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Pramana

, 92:22 | Cite as

Instability analysis of a streaming electrified cylindrical sheet through porous media

  • G M Moatimid
  • Y O El-Dib
  • M H ZekryEmail author
Article
  • 19 Downloads

Abstract

The current study deals with the influence of a uniform electric field on a cylindrical streaming sheet. This paper investigates a few representatives of porous media. These media are considered to be uniform, homogeneous and isotropic. The analysis is based on viscous potential theory, which assumes that the viscous forces affect only the interface between the fluids. The mathematical treatment is based on the normal modes analysis. For convenience, cylindrical coordinates are used. The boundary-value problem yields coupled second-order and damped differential equations with complex coefficients. These equations are combined with a single equation under the concepts of the symmetric and antisymmetric deformations. The Routh–Hurwitz criterion is adopted to govern the stability of the system. Several special cases are recovered upon appropriate data choices. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through some sets of figures. These parameters are the Darcy’s coefficients, basic velocities, dielectric constants, viscosity and thickness of the inner cylinder. We have found that the thickness of the inner cylinder plays a dual role on the stability picture. Also, the Darcy’s coefficient and dielectric constants have stabilising influence and the dynamic viscosity has a destabilising effect.

Keywords

Linear jets instability electric field porous media viscous potential flow 

PACS Nos

68.05.Cf 47.20.−k 47.56.+r 

References

  1. 1.
    J Eggers and E Villermaux, Rep. Prog. Phys. 71, 036601 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    G Amini, Y Lv, A Dolatabadi and M Ihme, Phys. Fluids 26, 114105 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    S Chandrasekhar, Hydrodynamic and hydromagnetic stability (Clarendon Press, Oxford, 1961)zbMATHGoogle Scholar
  4. 4.
    A R Seadawy and K El-Rashidy, Pramana – J. Phys. 87: 20 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    C H Chen, Electrokinetics and electrohydrodynamics in microsystems edited by Ramos (Springer, New York, 2011)Google Scholar
  6. 6.
    S Korkut, D A Saville and I A Akasy, Phys. Rev. Lett. 100, 034503 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    M F Elsayed, G M Moatimid, F M F Elsabaa and M F E Amer, J. Porous Media 19, 751 (2016)CrossRefGoogle Scholar
  8. 8.
    G M Moatimid, Phys. Scr. 79, 065403 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    K Vafai, Handbook of porous media 2nd edn (CRC Press, Taylor and Francis Group, Boca Raton, 2005)zbMATHGoogle Scholar
  10. 10.
    M F El-Sayed, G M Moatimid, F M F Elsabaa and M F E Amer, Atomization Sprays 26, 349 (2016)CrossRefGoogle Scholar
  11. 11.
    A E K Elcoot and G M Moatimid, Physica A 343, 15 (2004)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    G M Moatimid, Physica A 328, 525 (2003)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    D D Joseph, Int. J. Multiphase Flow 32, 285 (2006)CrossRefGoogle Scholar
  14. 14.
    G M Moatimid and M A Hassan, Math. Probl. Eng. 2013, 416562 (2013)CrossRefGoogle Scholar
  15. 15.
    G M Moatimid, M A Hassan and B E M Tantawy, J. Nat. Sci. Math. 7, 129 (2014)Google Scholar
  16. 16.
    G M Moatimid and M A Hassan, Int. J. Eng. Sci. 54, 15 (2012)CrossRefGoogle Scholar
  17. 17.
    M K Awasthi, Eur. Phys. J. Plus 129, 78 (2014)CrossRefGoogle Scholar
  18. 18.
    F Li, O Ozen, N Aubry and D T Papageorgiou, J. Fluid Mech. 583, 347 (2007)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    J R Melcher, Field coupled surface waves (MIT Press, Cambridge, MA, 1963)Google Scholar
  20. 20.
    N T El-Dabe, E F El-Shehawey, G M Moatimid and A A Mohamed, J. Math. Phys. 26, 2072 (1985)ADSCrossRefGoogle Scholar
  21. 21.
    Z Zahreddin and E F El-Shehawey, Indian J. Pure Appl. Math. 19, 963 (1988)MathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationAin Shams UniversityRoxyEgypt
  2. 2.Department of Mathematics and Computer Science, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt

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