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Numerical computation of the domain of operation of an electrospray of a very viscous liquid

Published online by Cambridge University Press:  07 April 2010

F. J. HIGUERA
F. J. HIGUERA*
Affiliation:
E. T. S. Ingenieros Aeronáuticos, UPM, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
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Abstract

A numerical study is carried out of the injection of a very viscous liquid of small electrical conductivity at a constant flow rate through an orifice in a metallic plate under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet emanating from its tip are investigated by computing the flow, the electric field and the transport of electric charge in the meniscus and a leading region of the jet. A stationary solution is found only for values of the flow rate above a certain minimum. At moderate values of the applied field, this minimum flow rate decreases when the applied field or the conductivity of the liquid increase. The electric shear stress acting on the surface of the liquid is not able to drive the liquid into the jet at flow rates smaller than the minimum while, for any flow rate higher than the minimum, the transfer of electric current to the surface may occur in a slender region of the jet where charge relaxation effects are small and the field induced by the electric charge of the jet is important. At high values of the applied field, the flow rate must be higher than another minimum, which increases with the applied field, in order for the viscous stress to balance the strong electric stress acting on the meniscus. The two conditions taken together determine lower and upper bounds for the applied field at a given flow rate, but the value of the applied field at which a stationary jet is first established when this parameter is gradually increased is higher than the lower bound, leading to hysteresis. When the liquid is electrosprayed in a surrounding dielectric fluid, the viscous shear stress that this fluid exerts on the surface of the jet eventually balances the electric shear stress and stops the continuous stretching of the jet. A fraction of the conduction current is left in the jet when the effect of the outer liquid comes into play in the region where this current is transferred to the surface, and no stationary solution is found above a maximum flow rate that decreases when the viscosity of the outer liquid increases or the applied field decreases. Order of magnitude estimates of the electric current and the conditions in the current transfer region are worked out.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 35 - 52
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies, Ch. 6. Addison-Wesley.Google Scholar
Barrero, A., López-Herrera, J. M., Boucard, A., Loscertales, I. G. & Márquez, M. 2004 Steady cone-jet electrosprays in liquid insulator baths. J. Colloid Interface Sci. 272, 104–108.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics Cambridge University Press, p. 132.Google Scholar
Chen, D.-R. & Pui, D. Y. H. 1997 Experimental investigation of scaling laws for electrospraying: dielectric constant effects. Aerosol Sci. Technol. 27, 367–380.CrossRefGoogle Scholar
Cherney, L. T. 1999 Structure of Taylor cone-jets: limit of low flow rates. J. Fluid Mech. 378, 167–196.CrossRefGoogle Scholar
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquid in cone-jet mode. J. Electrost. 22, 135–159.CrossRefGoogle Scholar
Cloupeau, M. & Prunet-Foch, B. 1990 Electrostatic spraying of liquid. Main functioning modes. J. Electrost. 23, 165–184.CrossRefGoogle Scholar
Cloupeau, M. & Prunet-Foch, B. 1994 Electrohydrodynamic spraying functioning modes: a critical review. J. Aerosol Sci. 25, 1021–1036.CrossRefGoogle Scholar
Feng, J. J. 2002 The stretching of an electrified non-Newtonian jet: a model for electrospinning. Phys. Fluids 14, 3912–3926.CrossRefGoogle Scholar
Fernández de la Mora, J. 1992 The effect of charge emission from electrified liquid cones. J. Fluid Mech. 243, 561–573.CrossRefGoogle Scholar
Fernández de la Mora, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39, 217–243.CrossRefGoogle Scholar
Fernández de la Mora, J. & Loscertales, I. G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260, 155–184.CrossRefGoogle Scholar
Gañán-Calvo, A. M., Dávila, J. & Barrero, A. 1997 Current and drop size in the electrospraying of liquids. Scaling laws. J. Aerosol Sci. 28, 249–275.CrossRefGoogle Scholar
Guerrero, I., Bocanegra, R., Higuera, F. J. & Fernández de la Mora, J. 2007 Ion evaporation from Taylor cones of propylene carbonate mixed with ionic liquids. J. Fluid Mech. 591, 437–459.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Hayati, I., Bailey, A. I. & Tadros, Th. F. 1987 Investigations into the mechanisms of electrohydrodynamic spraying of liquids. J. Colloid Interface Sci. 117, 205–221.CrossRefGoogle Scholar
Higuera, F. J. 2003 Flow rate and electric current emitted by a Taylor cone. J. Fluid Mech. 484, 303–327.CrossRefGoogle Scholar
Higuera, F. J. 2006 Stationary viscosity-dominated electrified capillary jets. J. Fluid Mech. 558, 143–152.CrossRefGoogle Scholar
Higuera, F. J. 2007 a Stationary coaxial electrified jet of a dielectric liquid surrounded by a conductive liquid. Phys. Fluids 19, 012102.CrossRefGoogle Scholar
Higuera, F. J. 2007 b Emission of drops from the tip of an electrified jet of an inviscid liquid of infinite electrical conductivity. Phys. Fluids 19, 072113.CrossRefGoogle Scholar
Higuera, F. J. 2008 a Breakup of a supported drop of a viscous conducting liquid in a uniform electric field. Phys. Rev. E 77, 016314.CrossRefGoogle Scholar
Higuera, F. J. 2008 b Model of the meniscus of an ionic-liquid ion source. Phys. Rev. E 77, 026308.CrossRefGoogle ScholarPubMed
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Jaworek, A. & Krupa, A. 1999 Classification of the modes of EHD spraying. J. Aerosol Sci. 30, 873–893.CrossRefGoogle Scholar
Kim, K. & Turnbull, R. J. 1976 Generation of charged drops of insulating liquids by electrostatic spraying. J. Appl. Phys. 47, 1964–1969.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
Larriba, C. & Fernández de la Mora, J. 2009 Electrospraying insulating liquids via charged nanodrops injection from the Taylor cone of an ionic liquid. Phys. Fluids. (submitted).Google Scholar
Miksis, M. J. 1981 Shape of a drop in an electric field. Phys. Fluids 24, 1967–1972.CrossRefGoogle Scholar
Pantano, C., Gañán-Calvo, A. M. & Barrero, A. 1994 Zeroth order, electrohydrostatic solution for electrospraying in cone-jet mode. J. Aerosol Sci. 25, 1065–1077.CrossRefGoogle Scholar
Rosell-Llompart, J. & Fernández de la Mora, J. 1994 Generation of monodisperse droplets 0.3 to 4 μm in diameter from electrified cone-jets of highly conducting and viscous liquids. J. Aerosol Sci. 25, 1093–1119.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.CrossRefGoogle Scholar
Smith, D. P. H. 1986 The electrohydrodynamic atomization of liquids. IEEE Trans. Ind. Appl. IA22, 527–535.CrossRefGoogle Scholar
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383–397.Google Scholar
Wohlhuter, F. K. & Basaran, O. A. 1992 Shapes and stability of pendant and sessile drops in an electric field. J. Fluid Mech. 235, 481–510.CrossRefGoogle Scholar
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, 1–6.Google Scholar
Zeleny, J. 1935 The role of surface instability in electrical discharges from drops of alcohol and water in air at atmospheric pressure. J. Franklin Inst. 219, 659–675.CrossRefGoogle Scholar