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Modelling the electric microdripping from a needle

Published online by Cambridge University Press:  15 June 2021

A.J. Hijano Open the ORCID record for A.J. Hijano [Opens in a new window] ,
I.G. Loscertales Open the ORCID record for I.G. Loscertales [Opens in a new window]  and
F.J. Higuera Open the ORCID record for F.J. Higuera [Opens in a new window]
A.J. Hijano
Affiliation:
Universidad de Málaga, Andalucía Tech, Escuela de Ingenierías Industriales, 29071Málaga, Spain
I.G. Loscertales*
Affiliation:
Universidad de Málaga, Andalucía Tech, Escuela de Ingenierías Industriales, 29071Málaga, Spain
F.J. Higuera
Affiliation:
Universidad Politécnica de Madrid, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, 28040Madrid, Spain
*
†Email address for correspondence: loscertales@uma.es
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Abstract

Droplet emission from an electrified meniscus in the microdripping regime has been investigated experimentally and numerically. In this regime, the meniscus of a low viscosity, high electrical conductivity liquid hanging from the tip of a metallic tube, oscillates when subjected to a high electric field. When the liquid is fed at a constant flow rate, and for a certain range of voltages, the oscillations are periodic and, in each oscillation, the meniscus develops a ligament that eventually detaches forming a single drop. Thus, this technique is a simple way to produce monodisperse droplets at relatively high frequencies, whose diameters may be one-tenth of that of the tube. The process, governed by a dimensionless flow rate $q$ and an electric Bond number ${B_{E}}$, has been modelled as the axisymmetric motion of an inviscid meniscus of infinite conductivity, and compared against experiments. For moderate and high values of $q$, the computed meniscus mean volume and oscillation frequency agree with the experimental results, although the volume and number of emitted droplets do not. An ultrafine electrospray emitted from the ligament's conical tip during part of the oscillation cycle is probably the cause of the disagreements. To tackle this, we combine the one-dimensional approximation of an electrified meniscus with experimental meniscus profiles to compute the electric field on the meniscus. Around the tip, this electric field turns out to be substantially smaller than the field computed by the model in the absence of the space charge, and agrees with the field induced by an electrospray emitted from a Taylor cone in air.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Electrohydrodynamic effects Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A47
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Acero, A.J., Ferrera, C., Montanero, J.M., Herrada, M.A. & López-Herrera, J.M. 2013 Experimental analysis of the evolution of an electrified drop following high voltage switching. Eur. J. Mech. B/Fluids 38, 58–64.CrossRefGoogle Scholar
Cloupeau, M. & Prunet-Foch, B. 1994 Electrohydrodynamic spraying functioning modes: a critical review. J. Aerosol Sci. 25 (6), 1021–1036.CrossRefGoogle Scholar
Collins, R.T., Jones, J.J., Harris, M.T. & Basaran, O.A. 2008 Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4, 149–154.CrossRefGoogle Scholar
Collins, R.T., Sambath, K., Harris, M.T. & Basaran, O.A. 2013 Universal scaling laws for the disintegration of electrified drops. Proc. Natl Acad. Sci. 110 (13), 4905–4910.CrossRefGoogle ScholarPubMed
Day, R.F., Hinch, E.J. & Lister, J.R. 1998 Self-similar capillary pinch-off of an inviscid fluid. Phys. Rev. Lett. 80, 704–707.CrossRefGoogle Scholar
Decent, S.P. & King, A.C. 2008 Surface-tension-driven flow in a slender cone. IMA J. Appl. Maths 73, 37–68.CrossRefGoogle Scholar
Eggers, J. & Dupont, M. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262 (4), 205–221.CrossRefGoogle Scholar
Fernández de la Mora, J. 1992 The effect of charge emission from electrified liquid cones. J. Fluid Mech. 243, 561–574.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
Ferrera, C., López-Herrera, J.M., Herrada, M.A., Montanero, J.M. & Acero, A.J. 2013 Dynamical behavior of electrified pendant drops. Phys. Fluids 25, 012104.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., Ibáñez, S.E., Hijano, A.J. & Loscertales, I.G. 2013 Pulsating emission of droplets from an electrified meniscus. J. Aerosol Sci. 66 (1), 193–208.CrossRefGoogle Scholar
Hijano, A.J., Loscertales, I.G., Ibáñez, S.E. & Higuera, F.J. 2015 Periodic emission of droplets from an oscillating electrified meniscus of a low-viscosity, highly conductive liquid. Phys. Rev. E 91 (1), 013011.CrossRefGoogle ScholarPubMed
Hohman, M.M., Shin, M., Rutledge, G. & Brenner, M.P. 2001 Electrospinning and electrically forced jets. I. Stability theory. Phys. Fluids 13 (8), 2201–2220.CrossRefGoogle Scholar
Ibáñez, S.E. 2015 Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray. PhD thesis, Universidad Politécnica de Madrid.Google Scholar
Juraschek, R. & Röllgen, F.W. 1998 Pulsation phenomena during electrospray ionization. Intl J. Mass Spectrom. 177, 1–15.CrossRefGoogle Scholar
Keller, J.B., King, A. & Ting, L. 1995 Blob formation. Phys. Fluids 7, 226–228.CrossRefGoogle Scholar
Krupa, A. & Jaworek, A. 1999 Spherical probe for measuring aerosol mass flow rate. J. Aerosol Sci. 30 (1), 377–378.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1984 Electrodynamics of Continuous Media; 2nd Edition, vol. 8. Butterworth-Heinemann.Google Scholar
Landau, L.D. & Lifshitz, E.M. 1987 Fluid Mechanics; 2nd Edition, vol. 6. Butterworth-Heinemann.Google Scholar
Leppinen, D. & Lister, J.R. 2003 Capillary pinch-off of inviscid fluids. Phys. Fluids 15, 568–578.CrossRefGoogle Scholar
Marginean, I., Nemes, P. & Vertes, A. 2006 Order-chaos-order transitions in electrosprays: the electrified dripping faucet. Phys. Rev. Lett. 97 (6), 064502.CrossRefGoogle ScholarPubMed
Mathews, J.H. & Fink, K.D. 1999 Numerical methods using MATLAB. Prentice Hall.Google Scholar
Pozrikidis, C. 2002 A practical guide to boundary element methods with the software library BEMLIB. CRC Press.CrossRefGoogle Scholar
Rayleigh, Lord 1882 XX. On the equilibrium of liquid conducting masses charged with electricity. Phil. Mag. 14 (87), 184–186.CrossRefGoogle Scholar
Rosell-Llompart, J., Grifolls, J. & Loscertales, I.G. 2018 Electrosprays in the cone-jet mode: from Taylor cone formation to spray development. J. Aerosol Sci. 125 (4), 2–31.CrossRefGoogle Scholar
Taylor, G.I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280 (1382), 383–397.Google Scholar
Yildirim, O.E. & Basaran, O.A. 2001 Deformation and breakup of stretching bridges of newtonian and shear-thinning liquids: comparison of one-and two-dimensional models. Chem. Engng Sci. 56 (1), 211–233.CrossRefGoogle Scholar