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Volume-Charged Cones on a Liquid Interface in an Electric Field

  • Condensed Matter
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Abstract

In this study, we explore a novel type of slender conical liquid meniscus arisen in high electric field, which carries surface charge and net bulk charge of opposite sign. Stability of such dissipative structure is ensured by the balance between capillary and electrostatic forces and competition between the surface and bulk electric currents. The bulk charge is governed by the applied voltage being generated by the electric field of the cone due to dissociation/associations reactions at its apex. The effect of the physical parameters of the liquid on the microcone structure is elucidated. It is shown that the cone angle cannot exceed a critical value, which is a function of dielectric permittivity of the liquid. The electric current through the cone is found to be proportional to the square of the applied voltage. The obtained results can be applied for analysis of atomization processes of various liquids.

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References

  1. J. Zeleny, J. Phys. Rev. 10, 1 (1917).

    Article  ADS  Google Scholar 

  2. G. I. Taylor, Proc. R. Soc. London, Ser. A 280, 383 (1964).

    Article  ADS  Google Scholar 

  3. J. Fernández de la Mora, Ann. Rev. Fluid Mech. 39, 217 (2007).

    Article  ADS  Google Scholar 

  4. H.-H. Kim, J.-H. Kim, and A. Ogata, J. Aerosol Sci. 42, 249 (2011).

    Article  ADS  Google Scholar 

  5. D. H. Reneker, A. L. Yarin, E. Zussman, and H. Xu, Adv. Appl. Mech. 41, 43 (2007).

    Article  Google Scholar 

  6. J. Xie, J. Jiang, P. Davoodi, M. P. Srinivasan, and C.-H. Wang, Chem. Eng. Sci. 125, 32 (2015).

    Article  Google Scholar 

  7. N. Kirichenko, I. V. Petryanov-Sokolov, N. N. Suprun, and A. A. Shutov, Sov. Phys. Dokl. 31, 611 (1986).

    ADS  Google Scholar 

  8. A. M. Gañán-Calvo, Phys. Rev. Lett. 79, 217 (1997).

    Article  ADS  Google Scholar 

  9. F. J. Higuera, J. Fluid Mech. 484, 303 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  10. J. J. Feng, Phys. Fluids 14, 3912 (2002).

    Article  ADS  Google Scholar 

  11. R. T. Collins, J. J. Jones, M. T. Harris, and O. A. Basaran, Nat. Phys. 4, 149 (2008).

    Article  Google Scholar 

  12. S. N. Reznik and E. Zussmann, Phys. Rev. E 81, 026313 (2010).

    Article  ADS  Google Scholar 

  13. A. Ramos and A. Castellanos, Phys. Lett. A 184, 268 (1994).

    Article  ADS  Google Scholar 

  14. H. Li, T. C. Halsey, and A. Lobkovsky, Europhys. Lett. 27, 575 (1994).

    Article  ADS  Google Scholar 

  15. A. V. Subbotin, JETP Lett. 100, 657 (2014).

    Article  ADS  Google Scholar 

  16. A. V. Subbotin and A. N. Semenov, Proc. R. Soc. London, Ser. A 471, 20150290 (2015).

    Article  ADS  Google Scholar 

  17. A. V. Subbotin and A. N. Semenov, JETP Lett. 102, 815 (2015).

    Article  ADS  Google Scholar 

  18. L. M. Martyushev and V. D. Seleznev, Phys. Rep. 426, 1 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  19. K. Tang and A. Gomez, J. Colloid Interface Sci. 175, 326 (1995).

    Article  ADS  Google Scholar 

  20. A. Jaworek, A. T. Sobczyk, T. Czech, and A. Krupa, J. Electrostat. 72, 166 (2014).

    Article  Google Scholar 

  21. A. I. Zhakin and P. A. Belov, Surf. Eng. Appl. Electrochem. 49, 141 (2013).

    Article  Google Scholar 

  22. J. Fernández de la Mora and I. G. Loscertales, J. Fluid Mech. 260, 155 (1994).

    Article  ADS  Google Scholar 

  23. D. A. Saville, Ann. Rev. Fluid Mech. 29, 27 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Subbotin, R. Stepanyan, A. Chiche, J. J. M. Slot, and G. ten Brinke, Phys. Fluids 25, 103101 (2013).

    Article  ADS  Google Scholar 

  25. N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford, London, 1940).

    MATH  Google Scholar 

  26. F. W. Peek, Dielectric Phenomena in High Voltage Engineering (McGraw-Hill, New York, 1920).

    Google Scholar 

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Subbotin, A.V., Semenov, A.N. Volume-Charged Cones on a Liquid Interface in an Electric Field. Jetp Lett. 107, 186–191 (2018). https://doi.org/10.1134/S0021364018030025

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  • DOI: https://doi.org/10.1134/S0021364018030025

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