Title
Nonlinear electrohydrodynamic stability of two superposed bounded fluids in the presence of interfacial surface chargesNonlinear electrohydrodynamic stability of two superposed bounded fluids in the presence of interfacial surface charges
Author
Faculty/Department
Faculty of Sciences. Physics
Research group
Department of Physics
Non-linear Waves
Publication type
article
Publication
Tübingen,
Subject
Physics
Chemistry
Source (journal)
Zeitschrift für Naturforschung: A: a journal of physical sciences. - Tübingen
Volume/pages
53(1998):5, p. 217-232
ISSN
0932-0784
ISI
000074251500003
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between two superposed dielectric fluids with uniform depths in the presence of a normal electric field, taking into account the interfacial surface charges. The evolution of the amplitude for travelling waves is governed by a nonlinear Schrodinger equation which gives the criterion for modulational instability. Numerical results are given in graphical form, and some limiting cases are recovered. Three cases, in the pure hydrodynamical case, depending on whether the depth of the lower fluid is equal to or greater than or smaller than the one of the upper fluid are considered, and the effect of the electric field on the stability regions is determined. It is found that the effect of the electric field is the same in all the cases for small values of the field, and there is a value of the electric field after which the effect differs from case to case. It is also found that the effect of the electric field is stronger in the case where the depth of the lower fluid is larger than the one of the upper fluid. On the other hand, the evolution of the amplitude for standing waves near the cut-off wavenumber is governed by another type of nonlinear Schrodinger equation with the roles of time and space are interchanged. This equation makes it possible to determine the nonlinear dispersion relation, and the nonlinear effect on the cut-off wavenumber.
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