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Nonlinear instability of charged liquid jets: Effect of interfacial charge relaxation

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  • Elmonem Khalil Elcoot, Abd

Abstract

A linear and nonlinear study has been made of cylindrical interface, carrying a uniform surface charge in the presence of a finite rate of charge relaxation, is investigated by using multiple scales method. The linear stability flow is analyzed by deriving a dispersion relation for the growth waves, and solving it analytically and numerically to find marginal stability curves. We investigate the electric charge relaxation effects on the stability of the flow by considering various limiting cases. We also examine the effects of finite charge relaxation times in axisymmetric and nonaxisymmetric modes. In the nonlinear approach, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. There is also obtained a nonlinear modified Schrödinger equation describing the evolution of wave packets for small charge relaxation time. Further, the classic Schrödinger equation is obtained when the influence of relaxation time charge is neglected. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similarly type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber. The nonlinear theory, when used to investigate the stability of charged liquid jet, appears accurately to predict a new unstable regions. The effects of the surface charge and charge relaxation on the stability are identified. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.

Suggested Citation

  • Elmonem Khalil Elcoot, Abd, 2007. "Nonlinear instability of charged liquid jets: Effect of interfacial charge relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 411-428.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:2:p:411-428
    DOI: 10.1016/j.physa.2006.09.032
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    References listed on IDEAS

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    1. Mohamed, A.A. & Elhefnawy, A.R.F. & Mahmoud, Y.D., 1994. "Nonlinear electrohydrodynamic Kelvin-Helmholtz instability with mass and heat transfer. Effect of a tangential field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 264-290.
    2. Khalil Elcoot, Abd Elmonem & Moatimid, Galal M., 2004. "Nonlinear instability of finitely conducting cylindrical flows through porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 15-35.
    3. Elhefnawy, Abdel Raouf F. & Agoor, Bothaina M.H. & Elcoot, Abd Elmonem Khalil, 2001. "Nonlinear electrohydrodynamic stability of a finitely conducting jet under an axial electric field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 368-388.
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    Cited by:

    1. Zubarev, Nikolay M. & Zubareva, Olga V., 2007. "Equilibrium configurations of uncharged conducting liquid jets in a transverse electric field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 35-45.

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    1. Khalil Elcoot, Abd Elmonem & Moatimid, Galal M., 2004. "Nonlinear instability of finitely conducting cylindrical flows through porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 15-35.

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