International Journal of Theoretical Physics

, Volume 28, Issue 12, pp 1533–1558 | Cite as

Nonlinear electrohydrodynamic instability conditions of an interface between two fluids under the effect of a normal periodic electric field. III

  • E. F. El Shehawey
  • N. R. Abd El Gawaad


A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal periodic electric field is subjected to nonlinear deformations. We use the method of multiple scales in order to solve the nonlinear equations. In the first-order problem we obtained Mathieu's differential equation. For the second order, we obtain the nonhomogeneous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third order we obtain the second-order differential equation of periodic coefficients. Also, we obtain a formula for surface elevation. The stability conditions are determined.


Differential Equation Field Theory Elementary Particle Quantum Field Theory Stability Condition 
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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • E. F. El Shehawey
    • 1
  • N. R. Abd El Gawaad
    • 2
  1. 1.Department of Mathematics and Computer Sciences, Faculty of ScienceUAE UniversityAl-AinUnited Arab Emirates
  2. 2.Department of Mathematics, University College for WomenAin Shams UniversityCairoEgypt

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