Skip to main content
SpringerLink
Log in

On stability and spontaneous capillary disintegration of charged jets. Part II: Nonlinear analytical investigations

  • Published:
Surface Engineering and Applied Electrochemistry Aims and scope Submit manuscript

Abstract

A review of the analytical computations of the stability of capillary wave motion on the surface of charged jets of an incompressible liquid in a nonlinear approximation with a small parameter, as well as experimental studies with certain problems, is presented. The relation of the wave amplitude to the radius of the jet is considered as a small parameter. The effect of the longitudinal electrostatic field and viscosity of the liquid are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yuen, M., Non-linear capillary instability of a liquid jet, J. Fluid Mech., 1968, vol. 33,Part 1, pp. 151–163.

    Article  MATH  Google Scholar 

  2. Wang, D.P., Finite amplitude effect on the stability of a jet of circular cross-section., J. Fluid Mech., 1968, vol. 34,Part 2, pp. 299–313.

    Article  MATH  Google Scholar 

  3. Strutt, J.W., (Lord Rayleigh), On the instability of jets, Proc. London Math. Soc., 1878, vol. 10, pp. 4–13.

    Google Scholar 

  4. Nayfeh, F.H., Nonlinear stability of a liquid jet, Phys. Fluids, 1970, vol. 13, no. 4, pp. 841–847.

    Article  MATH  Google Scholar 

  5. Malik, S.K. and Singh, M., Nonlinear breakup of an electrohydrodynamic jet, Quart. Appl. Math., 1983, vol. 41, no. 3, pp. 273–287.

    MATH  MathSciNet  Google Scholar 

  6. Kant, R. and Malik, S.K., Nonlinear electrohydrodynamic instability of a jet, Quart. Appl. Math., 1986, vol. 43, no. 4, pp. 407–419.

    MATH  MathSciNet  Google Scholar 

  7. Shiryaeva, S.O., Grigor’ev, A.I., and Levchuk, T.V., Nonlinear asymptotic analysis of oscillations of nonaxisymmetric modes of the charged jet of ideal liquid, Zh. Tekh. Fiz., 2004, vol. 74, no. 8, pp. 6–14.

    Google Scholar 

  8. Grigor’ev, A.I., Shiryaeva, S.O., and Egorova, E.V., On certain peculiarities of a nonlinear resonance interaction of modes of a charged jet, Electron. Obrab. Mater., 2005, no. 1, pp. 42–50.

    Google Scholar 

  9. Shiryaeva, S.O., Voronina, N.V., and Grigor’ev, A.I., Nonlinear oscillations of a charged jet of electrocon-ducting liquid at a multimode initial deformation of its surface, Zh. Tekh. Fiz., 2006, vol. 76, no. 9, pp. 31–41.

    Google Scholar 

  10. Shiryaeva, S.O., Voronina, N.V., and Grigor’ev, A.I., On nonlinear corrections to the frequencies of the oscillation modes of a charged jet of an ideal liquid, Zh. Tekh. Fiz., 2007, vol. 77, no. 2, pp. 46–55.

    Google Scholar 

  11. Shiryaeva, S.O., Grigor’ev, A.I., and Volkova, M.V., Spontannyi kapillyarnyi raspad zaryazhennykh strui (Spontaneous Capillary Disintegration of Charged Jets), Yaroslavl: Izd. Yaroslavl Gos. Univ., 2007.

    Google Scholar 

  12. Filips, O.M., Vzaimodeistvie voln Nelineinye volny (Interaction of Waves. Nonlinear Waves), Moscow: Mir, 1977, pp. 197–220

    Google Scholar 

  13. Shutov, A.A., Formation and stability of a charged jet in a strong electric field, Izv. Russ. Akad. Nauk. Mekh. Zhidk. Gaza, 2006, no. 6, pp. 52–67.

    Google Scholar 

  14. Ganan-Calvo, A.M., On the theory of electrohydrodynamically driven capillary jets, J. Fluid Mechanics, 1997, vol. 335, pp. 165–188.

    Article  MATH  MathSciNet  Google Scholar 

  15. Turnbull, R., Self-acceleration of a charged jet, IEEE Trans. Ind. Appl., 1989, vol. 25, no. 4, pp. 699–704.

    Article  Google Scholar 

  16. Doo-Sung Lee, Nonlinear breakup of an asymmetric elecrodynamic jet, The European Phys. J., Ser B, 2003, vol. 33, pp. 487–494.

    Article  Google Scholar 

  17. Voronina, N.V., Shiryaeva, S.O., and Grigor’ev, A.I., On nonlinear corrections to the frequencies of nonaxi-symmetric modes of a volumetrically charged jet of a dielectric liquid, Zh. Tekh. Fiz., 2008, vol. 78, no. 6, pp. 1–14.

    Google Scholar 

  18. Grigor’ev, A.I., Voronina, N.V., and Shiryaeva, S.O., Nonlinear nonaxisymmetric oscillations of a volumetrically charged jet, Zh. Tekh. Fiz., 2008, vol. 78, no. 7, pp. 21–29.

    Google Scholar 

  19. Grigor’ev, A.I., Petrushov, N.A., and Shiryaeva, S.O., Nonlinear analysis of the laws for realization of the wave motion on the surface of a charged jet that moves with respect to the material medium, Izv. Russ. Akad. Nauk. Mekh. Zhidk. Gaza, 2012, no. 1, pp. 81–92.

    Google Scholar 

  20. Grigor’ev, A.I., Petrushov, N.A., Shiryaeva, S.O., and Polyantsev, N.A., Nonlinear analysis of the wave motion on the jet surface in the longitudinal electric field that moves in the dielectric medium, Zh. Tekh. Fiz., 2012, no. 8, pp. 35–41.

    Google Scholar 

  21. Grigor’ev, A.I., Voronina, N.V., and Shiryaeva, S.O., Asymptotic study of nonlinear nonaxisymmetric waves on the surface of uncharged jet in a longitudinal electrostatic field, Zh. Tekh. Fiz., 2010, vol. 80, no. 10, pp. 22–29.

    Google Scholar 

  22. Grigor’ev, A.I., Voronina, N.V., and Shiryaeva, S.O., Degenerate internal nonlinear resonance interaction of the waves on the surface of an uncharged dielectric jet in a longitudinal electrostatic field, Surf. Eng. Appl. Electrochem., 2011, vol. 47, no. 3, pp. 235–241.

    Article  Google Scholar 

  23. Grigorev, A.I. and Petrushov, N.A. Nonlinear analysis of the internal resonant interaction of nonaxisymmetric waves on the surface of a jet moving in reference to a medium in a collinear electrostatic field, Surf. Eng. Appl. Electrochem., 2012, vol. 48, no. 5, pp. 450–455.

    Article  Google Scholar 

  24. Petrushov, N.A. and Grigorev, A.I., Nonlinear resonance interaction of waves on a jet in a radial electric field., Surf. Eng. Appl. Electrochem., 2013, vol. 49, no. 6, pp. 468–473.

    Article  Google Scholar 

  25. Ganan-Calvo, A.M., Lopez-Herera, J.M., and Riesco-Chueca, P., The combination of electrospray and flow focusing., J. Fluid Mech., 2006, vol. 566, pp. 421–445.

    Article  MATH  Google Scholar 

  26. Markova, M.P., and Shkadov, V.Ya., On a nonlinear development of capillary waves in a jet of liquid, Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, 1972, no. 3, pp. 30–37.

    Google Scholar 

  27. Novikov, A.A., Nonlinear capillary waves on the surface of a jet of viscous liquid, Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, 1977, no. 2, pp. 179–182.

    Google Scholar 

  28. Levich, V.G., Fiziko-khimicheskaya gidrodinamika (Physicochemical Hydrodynamics), Moscow: Fizmatgiz, 1950.

    Google Scholar 

  29. Feng, J.J., Stretching of a straight electrically charged viscoelastics jet, J. Non-Newtonian Fluid Mechanics, 2003, vol. 116, pp. 55–70.

    Article  MATH  Google Scholar 

  30. Cloupeau, M. and Prunet Foch B., Electrostatic spraying of liquids: Main functioning modes, J. Electrostatics, 1990, vol. 25, pp. 165–184.

    Article  Google Scholar 

  31. Jaworek, A. and Krupa, A., Classification of the modes of EHD spraying. J. Aerosol Sci., 1999, vol. 30, no. 7, pp. 873–893.

    Article  Google Scholar 

  32. Lopez-Herera, J.M., Riesco-Chueca, P., and Ganan-Calvo, A.M., Linear stability analysis of axisymmetric perturbations in imperfectly conducting liquid jets, Phys. Fluids, 2005, vol. 17(034106), pp. 1–22.

    Google Scholar 

  33. Shiryaeva, S.O., On modification of the theory of a boundary layer for the calculation of the wave motions in a cylindrical jet of a viscous liquid, Zh. Tekh. Fiz., 2008, vol. 78, no. 12, pp. 12–20.

    Google Scholar 

  34. Shiryaeva, S.O., Analytical asymptotic solution of the problem on the nonlinear oscillations of a thick charged jet of a viscous liquid, Izv. Russ. Akad. Nauk. Mekh. Zhidk. Gaza, 2008, no. 5, pp. 14–29.

    Google Scholar 

  35. Shiryaeva, S.O. and Grigor’ev, A.I., An experiment of semiphenomenologic classification of the observed modes of electrostatic dispersion of a liquid, Zh. Tekh. Fiz., 1994, vol. 64, no. 3, pp. 13–25.

    Google Scholar 

  36. Buraev, T.K., Vereshchagin, I.P., and Pashin, N.M., Investigation into the process of the dispersion of liquids in an electrostatic field, Energiya, 1979, no. 3, pp. 87–105.

    Google Scholar 

  37. Drozin, V.G., The electrical dispersion of liquids as aerosols, J. Coll. Sci., 1955, vol. 10, no. 1, pp. 158–164.

    Article  Google Scholar 

  38. Carson, H.S. and Hendrics, C.D., Natural pulsations in electrical spraying of liquids, J. Coll. Sci., 1965, vol. 6, pp. 1072–1075.

    Google Scholar 

  39. Kozhenkov, V.I., Kirsh, A.A., and Fuks, N.A., Study of the process of formation of monodisperse aerosols during electrostatic dispersion, KZh, 1974, vol. 36, no. 6, pp. 1168–1171.

    Google Scholar 

  40. Hendrics, C.D., Carson, H.S., Hogan, J.J., and Schneider J.M., Photomicrography of electrically sprayed heavy particles, AIAA J., 1964, vol. 2, no. 4, pp. 733–737.

    Article  Google Scholar 

  41. Hayati, I., Bailey, A.I., and Tadros, Th.F., Investigations into the mechanisms of electrohydrodynamic spraying of liquids. I. Effect of electric field and the environment on pendant drops and factors affecting the formation of stable jet and atomization, J. Coll. Int. Sci., 1987, vol. 117, no. 1, pp. 205–221.

    Article  Google Scholar 

  42. Hayati, I., Bailey, A.I., and Tadros, Th. F., Investigations into the mechanisms of electrohydrodynamic spraying of liquids. II. Mechanism of stable jet formation and electrical forces acting on a liquid cone, J. Coll. Int. Sci., 1987, vol. 117, no. 1, pp. 222–230.

    Article  Google Scholar 

  43. Popov, S.I. and Petryanov, I.V., On the mechanism of electrostatic dispersion of liquids, Dokl. Akad. Nayk SSSR, 1970, vol. 195, no. 4, pp. 893–895.

    Google Scholar 

  44. Fernandes de la Mora, J. and Loscertales, I.G., The current emitted by highly conducting Taylor cones, J. Fluid Mech., 1994, vol. 260, pp. 155–184.

    Article  Google Scholar 

  45. Marginean, I., Parvin, L., Hefferman, L., and Vertes, A., Flexing the electrified meniscus: The birth of a jet in electrosprays, Anal. Chem., 2004, vol. 76, pp. 4202–4207.

    Article  Google Scholar 

  46. Ganan-Calvo, A.M., Lopez-Herera, J.M., P. Riesco-Chuera, The combination of electrospray and flow focusing, J. Fluid Mech., 2006, vol. 566, pp. 421–445.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, 150000, Russia

    S. O. Shiryaeva & A. I. Grigor’ev

Authors
  1. S. O. Shiryaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Grigor’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. O. Shiryaeva.

Additional information

Original Russian Text © S.O. Shiryaeva, A.I. Grigor’ev, 2014, published in Elektronnaya Obrabotka Materialov, 2014, No. 5, pp. 35–44.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shiryaeva, S.O., Grigor’ev, A.I. On stability and spontaneous capillary disintegration of charged jets. Part II: Nonlinear analytical investigations. Surf. Engin. Appl.Electrochem. 50, 405–413 (2014). https://doi.org/10.3103/S106837551405010X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S106837551405010X

Keywords

Search

Navigation