Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Flow and Displacement of Non-Newtonian Fluid(Power-Law Model) by Surface Tension and Gravity Force in Inclined Circular Tube

경사진 원형관에서 표면장력과 중력에 의한 비뉴턴 유체(멱법칙 모델)의 유동 및 변위

  • Moh, Jeong Hah (Division of Mechanical & Automotive Engineering, Wonkwang Univ.) ;
  • Cho, Y.I. (Department of Mechanical Engineering and Mechanics, Drexel Univ.)
  • 모정하 (원광대학교 기계자동차공학부) ;
  • Received : 2013.01.09
  • Accepted : 2013.10.15
  • Published : 2014.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents the theoretical analysis of a flow driven by surface tension and gravity in an inclined circular tube. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Power-law model) that continuously flows into a circular tube owing to surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that quantitatively, the theoretical predictions of the governing equation were in excellent agreement with the solutions of the equation for horizontal tubes and the past experimental data. In addition, the predictions compared very well with the results of the force balance equation for steady.

본 논문은 경사진 원형관에서 표면장력과 중력으로 구동되는 비뉴턴 유체(멱법칙 모델)의 유동 및 변위를 이론적으로 연구한 것이다. 그리고 표면장력에 의하여 연속적으로 원형관 내로 유입되는 비뉴턴 유체의 변위를 기술하기 위한 지배방정식을 처음으로 개발하였다. 뉴턴의 운동방정식으로부터 유도된 식은 2계 비선형이며 비제차인 형태의 상미분 방정식이다. 지배방정식의 해를 수평관에서 변위를 시간의 함수로 기술한 식 및 실험과 비교한 결과 정량적으로 동일한 일치를 보였다. 여기에 더하여 정상상태인 힘의 균형식의 결과에 대해서도 정확한 일치로 나타남을 확인할 수 있었다.

Keywords

Acknowledgement

Supported by : 원광대학교

References

  1. Tokaty, G. A., 1994, A History and Philosophy of Fluid Mechanics, New York(Dover).
  2. Bell, J. M. and Cameron, F. K., 1906, "The Flow of Liquid Through Capillary Spaces," J. Phys. Chem., 10, pp. 658-674.
  3. Washburn, E. W., 1921, "The Dynamics of Capillary Flow," Phys. Rev. 17, pp. 273-283. https://doi.org/10.1103/PhysRev.17.273
  4. van Remoortere, P. and Joos, P., 1993, "About the Kinetics of Partial Wetting," J. Colloid Interfac Sci. 160, pp. 387-396. https://doi.org/10.1006/jcis.1993.1410
  5. Ichikawa, N. and Satoda, Y, 1994, "Interface Dynamics of Capillary Flow in a Tube under Negligible Gravity Condition," J. Colloid Interface Sci. 162, pp. 350-355. https://doi.org/10.1006/jcis.1994.1049
  6. Weislogel, M. M., 1997, "Steady Spontaneous Capillary Flow in Partially Coated Tubes," AICHE J. 43, pp. 645-654. https://doi.org/10.1002/aic.690430310
  7. Huang, W., Bhullar, R. S. and Fung, Y. C., 2001, "The Surface-Tension-Driven Flow of Blood from a Droplet into a Capillary Tube," Trans. ASME J. Biomech. Eng.123, pp. 446-454. https://doi.org/10.1115/1.1389096
  8. Yang, L. J., Yao, T. J. and Tai, Y. C., 2004, "The Marching Velocity of the Capillary Meniscus in a Microchannel," J. Micromech. Microeng. 14, pp. 220-225. https://doi.org/10.1088/0960-1317/14/2/008
  9. Chan, W. K. and Yang, C., 2005, "Surface- Tension-Driven Liquid-Liquid Displacement in Capillary," J. Micromech. Microeng. 15, pp. 1722-1728. https://doi.org/10.1088/0960-1317/15/9/014
  10. Kung, C. F., Chiu, C. F., Chen, C. F., Chang, C. C. and Chu, C. C., 2009, "Blood Flow Driven by Surface Tension in a Microchannel," Microfluid Nanofluid, 6, pp. 693-697. https://doi.org/10.1007/s10404-008-0345-x
  11. Chebbi, R., 2007, "Dynamics of Liquid Penetration into Capillary Tubes," J. Colloid Interface Sci. 315, pp. 255-260. https://doi.org/10.1016/j.jcis.2007.06.073
  12. Fries, M. and Dreyer, M., 2008, "An Analytic Solution of Capillary Rise Restrained by Gravity," J. Colloid Interface Sci. 320, pp. 259-263. https://doi.org/10.1016/j.jcis.2008.01.009
  13. Yang, C. and Li, D., 1996, "A Method of Determining the Thickness of Liquid-Liquid Interface," Colloids Surf. A 113, pp. 51-60. https://doi.org/10.1016/0927-7757(96)03544-3