Nonlinear Streaming Instability of Cylindrical Structures in Finitely Conducting Fluids under the Influence of a Radial Electric Field

Abstract

Linear and weakly nonlinear stabilities of two-layer flows between two concentric circular cylinders are investigated. Two different dielectric inviscid fluids are assumed to flow with different velocities in the two separate layers, whose interface is cylindrical. Hence the flow field is assumed to be axisymmetric. The two fluids are influenced by a radial electric field due to surface charges at the interface. The critical magnitude of the electric field is obtained as a function of the velocity difference in the linear stability analysis. Based on the multiple scales technique, two nonlinear Schro¨dinger and Klein-Gordon equations are derived. The modulation instability of a finite wavetrain solution is discussed and compared with the linear instability condition. The analytical results are numerically confirmed, hence stability diagrams are obtained for different sets of physical parameters. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

Modulation instability of electrohydrodynamic waves on liquid jet

“…Combining the two Eqs. (2.43) and (2.44) following similar arguments as given by Elhefnawy et al [26], one finds the Ginzburg-Landau equation where the symbols Im and Re denote the imaginary and real parts and the upper bar refer to the complex conjugate terms.…”

“…He applied the method of strained coordinates for studying the non-linear breakup of capillary jet instability. Elhefnawy et al [25,26] studied the non-linear stability of cylindrical structures of finitely conducting fluids. In their analysis, two non-linear Schrödinger and Klein-Gordon equations are derived.…”

Viscous potential flow analysis of electrohydrodynamic capillary instability with heat and mass transfer: Effect of free surface charge

“…The dynamic instability of an excited horizontal interface supporting surface charge and admitting heat and mass was carried out by Moatimid [2]. Elhefnawy et al [3] studied the instability of finitely conducting fluids in cylindrical geometry under the influence of radial electric field with surface charges at the interface and it was found that dielectric constant plays a distinctive role in the analysis. El-Sayed et al [4] investigated the effect of general applied electric field on conducting inviscid liquid jets instability in the presence of heat and mass transfer taking surface charges into consideration.…”