Skip to main content

Advertisement

SpringerLink
Log in

Electric-permittivity-based instability of two dielectric miscible liquids under DC field

  • Regular Article - Flowing Matter
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

This paper considers the mixing of two dielectric miscible viscous liquids with different electric permittivities bounded by solid walls in an external electric field normal to the interface of the liquids. The mutual diffusion of these two liquids leads to the formation of an unsteady self-similar 1D diffusion layer. This layer is found to be unstable to the perturbations of the interface. A special sophisticated mathematical approach in self-similar variables is developed to estimate its stability. The results of a linear stability theory are verified by direct numerical simulations of the full nonlinear problem. A mixing efficiency based on the separation amplitude and an optimal electric field strength to achieve the fastest mixing are proposed in the present study.

Graphical abstract

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. S.R. Deshmukh, D.G. Vlachos, AIChE J. 51, 3193 (2005)

    Article  Google Scholar 

  2. J.S.H. Lee, D. Li, Microfluid. Nanofluid. 2, 361 (2006)

    Article  Google Scholar 

  3. Y. Gao, T.N. Wong, C. Yang, K.T. Ooi, Colloids Surfaces Physicochem. Eng. Asp. 266, 117 (2005)

    Article  Google Scholar 

  4. Y. Gao, T.N. Wong, C. Yang, K.T. Ooi, J. Colloids Interface Sci. 284, 306 (2005)

    Article  ADS  Google Scholar 

  5. C.J. Campbell, B.A. Grzybowski, Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 362, 1069 (2004)

  6. L. Haiwang, T.N. Wong, N.-T. Nguyen, Int. J. Heat Mass Tran 53, 772 (2010)

    Article  Google Scholar 

  7. V.M. Ugaz, R.D. Elms, R.C. Lo, F.A. Shaikh, M.A. Burns, Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 362, 1105 (2004)

  8. T.M. Squires, M.Z. Bazant, Induced-charge electro-osmosis. J. Fluid Mech. 509, 217 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. D.L. Zhang, S. Liu, M. Puerto, C.A. Miller, G.J. Hirasaki, J. Petrol. Sci. Eng. 52, 213 (2006)

    Article  Google Scholar 

  10. S.K. Griffiths, R.H. Nilson, Anal. Chem. 78, 8134 (2006)

    Article  Google Scholar 

  11. A. Bandopadhyaya, S. Hardt, Phys. Fluids 29, 124101 (2017)

    Article  ADS  Google Scholar 

  12. J.-L. Chen, W.-H. Shih, W.-H. Hsieh, Sens. Actuators B Chem. 188, 11–21 (2013)

    Article  Google Scholar 

  13. G. Orsi, M. Roudgar, E. Brunazzi, C. Galletti, R. Mauri, Chem. Eng. Sci. 95, 174–183 (2013)

    Article  Google Scholar 

  14. Ch.Y. Lim, YCh. Lam, Microfluid. Nanofluid. 12, 127–141 (2012)

    Article  Google Scholar 

  15. H. Sugioka, Phys. Rev. E 81, 036306 (2010)

    Article  ADS  Google Scholar 

  16. H. Lin, B.D. Storey, M.H. Oddy, C.-H. Chen, J.G. Santiago, Phys. Fluids 16(6), 301–311 (2004)

    Article  Google Scholar 

  17. C. Chen, H. Lin, S. Lele, J. Santiago, J. Fluid Mech. 524, 263–303 (2005)

    Article  ADS  Google Scholar 

  18. B.D. Storey, B.S. Tilley, H. Lin, J.G. Santiago, Phys. Fluids 17, 018103 (2005)

    Article  ADS  Google Scholar 

  19. J.D. Posner, J.G. Santiago, J. Fluid Mech. 555, 1–42 (2006)

    Article  ADS  Google Scholar 

  20. J.D. Posner, C.L. Perez, J. G. Santiago, PNAS Early Edition (2012), pp. 1–4

  21. Y. Suh, S. Kang, Micromachines 1, 82–111 (2010)

    Article  Google Scholar 

  22. A. Nigam, E.B. Nauman, Trans. IChemE Part A Chem. Eng. Res. Design 83(A7), 777–781 (2005)

    Article  Google Scholar 

  23. E.B. Nauman, A. Nigam, Trans. IChemE 85(A5), 612–615 (2007)

    Article  Google Scholar 

  24. D. Bothe, C. Stemich, H.-J. Warnecke, Chem. Eng. Sci. 61, 2950–2958 (2006)

    Article  Google Scholar 

  25. F. Zoueshtiagh, S. Amiroudine, R. Narayanan, J. Fluid Mech. 628, 43–55 (2009)

    Article  ADS  Google Scholar 

  26. S. Amiroudine, F. Zoueshtiagh, R. Narayanan, Phys. Rev. E 85, 016326 (2012)

    Article  ADS  Google Scholar 

  27. S.V. Diwakar, F. Zoueshtiagh, S. Amiroudine, R. Narayanan, Phys. Fluids 27, 084111 (2015)

    Article  ADS  Google Scholar 

  28. J.F. Hoburg, J.R. Melcher, Phys. Fluids 20, 903 (1977)

    Article  ADS  Google Scholar 

  29. J.R. Melcher, G.I. Taylor, Ann. Rev. Fluids 1, 111 (1969)

    Article  ADS  Google Scholar 

  30. J.R. Melcher, Continuum Electromechanics (MIT Press, Cambridge, 1981)

    Google Scholar 

  31. D.A. Saville, Annu. Rev. Fluid Mech. 29, 401–426 (1997)

    Article  MathSciNet  Google Scholar 

  32. J.C. Baygents, F. Baldessari, Phys. Fluids 10, 301–311 (1998)

    Article  ADS  Google Scholar 

  33. M.H. Oddy, J.G. Santiago, J.C. Mikkelsen, Anal. Chem. 73, 5822–5832 (2001)

    Article  Google Scholar 

  34. S. Di Fraia, N. Massarotti, P. Nithiarasu, Modelling electro-osmotic flow in porous media: a review. Int. J. Numer. Methods Heat Fluid Flow 28, 472–497 (2018)

    Article  Google Scholar 

  35. I. Rubinstein, B. Zaltzman, Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 62, 2238–2251 (2000)

    Article  ADS  Google Scholar 

  36. W. Liu, Y. Zhou, P. Shi, Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws. Phys. Rev. E 101, 043105 (2020)

    Article  ADS  Google Scholar 

  37. P. Shi, W. Liu, Length-dependent instability of shear electroconvective flow: from electroconvective instability to Rayleigh–Bénard instability. J. Appl. Phys. 124, 204304 (2018)

    Article  ADS  Google Scholar 

  38. J.F. Hoburg, J.R. Melcher, Electrohydrodynamic mixing and instability induced by co-linear fields and conductivity gradients. Phys. Fluids 20, 903–911 (1977)

    Article  ADS  MATH  Google Scholar 

  39. M. Jalaal, B. Khorshidi, E. Esmaeilzadeh, Electrohydrodynamic (EHD) mixing of two miscible dielectric liquids. Chem. Eng. J. 219, 118–123 (2013)

    Article  Google Scholar 

  40. M.-H. Chang, A.-C. Ruo, F. Chen, J. Fluid Mech. 634, 191 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  41. S. Sharan, P. Gupta, S.S. Bahga, Phys. Rev. E 95, 023103 (2017)

    Article  ADS  Google Scholar 

  42. C.C. Lin, The Theory of Hydrodynamic Instability (Cambridge University Press, Cambrige, 1967)

    Google Scholar 

  43. P.G. Drazin, W.H. Reid, Hydrodynamic Stability, 2nd edn. (Cambridge Mathematical Library, Cambridge, 2004)

    Book  MATH  Google Scholar 

  44. Y.M. Shtemler, Dokl. Phys. 16(4), 601–605 (1979)

    Google Scholar 

  45. A. Kheniene, A. Vorobev, Phys. Rev. E 88, 022404 (2013)

    Article  ADS  Google Scholar 

  46. E.A. Demekhin, S.V. Polyanskikh, Y.M. Shtemler, e-print arXiv: 1001.4502

  47. E.A. Demekhin, V.S. Shelistov, S.V. Polyanskikh, Phys. Rev. E 84, 036318 (2011)

    Article  ADS  Google Scholar 

  48. M.C. Cross, P.G. Hohenberg, Rev. Mod. Phys. 65(3), 851 (1993)

    Article  ADS  Google Scholar 

  49. E.A. Demekhin, N.V. Nikitin, V.S. Shelistov, Phys. Fluids 25, 122001 (2013)

    Article  ADS  Google Scholar 

  50. N. Nikitin, Int. J. Numer. Methods Fluids 51, 221–233 (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The investigation of the self-similar solution and its linear stability analysis were supported by the Russian Science Foundation, project N 20-79-00044, and the direct numerical simulation was supported by “Projets de Recherche Conjoints” (PRCCNRS). The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

Author information

Authors and Affiliations

  1. Institute of Mechanics and Engineering (I2M) CNRS, University of Bordeaux, 33400, Talence, France

    S. Amiroudine

  2. Department of Mathematics and Computer Science, Financial University, Krasnodar, Russian Federation, 350051

    E. A. Demekhin

  3. Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, Krasnodar, Russian Federation, 350051

    E. A. Demekhin, V. S. Shelistov & G. S. Ganchenko

  4. Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, Moscow, Russian Federation, 119192

    E. A. Demekhin

Authors
  1. S. Amiroudine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Demekhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. S. Shelistov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. S. Ganchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Amiroudine.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amiroudine, S., Demekhin, E.A., Shelistov, V.S. et al. Electric-permittivity-based instability of two dielectric miscible liquids under DC field. Eur. Phys. J. E 45, 1 (2022). https://doi.org/10.1140/epje/s10189-021-00157-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/s10189-021-00157-z

Search

Navigation