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Dynamics of drop formation from a capillary in the presence of an electric field

  • Xiaoguang Zhang (a1) and Osman A. Basaran (a2) (a3)
Abstract

This paper reports an experimental study of the effects of an externally applied electric field on the dynamics of drop formation in the dripping mode from a vertical metal capillary. The fluid issuing out of the capillary is a viscous liquid, the surrounding ambient fluid is air, and the electric field is generated by establishing a potential difference between the capillary and a horizontal, circular electrode of large radius placed downstream of the capillary outlet. By means of an ultra-high-speed video system that is capable of recording up to 12000 frames per second, special attention is paid to the dynamics of the liquid thread that connects the primary drop that is about to detach and fall from the capillary to the rest of the conical liquid mass that is hanging from it. The experiments show that as the strength of the electric field increases, the volume of the primary drop decreases whereas the maximum length attained by the thread increases. The reduction in the volume of primary drops and the increase in the length of threads occur because the effective electromechanical surface tension of the fluid interface falls as the field strength rises. For the highly conducting drops of aqueous NaCl solutions studied in this work, the increase in thread length is due solely to the rising importance of normal electric stress relative to the falling importance of surface tension. However, as the conductivity of the drop liquid decreases, the thread length is further increased on account of the stabilizing influence exerted by the increasing electric shear stress that acts on the charged liquid–gas interface. Two new phenomena are also reported that have profound implications for electrohydrodynamics and practical applications. First, it is shown that whereas the liquid thread always ruptures at its downstream end in the absence of an applied electric field or when the field strength is low, it ruptures at its upstream end when the field strength is sufficiently high. Since satellite drops are produced directly from the thread once both of its ends have ruptured, the change in the mechanism of breakup with field strength influences the dynamics and fate of satellite drops. Second, it is demonstrated that the generation of satellites, which are often undesirable in applications, can be suppressed by the judicious application of an electric field. This is accomplished by using a field of moderate strength to induce charges of the opposite sign on the nearby surfaces of the satellite drop and the liquid that remains pendant from the tube following thread rupture. At high field strengths, induced charge effects are too weak to compete with net charge effects: the satellite is repelled by the pendant drop and falls under gravity as a distinct entity.

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References
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Bailey, A. G. 1988 Electrostatic Spraying of Liquids. Research Studies Press Ltd., Taunton, England.
Basaran, O. A. & Scriven, L. E. 1982 Profiles of electrified drops and bubbles. In Proc. 2nd Intl Colloq. on Drops Bubbles (ed. D. H. Le Croissette). Jet Propulsion Laboratory, Pasadena, California.
Basaran, O. A. & Scriven, L. E. 1990 Axisymmetric shapes and stability of pendant and sessile drops in an electric field. J. Colloid Interface Sci. 140, 1030.
Byers, C. H. & Perona, J. J. 1988 Drop formation from an orifice in an electric field. AIChE J. 34, 15771580.
Chang, L. S. & Berg, J. C. 1985 The effect of interfacial tension gradients on the flow structure of single drops or bubbles translating in an electric field. AIChE J. 31, 551557.
Cloupeau, M. & Prunet-Foch, B. 1990 Electrostatic spraying of liquids: Main functioning modes. J. Electrostatics 25, 165184.
Davis, M. H. 1964 Two charged spherical conductors in a uniform electric field: Forces and field strength. Q. J. Mech. Appl. Maths 17, 499511.
Dean, J. A. 1979 Lange's Handbook of Chemistry. McGraw-Hill.
Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262, 205221.
Feng, J. Q. & Basaran, O. A. 1995 Interactions between two electrified liquid columns pinned on a dielectric solid surface. Phys. Fluids 7, 667679.
Fernandez de la Mora, J. & Loscertales, I. G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260, 155184.
Fillmore, G. L., Buehner, W. L. & West, D. L. 1977 Drop charging and deflection in an electrostatic ink jet printer. IBM J. Res. Develop. 21, 3747.
Harris, M. T. & Basaran, O. A. 1993 Capillary electrohydrostatics of conducting drops hanging from a nozzle in an electric field. J. Colloid Interface Sci. 161, 389413.
Harris, M. T. & Basaran, O. A. 1995 Equilibrium shapes and stability of nonconducting pendant drops surrounded by a conducting fluid in an electric field. J. Colloid Interface Sci. 170, 308319.
Harris, M. T. & Byers, C. H. 1989 An Advanced Technique for Interfacial Tension Measurement in Liquid-Liquid Systems. ORNL/TM-10734.
Hayati, I., Bailey, A. I. & Tadros, Th. F. 1986 Mechanism of stable jet formation in electrohydrodynamic atomization. Nature 319, 4143.
Inkpen, S. L. & Melcher, J. R. 1987 Dominant mechanisms for color differences in the mechanical and the electrostatic spraying of metallic paints. Indust. Engng Chem. Res. 26, 16451653.
Joffre, G., Prunet-Foch, B., Berthomme, S. & Cloupeau, M. 1982 Deformation of liquid menisci under the action of an electric field. J. Electrostatics 13, 151165.
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: A review of the role of interfacial shear stresses. Ann. Rev. Fluid Mech. 1, 111146.
Mestel, A. J. 1994 Electrohydrodynamic stability of a slightly viscous jet. J. Fluid Mech. 274, 93113.
Michael, D. H. 1981 Meniscus stability. Ann. Rev. Fluid Mech. 13, 189215.
Miller, C. A. & Scriven, L. E. 1970 Interfacial instability due to electrical forces in double layers. I. General considerations. J. Colloid Interface Sci. 33, 360370.
Peregrine, D. H., Sholer, G. & Symon, A. 1990 The bifurcation of liquid bridges. J. Fluid Mech. 212, 2539.
Rayleigh, Lord 1882 On the equilibrium of liquid conducting masses charged with electricity. Phil. Mag. 14, 184186.
Reitz, J. R. & Milford, F. J. 1967 Foundations of Electromagnetic Theory. Addison-Wesley.
Sankaran, S. & Saville, D. A. 1993 Experiments on the stability of a liquid bridge in an axial electric field. Phys. Fluids A 5, 10811083.
Saville, D. A. 1970 Electrohydrodynamic stability: fluid cylinders in longitudinal electric fields. Phys. Fluids 13, 29872994.
Saville, D. A. 1971 Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet. J. Fluid Mech. 48, 815827.
Schulkes, R. M. S. M. 1994 The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278, 83100.
Shi, X. D., Brenner, M. P. & Nagel, S. R. 1994 A cascade of structure in a drop falling from a faucet. Science 265, 219222.
Takamatsu, T., Hashimoto, Y., Yamaguchi, M. & Katayama, T. 1981 Theoretical and experimental studies of charged drop formation in a uniform electric field. J. Chèm. Engng Japan 14, 178182.
Takamatsu, T., Yamaguchi, M. & Katayama, T. 1983 Formation of single charged drops in a non-uniform electric field. J. Chem. Engng Japan 16, 267272.
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383397.
Taylor, G. I. 1969 Elactrically driven jets. Proc. R. Soc. Lond. A 313, 453475.
Vu, N. & Carleson, T. E. 1986 Electric field effects on drop size and terminal velocity in liquid-liquid systems. AIChE J. 32, 17391742.
Wham, R. M. & Byers, C. H. 1987 Mass transport from single droplets in imposed electric fields. Sep. Sci. Technol. 22, 447453.
Zeleny, J. 1915 On the conditions of instability of electrified drops, with applications to the electrical discharge from liquid points. Proc. Camb. Phil. Soc. 18, 7183.
Zeleny, J. 1917 Instability of electrified liquid surfaces. Phys. Rev. 10, 16.
Zhang, X., Harris, M. T. & Basaran, O. A. 1994 Measurement of dynamic surface tension by a growing drop technique. J. Colloid Interface Sci. 168, 4760.
Zhang, X. & Basaran, O. A. 1995 An experimental study of dynamics of drop formation. Phys. Fluids 7, 11841203.
Zhang, X., Basaran, O. A. & Wham, R. M. 1995 Theoretical prediction of electric field-enhanced coalescence of spherical drops. AIChE J. 41, 16291639.
Zhang, X., Padgett, R. S. & Basaran, O. A. 1996 Nonlinear deformation and breakup of stretching liquid bridges. J. Fluid Mech. in press.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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