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Motion of Miscible Magnetic Fluids in a Vertical Capillary Tube

Published online by Cambridge University Press:  05 May 2011

C.-Y. Chen ,
H.-C. Lin ,
W.-K. Tsai  and
C.-H. Lin
C.-Y. Chen*
Affiliation:
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, R.O.C.
H.-C. Lin*
Affiliation:
Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin, Taiwan 64002, R.O.C.
W.-K. Tsai*
Affiliation:
Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin, Taiwan 64002, R.O.C.
C.-H. Lin*
Affiliation:
Department of Fashion Design and Management, Tainan University of Technology, Tainan, Taiwan 71002, R.O.C.
*
* Professor, corresponding author
** Graduate student
** Graduate student
*** Lecturer
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Abstract

An experimental study of miscible magnetic fluid motion in a vertical capillary tube is presented. Transporting ferrofluids is dominated by a dimensionless magnetic number Ma, which characterizes the ratio of upward magnetic force to the downward gravity. Two distinct stages of motion, referred to as the sub-critical mode of finite lift and the effective transportation, are identified. These two modes are determined by the values of the sub-critical magnetic number Masub and critical magnetic number Macr respectively. For the cases of sub-critical mode (Masub < Ma < Macr), the ferrofluids are lifted to quasiequilibrium heights, which are nearly proportional to the magnetic number Ma. As for the situations of effective transportation (Ma > Macr), a penetrating finger of ferrofluids is formed similar to the conventional miscible displacements. A dimensionless proportionality of fingertip velocity ν, magnetic number Ma and field distribution profile fz is obtained as ν ∼ Ma1/2fz by scaling arguments. This proportional correlation shows a good agreement with the experiments.

Keywords

Miscible ferrofluidCapillary tube
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 4 , December 2008 , pp. 311 - 317
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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References

1.Yamaguchi, H., Kobori, I. and Kobayashi, N., “Numerical Study of Flow State for a Magnetic Fluid Heat Transport Device,” J. Magn. Magn. Mater., 201, pp. 260–263 (1999).Google Scholar
2.Yamaguchi, H., Kobori, I. and Uehata, Y., “Heat Transfer in Natural Convection of Magnetic Fluids,” Journal of Thermophysics and Heat Transfer, 13, pp. 501–507 (1999).Google Scholar
3.Kamiyama, S., Ueno, K. and Yokota, Y., “Numerical Analysis of Unsteady Gas — Liquid Two-Phase Flow of Magnetic Fluid,” J. Magn. Magn. Mater., 201, pp. 271–275 (1999).CrossRefGoogle Scholar
4.Perez-Castillejos, R., Plaza, J. A., Esteve, J., Losantos, P., Acero, M., Cane, C. and Serra-Mestres, F., “The Use of Ferrofluid in Micromechanics,” Sens. Actuators A, 84, pp. 176–180 (2000).Google Scholar
5.Hatch, A., Kamholz, A., Holman, G., Yager, P. and Bohringer, K., “A Ferrofluid Magnetic Micropump,” J. Microelectromech Syst., 10, pp. 215–221 (2001).Google Scholar
6.Hartshorne, H., Backhouse, C. and Lee, W., “Ferrofluid-Based Microchip Pump and Valve,” Sens. Actuators B, 99, pp. 592–600 (2004).Google Scholar
7.Loukopoulos, V. and Tzirtzilakis, E., “Biomagnetic Channel Flow in Spatially Varying Magnetic Field,” Int. J. Eng. Sci., 42, pp. 571–590 (2004).CrossRefGoogle Scholar
8.Ganguly, R., “Analyzing Ferrofluid Transport for Magnetic Drug Targeting,” J. Magn. Magn. Mater., 289, pp. 331–334 (2005).CrossRefGoogle Scholar
9.Tzirtzilakis, E., “A Mathematical Model for Blood Flow in Magnetic Field,” Phys. Fluids, 17, 077103 (2005).Google Scholar
10.Petitjeans, P. and Maxworthy, T., “Miscible Displacements in Capillary Tubes, Part 1: Experiments,” J. Fluid Mech., 326, pp. 37–56 (1996).CrossRefGoogle Scholar
11.Chen, C.-Y. and Meiburg, E., “Miscible Displacements in Capillary Tubes, Part 2: Numerical Simulations,” J. Fluid Mech., 326, pp. 57–90 (1996).Google Scholar
12.Chen, C.-Y., Wang, L. and Meiburg, E., “Miscible Droplets in a Porous Medium and the Effect of Korteweg Stresses,” Phys. Fluids, 13, pp. 2447–2456 (2001).Google Scholar
13.Scoffoni, J., Lajeunesse, E. and Homsy, G., “Interface Instabilities During Displacement of Two Miscible Fluids in a Vertical Pipe,” Phys. Fluids, 13, pp. 552–556 (2001).CrossRefGoogle Scholar
14.Chen, C.-Y. and Meiburg, E., “Miscible Displacements in Capillary Tubes in the Presence of Korteweg Stresses and Divergence Effects,” Phys. Fluids, 14, pp. 2052–2058 (2002).Google Scholar
15.Kuang, J., Maxworthy, T. and Petitjeans, P., “Miscible Displacements Between Silicone Oils in Capillary Tubes,” Eur. J. Mech. B/Fluids, 22, pp. 271–277 (2003).CrossRefGoogle Scholar
16.Kuang, J. and Maxworthy, T., “The Effects of Thermal Diffusion on Miscible, Viscous Displacement in a Capillary Tube,” Phys. Fluids, 15, pp. 1340–1343 (2003).CrossRefGoogle Scholar
17.Chen, C.-Y. and Meiburg, E., “Miscible Displacement in Capillary: Effect of a Preexisting Wall Film,” Phys. Fluids, 16, pp. 602–609 (2004).Google Scholar
18.Wilhelm, D. and Meiburg, E., “Three-Dimensional Spectral Element Simulations of Variable Density and Viscosity, Miscible Displacements in a Capillary Tube,” Comput. Fluids, 33, pp. 485–508 (2004).CrossRefGoogle Scholar
19.Séon, T., Hulin, J.-P., Salin, D., Perrin, B. and Hinch, E., “Buoyant Mixing of Miscible Fluids in Tilted Tubes,” Phys. Fluids, 16, L103–L106 (2004).CrossRefGoogle Scholar
20.Kuang, J., Petitjeans, P. andMaxworthy, T., “Velocity Fields and Streamline Patterns of Miscible Displacements in Cylindrical Tubes,” Exp. Fluids, 37, pp. 301–308 (2004).Google Scholar
21.Balasubramaniam, R., Rashidnia, N., Maxworthy, T. and Kuang, J., “Instability of Miscible Interfaces in a Cylindrical Tube,” Phys. Fluids, 17, 052103 (2005).CrossRefGoogle Scholar
22.Chen, C.-Y. and Liu, K.-T., “Numerical Simulations of a Miscible Drop in a Spinning Drop Tensiometer,” Journal of Mechanics, 23, pp. 1–7 (2007).Google Scholar
23.Chen, C.-Y. and Liao, C.-Y., “Motion of Miscible Magnetic Fluids in a Dynamic Magnetic Field,” Int. J. Numer. Methods. Heat Fluid Flow, 13, pp. 244–261 (2003).Google Scholar
24.Chen, C.-Y., Hong, C.-Y. and Chang, L.-M., “Displacements of Miscible Magnetic Fluids in a Capillary Tube,” Fluid Dyn. Res., 32, pp. 85–98 (2003).Google Scholar
25.Taylor, G. I., “Deposition of a Viscous Fluid on the Wall of a Tube,” J. Fluid Mech., 10, pp. 161–165 (1961).Google Scholar