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Numerical Simulations of a Miscible Drop in a Spinning Drop Tensiometer

  • Ching-Yao Chen (a1) and K.-T. Liu (a1)


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.


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1.Joseph, D., “Fluid Dynamics of Two Miscible Liquids with Diffusion and Dradient Stresses,” Eur. J. Mech. B/Fluids, 9, pp. 565596 (1990).
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. 253267(1991).
3.Hu, H. and Joseph, D., “Miscible Displacement in a Hele-Shaw Cell,” Z. Angew. Math. Phys., 43, pp. 626644 (1992).
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).
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. 104125 (1996).
6.Kurowski, P. and Misbah, C., “A Non-Standard Effect of Diffusion on a Fictitious Front Between Miscible Fluids,” Europhys. Lett., 29, pp. 309314 (1994).
7.Petitjeans, P. and Maxworthy, T., “Miscible Displacements in Capillary Tubes, Part 1: Experiments,” J. Fluid Mech., 326, pp. 3756 (1996).
8.Chen, C.-Y. and Meiburg, E., “Miscible Displacements in Capillary Tubes, Part 2: Numerical Simulations,” J. Fluid Mech., 326, pp. 5790 (1996).
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. 24472456 (2001).
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. 20522058 (2002).
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. 10861090(2003).
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. 26 (2005).
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).
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. 124 (1901).
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).
16.Quinke, G., Die oberfä chenspannung an der Grenge von Alkohol mit wä sserigen Salzlö sungen, Ann. Phy., 9, 4 (1902).
17.Freundlich, H., Colloid and Capillary Chemistry, London, Mathuen and Co. Ltd. (1962).
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. 302303 (1981).
19.Petitjeans, P., “Une tension de surface pour les fluides miscibles,” P. C. R. Acad. Sci. Paris, Serie IIb, 322, pp. 673679 (1996).
20.Rousar, I. and Nauman, E., “A Continuum Analysis of Surface Tension in Non-Equilibrium Systems,” Chem. Eng. Comm., 129, pp. 1928 (1995).
21.Manning, C. and Scriven, L., “Interfacial Tension Measurement with a Spinning Drop in Gyrostatic Equilibrium,” Rev. Sci. Instrum., 40(12), pp. 16991705 (1977).
22.Currie, P. and van Nieuwkoop, J., “Buoyancy Effects in the Spinning-Drop Interfacial Tensiometer,” J. Colloid Interface Sci., 87(2), pp. 301316 (1982).
23.Seifert, A. and Wendorff, J., “Spinning Drop Experiments on Interfacial Phenomena: Theoretical Background and Experimental Evidence,” Colloid Polym. Sci., 270, pp. 962971 (1992).
24.Hu, H. and Joseph, D., “Evolution of a Liquid Drop in a Spinning Drop Tensiometer,” J. Colloid Interface Sci., 162, pp. 331337(1994).
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. 18671875 (1995).
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).
27.Vonnegut, B., “Rotating Bubble Method for the Determination of Surface and Interfacial Tensions,” Rev. Sci. Instrum., 13, pp. 69 (1942).
28.Pojman, J., Private Communications (2005).
29.Zoltouski, B., “Spinning Drop Tensiometry,” Master Thesis, University of Southern Mississippi (2003).


Numerical Simulations of a Miscible Drop in a Spinning Drop Tensiometer

  • Ching-Yao Chen (a1) and K.-T. Liu (a1)


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