Il Nuovo Cimento D

, Volume 8, Issue 2, pp 177–192 | Cite as

Electrohydrodynamic stability of a fluid layer. Effect of a tangential periodic field

  • Abou El Magd A. Mohamed
  • El Sayed F. El hehawey
  • Yusry O. El Dib


The electrohydrodynamic stability of a fluid layer influenced by a periodic tangential electric field is studied. The model allows for general forms of deformations of the interface. Two simultaneous ordinary differential equations of Mathieu type are obtained. The coupled equations are solved by the method of multiple-scale perturbations for small electric-field amplitude and stability conditions are discussed. It is found that the tangential field has a stabilizing effect except at resonance points. Graphs are drawn to illustrate the resonance regions in a parameter space. The tangential periodic field cannot stabilize a system which is unstable under a constant electric field.

PACS. 68.10

Fluid surfaces and fluid-fluid interfaces 


Si studia la stabilità elettrodinamica di una strato fluido influenzato da un campo elettrico tangente periodico. II modello tien conto delle forme generali di deformazioni dell’interfaccia. Si ottengono due equazioni simultanee differenziali ordinarie del tipo di Mathieu. Le equazioni accoppiate sono risolte col metodo delle perturbazioni su scala multipla per piccola ampiezza di campo, elettrico e si dicutono le condizioni di stabilità. Si è trovato che il campo tangente, ha un effetto stabilizzante eccetto nei punti di risonanza. I grafici sono fatti per illustrare le regioni di risonanza in uno spazio di parametri. Il campo periodico tangente non può stabilizzare un, sistema che è instabile in un campo elettrico costante.


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  1. (1).
    B. U. Flederhof:J. Chem. Phys.,49, 44 (1968).CrossRefADSGoogle Scholar
  2. (2).
    H. Wendel, D. Gallez andP. M. Bisch:J. Colloid Interface Sci.,84, 1 (1981).CrossRefGoogle Scholar
  3. (3).
    D. Gallez, P. M. Bish andH. Wendel:J. Colloid Interface Sci.,92, 121 (1983).CrossRefGoogle Scholar
  4. (4).
    D. H. Michael andM. E. O’Neil:J. Fluid Mech.,41, 571 (1970).MATHCrossRefADSGoogle Scholar
  5. (5).
    D. J. Wollkind andJ. I. D. Alexander:Math. Modeling,2, 319 (1981).MATHCrossRefGoogle Scholar
  6. (6).
    C. Moldarelli andR. K. Jain:J. Colloid Interface Sci.,90, 233 (1982).CrossRefGoogle Scholar
  7. (7).
    E. F. El Shehawey, Y. O. Dib andA. A. Mohamed:Nuovo Cimento D,6, 291 (1985).ADSGoogle Scholar
  8. (8).
    B. J. Hoskins:Baroclinic instability, inRotating Fluids in Geophysics, edited byP. H. Roberts andA. M. Soward (Academic Press, New York, N. Y., 1978).Google Scholar
  9. (9).
    H. Berg:Stud. Biophys. J.,90, 169 (1982).Google Scholar
  10. (10).
    A. A. Mohamed andN. K. Nayyar:Nuovo Cimento B,16, 286 (1973).CrossRefADSGoogle Scholar
  11. (11).
    U. Zimmerman:Biochim. Biophys. Acta,694, 227 (1982).Google Scholar
  12. (12).
    A. A. Mohamed andN. T. Dl Dabe:Proc. Math. Phys. Soc. Egypt,45, 53 (1978).MATHGoogle Scholar
  13. (13).
    N. T. El Dabe, E. F. El Shehawey, G. M. Moatimid andA. A. Mohamed:J. Math. Phys. (N. Y.),26, 2072 (1985).CrossRefADSGoogle Scholar
  14. (14).
    J. R. Melcher:Field Coupled Surface Waves (M.I.T. Press, Cambridge, Mass., 1963).Google Scholar
  15. (15).
    N. W. Mclachlan:Theory and Applications of the Mathieu Functions (Clarendon Press, Oxford, 1964).Google Scholar
  16. (16).
    A. H. Nayfeh:Nonlinear Oscillations (John Wiley and Sons, Inc., New York, N. Y., 1979).MATHGoogle Scholar
  17. (17).
    A. H. Nayfeh:J. Acoust. Soc. Am.,62, 375 (1977).MATHMathSciNetCrossRefADSGoogle Scholar
  18. (18).
    A. H. Nayfeh:Perturbation Methods (John Wiley and Sons, Inc., New York, N. Y., 1973).MATHGoogle Scholar
  19. (19).
    A. A. Mohamed andN. K. Nayyar:Ar. J. Sci. Eng.,8, 103 (1983).MATHMathSciNetGoogle Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • Abou El Magd A. Mohamed
    • 1
  • El Sayed F. El hehawey
    • 1
  • Yusry O. El Dib
    • 1
  1. 1.Department of Mathematics, Faculty of EducationAin Shams University HeliopolisCairoEgypt

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