the power exponent $n$ at the initial stage of capillary rise. And the larger the tortuousity fractal dimension $D_T $, the more the mass of imbibition at equilibrium will be.

Key words: a power law liquid, the height of imbibition,tortuousity fractal dimension,Lucas—Washburn equation

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