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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
Article

Abstract

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.

Keywords

Differential Equation Field Theory Elementary Particle Quantum Field Theory Stability Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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