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Numerical Simulations of a Miscible Drop in a Spinning Drop Tensiometer

Published online by Cambridge University Press:  05 May 2011

Ching-Yao Chen  and
K.-T. Liu
Ching-Yao Chen*
Affiliation:
Department of Mechanical Engineering, National Yunlin University of Science & Technology, Yunlin, Taiwan 64002, R.O.C.
K.-T. Liu*
Affiliation:
Department of Mechanical Engineering, National Yunlin University of Science & Technology, Yunlin, Taiwan 64002, R.O.C.
*
*Professor
**Graduate student
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Abstract

The present investigation addresses the estimation of the unconventional effective interfacial tension (EIT), the so-called Korteweg stress, for a miscible interface. Two independent characteristic estimations are calculated: (1) the measurement based on a Spinning Drop Tensiometer (SDT) commonly applied in an immiscible situation, and (2) the theoretical predication involving an unknown physical constant (Korteweg constant) and detailed concentration distributions. Excellent agreements between these two estimations are found. By demonstrating the excellent agreement between these two proposed measurements, the applicability of a SDT for measuring miscible EIT is numerically verified. This numerical conclusion provides a possible simple method for further estimations of currently unknown physical constants.

Keywords

Miscible InterfaceEffective Interfacial TensionSpinning Drop TensiometerKorteweg Constant.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 1 , March 2007 , pp. 1 - 7
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

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References

1.Joseph, D., “Fluid Dynamics of Two Miscible Liquids with Diffusion and Dradient Stresses,” Eur. J. Mech. B/Fluids, 9, pp. 565–596 (1990).Google Scholar
2.Galdi, G., Joseph, D., Prezisi, L. and Rionero, S., “Mathematical Problems for Miscible, Incompressible Fluids with Korteweg Stresses,” Eur. J. Mech., B/Fluids, 10, pp. 253–267(1991).Google Scholar
3.Hu, H. and Joseph, D., “Miscible Displacement in a Hele-Shaw Cell,” Z. Angew. Math. Phys., 43, pp. 626–644 (1992).CrossRefGoogle Scholar
4.Davis, H., A Theory of Tension at a Miscible Displacement Front. Numerical Simulation in Oil Recovery, IMA Volumes in Mathematics and Its Applications, 11, Springer (1988).Google Scholar
5.Joseph, D., Huang, A. and Hu, H., “Non-Solenoidal Velocity Effects and Korteweg Stresses in Simple Mixture of Incompressible Liquids,” Physica D, 97, pp. 104–125 (1996).CrossRefGoogle Scholar
6.Kurowski, P. and Misbah, C., “A Non-Standard Effect of Diffusion on a Fictitious Front Between Miscible Fluids,” Europhys. Lett., 29, pp. 309–314 (1994).CrossRefGoogle Scholar
7.Petitjeans, P. and Maxworthy, T., “Miscible Displacements in Capillary Tubes, Part 1: Experiments,” J. Fluid Mech., 326, pp. 37–56 (1996).CrossRefGoogle Scholar
8.Chen, C.-Y. and Meiburg, E., “Miscible Displacements in Capillary Tubes, Part 2: Numerical Simulations,” J. Fluid Mech., 326, pp. 57–90 (1996).CrossRefGoogle Scholar
9.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).CrossRefGoogle Scholar
10.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).CrossRefGoogle Scholar
11.Chen, C.-Y., “Numerical Simulations of Fingering Instabilities in Miscible Magnetic Fluids in a Hele-Shaw Cell and the Effects of Korteweg Stresses,” Phys. Fluids, 15, pp. 1086–1090(2003).CrossRefGoogle Scholar
12.Bessonov, N., Volpert, V., Pojman, J. and Zoltowski, B., “Numerical Simulations of Convection Induced by Korteweg Stresses in Miscible Polymer-Monomer Systems,” Microgravity Sci. Tech. XVII, pp. 2–6 (2005).Google Scholar
13.Chen, C.-Y., Chen, C.-H. and Miranda, J. A., “Numerical Study of Miscible Fingering in a Time-Dependent Gap Hele-Shaw Cell,” Phys. Rev. E,71, 056304 (2005).CrossRefGoogle Scholar
14.Korteweg, D., “Sur la forme que prennent les équations du movement des fluides si l'on tient compte des forces capillaires causées par des variations de densité,” Arch. Neel. Sci. Ex. Nat. (II), 6, pp. 1–24 (1901).Google Scholar
15.Chen, C.-Y., Chen, C.-H. and Miranda, J. A., “Numerical Study of Pattern Formation in Miscible Rotating Hele-Shaw Flows,” Phys. Rev. E, 73(4), 046306 (2006).CrossRefGoogle ScholarPubMed
16.Quinke, G., Die oberfä chenspannung an der Grenge von Alkohol mit wä sserigen Salzlö sungen, Ann. Phy., 9, 4 (1902).Google Scholar
17.Freundlich, H., Colloid and Capillary Chemistry, London, Mathuen and Co. Ltd. (1962).Google Scholar
18.Smith, P., van De Ven, T. and Mason, S., “The Transient Interfacial Tension between Two Miscible Fluids,” J. Colloid and Interface, Science, 80(1), pp. 302–303 (1981).CrossRefGoogle Scholar
19.Petitjeans, P., “Une tension de surface pour les fluides miscibles,” P. C. R. Acad. Sci. Paris, Serie IIb, 322, pp. 673–679 (1996).Google Scholar
20.Rousar, I. and Nauman, E., “A Continuum Analysis of Surface Tension in Non-Equilibrium Systems,” Chem. Eng. Comm., 129, pp. 19–28 (1995).CrossRefGoogle Scholar
21.Manning, C. and Scriven, L., “Interfacial Tension Measurement with a Spinning Drop in Gyrostatic Equilibrium,” Rev. Sci. Instrum., 40(12), pp. 1699–1705 (1977).CrossRefGoogle Scholar
22.Currie, P. and van Nieuwkoop, J., “Buoyancy Effects in the Spinning-Drop Interfacial Tensiometer,” J. Colloid Interface Sci., 87(2), pp. 301–316 (1982).CrossRefGoogle Scholar
23.Seifert, A. and Wendorff, J., “Spinning Drop Experiments on Interfacial Phenomena: Theoretical Background and Experimental Evidence,” Colloid Polym. Sci., 270, pp. 962–971 (1992).CrossRefGoogle Scholar
24.Hu, H. and Joseph, D., “Evolution of a Liquid Drop in a Spinning Drop Tensiometer,” J. Colloid Interface Sci., 162, pp. 331–337(1994).CrossRefGoogle Scholar
25.Quirion, F. and Pageau, J., “Interfacial Tension between Low Molecular Weight Polymers from the Static Analysis of Cylindrical Drops and Their Break-up Dynamics,” J. Polym. Sci. Pol. Phy., 33, pp. 1867–1875 (1995).CrossRefGoogle Scholar
26.Pojman, J., Chekanov, Y., Masere, J., Volpert, V., Dumont, T. and Wilke, H., “Effective Interfacial Tension Induced Convection in Miscible Fluids,” AIAA Paper, 33, 0764 (2001).Google Scholar
27.Vonnegut, B., “Rotating Bubble Method for the Determination of Surface and Interfacial Tensions,” Rev. Sci. Instrum., 13, pp. 6–9 (1942).CrossRefGoogle Scholar
28.Pojman, J., Private Communications (2005).Google Scholar
29.Zoltouski, B., “Spinning Drop Tensiometry,” Master Thesis, University of Southern Mississippi (2003).Google Scholar