Skip to main content
SpringerLink
Log in

The effect of normal electric field on the evolution of immiscible Rayleigh-Taylor instability

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

Manipulation of the Rayleigh-Taylor instability using an external electric field has been the subject of many studies. However, most of these studies are focused on early stages of the evolution. In this work, the long-term evolution of the instability is investigated, focusing on the forces acting on the interface between the two fluids. To this end, numerical simulations are carried out at various electric permittivity and conductivity ratios as well as electric field intensities using Smoothed Particle Hydrodynamics method. The electric field is applied in parallel to gravity to maintain unstable evolution. The results show that increasing top-to-bottom permittivity ratio increases the rising velocity of the bubble while hindering the spike descent. The opposite trend is observed for increasing top-to-bottom conductivity ratio. These effects are amplified at larger electric field intensities, resulting in narrower structures as the response to the excitation is non-uniform along the interface.

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. Taylor, G.: Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field. Proc. R. Soc. Lon. Ser. A 291(1425), 159–166 (1966). doi:10.1098/rspa.1966.0086

    Article  Google Scholar 

  2. Melcher, J.R., Schwarz, W.J.: Interfacial relaxation overstability in a tangential electric field. Phys. Fluids 11(12), 2604–2616 (1968). doi:10.1063/1.1691866

    Article  Google Scholar 

  3. Melcher, J.R., Taylor, G.I.: Electrohydrodynamics: a review of role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111–146 (1969). doi:10.1146/annurev.fl.01.010169.000551

    Article  Google Scholar 

  4. Saville, D.A.: Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64 (1997). doi:10.1146/annurev.fluid.29.1.27

    Article  MathSciNet  Google Scholar 

  5. Chen, X.P., Jia, L.B., Yin, X.Z., Cheng, J.S., Lu, J.: Spraying modes in coaxial jet electrospray with outer driving liquid. Phys. Fluids 17(3), 032101 (2005). doi:10.1063/1.1850691

    Article  MATH  Google Scholar 

  6. Higuera, F.J.: Stationary coaxial electrified jet of a dielectric liquid surrounded by a conductive liquid. Phys. Fluids 19(1), 012102 (2007). doi:10.1063/1.2431188

    Article  MATH  Google Scholar 

  7. Li, G., Luo, X., Si, T., Xu, R.X.: Temporal instability of coflowing liquid-gas jets under an electric field. Phys. Fluids 26(5), 054101 (2014). doi:10.1063/1.4875109

    Article  Google Scholar 

  8. Higuera, F.J.: Electrodispersion of a liquid of finite electrical conductivity in an immiscible dielectric liquid. Phys. Fluids 22(11), 112107 (2010). doi:10.1063/1.3493636

    Article  Google Scholar 

  9. Oddy, M.H., Santiago, J.G., Mikkelsen, J.C.: Electrokinetic instability micromixing. Anal. Chem. 73(24), 5822–5832 (2001). doi:10.1021/ac0155411

    Article  Google Scholar 

  10. El Moctar, A.O., Aubry, N., Batton, J.: Electro-hydrodynamic micro-fluidic mixer. Lab Chip 3(4), 273–280 (2003). doi:10.1039/b306868b

    Article  Google Scholar 

  11. Cimpeanu, R., Papageorgiou, D.T., Petropoulos, P.G.: On the control and suppression of the Rayleigh-Taylor instability using electric fields. Phys. Fluids 26(2), 022105 (2014). doi:10.1063/1.4865674

    Article  MATH  Google Scholar 

  12. Warner, M.R.E., Craster, R.V., Matar, O.K.: Pattern formation in thin liquid films with charged surfactants. J. Colloid Interface Sci. 268(2), 448–463 (2003). doi:10.1016/j.jcis.2003.08.013

    Article  Google Scholar 

  13. Craster, R.V., Matar, O.K.: Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17(3), 032104 (2005). doi:10.1063/1.1852459

    Article  MathSciNet  MATH  Google Scholar 

  14. Pease, L.F., Russel, W.B.: Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: a generalized linear stability analysis. J. Chem. Phys. 118(8), 3790–3803 (2003). doi:10.1063/1.1529686

    Article  Google Scholar 

  15. Shankar, V., Sharma, A.: Instability of the interface between thin fluid films subjected to electric fields. J. Colloid Interface Sci. 274(1), 294–308 (2004). doi:10.1016/j.jcis.2003.12.024

    Article  Google Scholar 

  16. Tilley, B.S., Petropoulos, P.G., Papageorgiou, D.T.: Dynamics and rupture of planar electrified liquid sheets. Phys. Fluids 13(12), 3547–3563 (2001). doi:10.1063/1.1416193

    Article  MATH  Google Scholar 

  17. Papageorgiou, D.T., Vanden-Broeck, J.M.: Large-amplitude capillary waves in electrified fluid sheets. J. Fluid Mech. 508, 71–88 (2004). doi:10.1017/S0022112004008997

    Article  MathSciNet  MATH  Google Scholar 

  18. Uguz, A.K., Aubry, N.: Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields. Phys. Fluids 20(9), 092103 (2008). doi:10.1063/1.2976137

    Article  MATH  Google Scholar 

  19. Rayleigh, L.: Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc s1–14(1), 170–177 (1882). doi:10.1112/plms/s1-14.1.170

    Article  MathSciNet  MATH  Google Scholar 

  20. Taylor, G.: The instability of liquid surfaces when accelerated in a direction perpendicular to their planes I. Proc. R. Soc. Lond. Ser. A 201(1065), 192–196 (1950). doi:10.1098/rspa.1950.0052

    Article  MathSciNet  MATH  Google Scholar 

  21. Mohamed, A.E.M.A., Shehawey, E.S.F.E.: Nonlinear electrohydrodynamic Rayleigh-Taylor instability. Part 1. A perpendicular field in the absence of surface charges. J. Fluid Mech. 129, 473–494 (1983). doi:10.1017/S0022112083000877

    Article  MathSciNet  MATH  Google Scholar 

  22. Mohamed, A.E.M.A., El Shehawey, E.S.F.: Nonlinear electrohydrodynamic Rayleigh-Taylor instability. II. A perpendicular field producing surface charge. Phys. Fluid 26(7), 1724–1730 (1983). doi:10.1063/1.864371

    Article  MathSciNet  MATH  Google Scholar 

  23. Eldabe, N.T.: Effect of a tangential electric-field on Rayleigh-Taylor instability. J. Phys. Soc. Jpn. 58(1), 115–120 (1989). doi:10.1143/JPSJ.58.115

    Article  Google Scholar 

  24. Joshi, A., Radhakrishna, M.C., Rudraiah, N.: Rayleigh-Taylor instability in dielectric fluids. Phys. Fluids 22(6), 064102 (2010). doi:10.1063/1.3435342

    Article  MATH  Google Scholar 

  25. Barannyk, L.L., Papageorgiou, D.T., Petropoulos, P.G.: Suppression of Rayleigh-Taylor instability using electric fields. Math. Comput. Simul 82(6,SI), 1008–1016 (2012). doi:10.1016/j.matcom.2010.11.015

    Article  MathSciNet  MATH  Google Scholar 

  26. Pease, L.F., Russel, W.B.: Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newton. Fluid Mech 102(2, SI), 233–250 (2002). doi:10.1016/S0377-0257(01)00180-X

    Article  MATH  Google Scholar 

  27. Thaokar, R.M., Kumaran, V.: Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17(8), 084104 (2005). doi:10.1063/.1.979522

    Article  MATH  Google Scholar 

  28. Hua, J., Lim, L.K., Wang, C.H.: Numerical simulation of deformation/motion of a drop suspended in viscous liquids under influence of steady electric fields. Phys. Fluids 20(11), 113302 (2008). doi:10.1063/1.3021065

    Article  MATH  Google Scholar 

  29. Shadloo, M.S., Rahmat, A., Yildiz, M.: A smoothed particle hydrodynamics study on the electrohydrodynamic deformation of a droplet suspended in a neutrally buoyant Newtonian fluid. Comput. Mech. 52, 693–707 (2013). doi:10.1007/s00466-013-0841-z

    Article  MathSciNet  MATH  Google Scholar 

  30. Tofighi, N., Yildiz, M.: Numerical simulation of single droplet dynamics in three-phase flows using ISPH. Comput. Math. Appl. 66(4), 525–536 (2013). doi:10.1016/j.camwa.2013.05.012

    Article  MathSciNet  Google Scholar 

  31. Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface-tension. J. Comput. Phys. 100(2), 335–354 (1992). doi:10.1016/0021-9991(92)90240-Y

    Article  MathSciNet  MATH  Google Scholar 

  32. Tomar, G., Gerlach, D., Biswas, G., Alleborn, N., Sharma, A., Durst, F., Welch, S.W.J., Delgado, A.: Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. J. Comput. Phys. 227(2), 1267–1285 (2007). doi:10.1016/j.jcp.2007.09.003

    Article  MathSciNet  MATH  Google Scholar 

  33. Melcher, J.R., Smith, C.V.: Electrohydrodynamic charge relaxation and interfacial perpendicular-field instability. Phys. Fluids 12(4), 778–790 (1969). doi:10.1063/1.1692556

    Article  Google Scholar 

  34. Dopazo, C., Lozano, A., Barreras, F.: Vorticity constraints on a fluid/fluid interface. Phys. Fluids 12(8), 1928–1931 (2000). doi:10.1063/1.870441

    Article  MathSciNet  MATH  Google Scholar 

  35. Wu, J.Z.: A theory of three-dimensional interfacial vorticity dynamics. Phys. Fluids 7(10), 2375–2395 (1995). doi:10.1063/1.868750

    Article  MathSciNet  MATH  Google Scholar 

  36. IEEE Trans. Dielectr. Electr. Insul. Recommended international standard for dimensionless parameters used in electrohydrodynamics. 10(1), 3–6 (2003). doi:10.1109/TDEI.2003.1176545

  37. Shadloo, M.S., Zainali, A., Yildiz, M.: Simulation of single mode Rayleigh-Taylor instability by SPH method. Comput. Mech. 51(5), 699–715 (2013). doi:10.1007/s00466-012-0746-2

    Article  MathSciNet  MATH  Google Scholar 

  38. Zainali, A., Tofighi, N., Shadloo, M.S., Yildiz, M.: Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method. Comput. Methods Appl. Mech. Eng. 254, 99–113 (2013). doi:10.1016/j.cma.2012.10.005

    Article  MathSciNet  MATH  Google Scholar 

  39. Yildiz, M., Rook, R.A., Suleman, A.: SPH with the multiple boundary tangent method. Int. J. Numer. Methods Eng. 77(10), 1416–1438 (2009). doi:10.1002/nme.2458

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences (FENS), Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey

    Nima Tofighi, Murat Ozbulut & Mehmet Yildiz

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    James J. Feng

  3. Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, V6T 1Z3, Canada

    James J. Feng

Authors
  1. Nima Tofighi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Murat Ozbulut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James J. Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mehmet Yildiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehmet Yildiz.

Additional information

Communicated by Oleg Zikanov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tofighi, N., Ozbulut, M., Feng, J.J. et al. The effect of normal electric field on the evolution of immiscible Rayleigh-Taylor instability. Theor. Comput. Fluid Dyn. 30, 469–483 (2016). https://doi.org/10.1007/s00162-016-0390-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-016-0390-0

Keywords

Search

Navigation