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Qualitative analysis of the minimum flow rate of a cone-jet of a very polar liquid

Published online by Cambridge University Press:  06 March 2017

F. J. Higuera Open the ORCID record for F. J. Higuera [Opens in a new window]
F. J. Higuera*
Affiliation:
ETSIAE, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
*
†Email address for correspondence: fhiguera@aero.upm.es
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Abstract

Electrostatic atomization of a liquid of finite electrical conductivity in the so-called cone-jet regime relies on the electric shear stresses that appear in a region of the liquid surface when a meniscus of the liquid is subjected to an intense electric field. An order of magnitude analysis is used to describe the flow induced by these stresses, which drive the liquid of the meniscus into a jet that issues from the tip of the meniscus and breaks into droplets at some distance from it. When the dielectric constant of the liquid is large, the electric shear stresses extend into the jet and cause a depression that sucks liquid from the meniscus. The induced flow rate is estimated and shown to represent approximately the minimum flow rate at which a cone-jet can be established. It is argued that the meniscus can be stabilized by the electric field that the charge of the jet induces on it. This stabilizing mechanism weakens when the flow rate supplied to the meniscus decreases, and its failure may determine an alternative minimum flow rate for the cone-jet regime. The instability of the jet and existing scaling laws for the size of the spray droplets are discussed.

JFM classification

Drops and Bubbles: Drops and Bubbles Drops and Bubbles: Electrohydrodynamic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , pp. 428 - 441
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Copyright
© 2017 Cambridge University Press 

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References

Alonso-Matilla, R., Fernández-García, J., Congdon, H. & Fernández de la Mora, J. 2014 Search for liquids electrospraying the smallest possible nanodrops in vacuo. J. Appl. Phys. 116, 224504.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.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.Google Scholar
Chen, D. R., Pui, D. Y. H. & Kaufman, S. L. 1995 Electrospraying of conducting liquids for monodisperse aerosol generation in the 4 nm to 1.8 μm diameter range. Aerosol Sci. Technol. 26, 963–977.CrossRefGoogle Scholar
Coffman, C., Martínez-Sánchez, M., Higuera, F. J. & Lozano, P. C. 2016 Structure of the menisci of leaky dielectric liquids during electrically-assisted evaporation of ions. Appl. Phys. Lett. 109, 231602.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. 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
Fernández de la Mora, J., Navascues, J., Fernández, F. & Rosell-Llompart, J. 1990 Generation of submicron monodisperse aerosols in electrosprays. J. Aero. Sci. 21 (Suppl.1), S673–S676.Google Scholar
Gamero-Castaño, M. 2010 Energy dissipation in electrosprays and the geometric scaling of the transition region of cone-jets. J. Fluid Mech. 662, 493–513.CrossRefGoogle Scholar
Gamero-Castaño, M. & Hruby, V. 2002 Electric measurements of charged sprays emitted by cone-jets. J. Fluid Mech. 459, 245–276.CrossRefGoogle Scholar
Gañán-Calvo, A. M. 1997 Cone-jet analytical extension of Taylor’s electrostatic solution and the asymptotic universal scaling laws in electrospraying. Phys. Rev. Lett. 79, 217–220.Google Scholar
Gañán-Calvo, A. M. 1999 The surface charge in electrostatic spraying: its nature and its universal scaling laws. J. Aero. Sci. 30, 863–872.Google Scholar
Gañán-Calvo, A. M. 2004 On the general scaling theory for electrospraying. J. Fluid Mech. 507, 203–212.Google Scholar
Gañán-Calvo, A. M., Dávila, J. & Barrero, A. 1997 Current and drop size in the electrospraying of liquids. Scaling laws. J. Aero. Sci. 28, 249–275.Google Scholar
Gañán-Calvo, A. M. & Montanero, J. M. 2009 Revision of capillary cone-jet physics: electrospray and flow focusing. Phys. Rev. E 79, 066305.Google Scholar
Gañán-Calvo, A. M., Rebollo-Muñoz, N. & Montanero, J. M. 2013 The minimum or natural rate of flow and droplet size injected by Taylor cone-jets: physical symmetries and scaling laws. New J. Phys. 15, 033035.Google Scholar
Gomez, A. & Tang, K. 1994 Charge and fission of droplets in electrostatic sprays. Phys. Fluids 6, 404–414.CrossRefGoogle Scholar
Higuera, F. J. 2003 Flow rate and electric current emitted by a Taylor cone. J. Fluid Mech. 484, 303–327.Google Scholar
Higuera, F. J. 2008 Breakup of a supported drop of a viscous conducting liquid in a uniform electric field. Phys. Rev. E 78, 016314.Google Scholar
Higuera, F. J. 2010 Numerical computation of the domain of operation of an electrospray of a very viscous liquid. J. Fluid Mech. 648, 35–52.Google Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.Google Scholar
Hohman, M. M., Shin, M., Rutledge, G. & Brenner, M. P. 2001a Electrospinning and electrically forced jets. I. Stability. Phys. Fluids 11, 2201–2220.Google Scholar
Hohman, M. M., Shin, M., Rutledge, G. & Brenner, M. P. 2001b Electrospinning and electrically forced jets. II. Applications. Phys. Fluids 11, 2221–2236.Google Scholar
Iooss, G. & Joseph, D. D. 1980 Elementary Stability and Bifurcation Theory. Springer.Google Scholar
Jayasinghe, S. N. & Edirisinghe, M. J. 2002 Effect of viscosity on the size of relics produced by electrostatic atomization. J. Aero. Sci. 33, 1379–1388.Google Scholar
de Juan, L. & Fernández de la Mora, J. 1997 Charge and size distributions of electrospray drops. J. Colloid Interface Sci. 186, 280–293.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
López-Herrera, J. M. & Gañán-Calvo, A. M. 2004 A note on charged capillary jet breakup of conducting liquids: experimental validation of a viscous one-dimensional model. J. Fluid Mech. 501, 303–326.Google Scholar
López-Herrera, J. M., Riesco-Chueca, P. & Gañán-Calvo, A. M. 2005 Linear stability analysis of axisymmetric perturbations in imperfectly conducting liquid jets. Phys. Fluids 17, 034106.Google Scholar
Loscertales, I. G., Barrero, A., Guerrero, I., Cortijo, R., Marquez, M. & Gañán-Calvo, A. M. 2002 Micro/nano encapsulation in electrified coaxial liquid jets. Science 33, 1379–1388.Google Scholar
Miksis, M. J. 1981 Shape of a drop in an electric field. Phys. Fluids 24, 1967–1972.Google Scholar
Pantano, C., Gañán-Calvo, A. M. & Barrero, A. 1994 Zeroth-order, electrohydrostatic solution for electrospraying in cone-jet mode. J. Aero. Sci. 25, 1065–1077.Google Scholar
Rayleigh, Lord 1882 On the equilibrium of conducting masses charged with electricity. Phil. Mag. 14, 184–186.Google Scholar
Rosell-Llompart, J. & Fernández de la Mora, J. 1994 Generation of monodisperse droplets 0.3–4 μm in diameter from electrified cone-jets of highly conducting viscous liquids. J. Aero. Sci. 25, 1093–1119.Google Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.Google Scholar
Tang, K. & Gomez, A. 1994 On the structure of an electrostatic spray of monodisperse droplets. Phys. Fluids 6, 2317–2332.Google 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 dielectric drops in an electric field. J. Fluid Mech. 235, 481–510.Google Scholar