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Physics of Fluids / Volume 22 / Issue 11 / ARTICLES / Interfacial Flows

Phys. Fluids 22, 112107 (2010); http://dx.doi.org/10.1063/1.3493636 (9 pages)

Electrodispersion of a liquid of finite electrical conductivity in an immiscible dielectric liquid

F. J. Higuera

E. T. S. Ingenieros Aeronáuticos, UPM Pza. Cardenal Cisneros 3, Madrid 28040, Spain

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(Received 26 April 2010; accepted 3 August 2010; published online 2 November 2010)

Order-of-magnitude estimates and numerical computations are used to analyze an electrospray operating in the cone-jet mode in a bath of an immiscible dielectric liquid. In agreement with experimental results in the literature, the analysis predicts that the electric current carried by the jet increases as the square root of the flow rate of dispersed liquid in a wide range of conditions of the flow. The characteristics of the current transfer region determining the electric current are estimated taking into account the viscous drag of the dielectric liquid that surrounds the jet. The electric current is predicted to depart from the square root law for small flow rates, when charge relaxation effects become important in the current transfer region, and also when the flow rate increases to values of the order of QM = ϵ0γ2a/μ22K, where ϵ0 and μ2 are the permittivity and viscosity of the dielectric liquid, K is the electrical conductivity of the dispersed liquid, a is the radius of the capillary needle through which this liquid is injected, and γ is the interfacial tension of the liquid pair. When the flow rate becomes of order QM, the meniscus at the tip of the capillary ceases to resemble a Taylor cone, the current transfer region ceases to be short compared to the size of the meniscus, the electric current levels to a constant value, and the stationary jet cannot extend very far downstream of the meniscus.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FORMULATION
  3. ORDER OF MAGNITUDE ESTIMATES
    1. Electrical estimates
    2. Mechanical estimates
    3. Small flow rates
    4. Modifications for high flow rates
  4. NUMERICAL RESULTS
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

capillarity, dielectric liquids, drag, electrohydrodynamics, emulsions, jets, numerical analysis, sprays, surface tension, two-phase flow, viscosity

PACS

  • 82.70.Kj

    Emulsions and suspensions

  • 47.57.Bc

    Foams and emulsions

  • 47.65.-d

    Magnetohydrodynamics and electrohydrodynamics

  • 77.84.Nh

    Liquids, emulsions, and suspensions; liquid crystals

  • 68.03.Cd

    Surface tension and related phenomena

  • 47.55.nb

    Capillary and thermocapillary flows

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3493636

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    M. S. Alexander, “Pulsating electrospray modes at the liquid-liquid interface,” Appl. Phys. Lett. 92, 144102 (2008)APPLAB000092000014144102000001.

    C. Larriba-Andaluz and J. Fernández de la Mora, “Electrospraying insulating liquids via charged nanodrop injection from the Taylor cone of an ionic liquid,” Phys. Fluids 22, 072002 (2010)PHFLE6000022000007072002000001.

    V. R. Gundabala, N. Vilanova, and A. Fernández-Nieves, Phys. Rev. Lett. 105, 154503 (2010).

    J. J. Feng, “The stretching of an electrified non-Newtonian jet: A model for electrospinning,” Phys. Fluids 14, 3912 (2002)PHFLE6000014000011003912000001.

    F. J. Higuera, “Charge separation in the conical meniscus of an electrospray of a very polar liquid: Its effect on the minimum flow rate,” Phys. Fluids 21, 032104 (2009)PHFLE6000021000003032104000001.

    M. M. Hohman, M. Shin, G. Rutledge, and M. P. Brenner, “Electrospinning and electrically forced jets. II. Applications,” Phys. Fluids 13, 2221 (2001)PHFLE6000013000008002221000001.


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