Advertisement

Fluid Dynamics

, Volume 52, Issue 2, pp 178–188 | Cite as

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

Article

Abstract

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.

Keywords

electrohydrodynamics viscosity electric field electric current surface electric current 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. R. Melcher and G. I. Taylor, “Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses,” Ann. Rev. Fluid Mech. 1, 111 (1969).ADSCrossRefGoogle Scholar
  2. 2.
    D. A. Saville, “Electrohydrodynamics: The Taylor–Melcher Leaky Dielectric Model,” J. Fluid Mech. 29, 27 (1997).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    S. Torza, R. G. Cox, and S. G. Mason, “ElectrohydrodynamicDeformation and Burst of Liquid Drops,” Phil. Trans. Roy. Soc. London A 269 (1198), 295 (1971).ADSCrossRefGoogle Scholar
  4. 4.
    O. O. Ajayi, “A Note on Taylor’s Electrohydrodynamic Theory,” Proc. Roy. Soc. London A 364 (1719), 499 (1978).ADSCrossRefMATHGoogle Scholar
  5. 5.
    C. Sozou, “Electrohydrodynamics of a Liquid Drop: The Time-Dependent Problem,” Proc. Roy. Soc. London A 331 (1585), 263 (1972).ADSCrossRefMATHGoogle Scholar
  6. 6.
    V. Ya. Shkadov and A. A. Shutov, “Drop and Bubble Deformation in an Electric Field,” Fluid Dynamics 37 (5), 713 (2002).CrossRefMATHGoogle Scholar
  7. 7.
    A. A. Shutov, “Drop Shape in a Constant Electric Field,” Zh. Tekhn. Fiz. 72(12), 15 (2002).Google Scholar
  8. 8.
    D. I. Kvasov, “Dielectric Liquid Drop in a Harmonic Electric Field,” Fluid Dynamics 51 (2), 224 (2016).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    A. N. Tyatyushkin, “Effect of Surface Electric Currents on the Electrohydrodynamic Flow inside and outside a Spherical Drop,” Moscow State Univ., Institute of Mechanics, Report No. 5147 (2011).Google Scholar
  10. 10.
    A. N. Tyatyushkin, “Effect of Surface Electric Currents on the Electrohydrodynamic Flow inside and outside a Spherical Drop,” in: Collection of Reports of 10 International Scientific Conference ‘Topical Problems of Electrophysics and Electrohydrodynamics of Fluids’ [in Russian], Solo, St. Petersburg (2012), p. 88.Google Scholar
  11. 11.
    M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York (1964).MATHGoogle Scholar
  12. 12.
    H. Lamb, Hydrodynamics, Cambridge Univ. Press, Cambridge (1932).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations