Nonlinear electrohydrodynamic stability of a finitely conducting jet under an axial electric field

Elhefnawy, Abdel Raouf F.; Agoor, Bothaina Mohamed; Elcoot, Abd Elmonem Khalil

doi:10.1016/s0378-4371(01)00173-x

Cited by 27 publications

(6 citation statements)

References 22 publications

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“…More recently, nonlinear effects have been specially studied in order to explain the experimental phenomena, such as the formation of satellite droplets (e.g. López-Herrera, Gañán-Calvo & Perez-Saborid 1999;López-Herrera & Gañán-Calvo 2004;Zakaria 2000;Elhefnawy, Agoor & Elcoot 2001;Elhefnawy, Moatimid & Elcoot 2004;Moatimid 2003).…”

Section: Introductionmentioning

confidence: 99%

Instability of a viscous coflowing jet in a radial electric field

Li¹,

Yin²,

Yin³

2008

J. Fluid Mech.

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A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

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Section: Introductionmentioning

confidence: 99%

Instability of a viscous coflowing jet in a radial electric field

Li¹,

Yin²,

Yin³

2008

J. Fluid Mech.

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“…Only axisymmetric perturbations resulting in high-quality aerosols were considered. Elhefnawy et al [29] analysed the nonlinear electrohydrodynamic stability of a finitelyconducting jet in an axial electric field. Elhefnawy et al [30] investigated the weakly nonlinear streaming instability of two conducting fluids in a cylindrical circular crosssection interface.…”

Section: Introductionmentioning

confidence: 99%

Electroviscoelstic Stability Analysis of Cylindrical Structures in Walters B Conducting Fluids Streaming through Porous Medium

Metwaly

Hafez

2022

Fluids

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In this research, the linear stability of a cylindrical interface between two viscoelstic Walters B conducting fluids moving through a porous medium is investigated theoretically and numerically. The fluids are influenced by a uniform axial electric field. The cylindrical structure preserves heat and mass transfer across the interface. The governing equations of motion and continuity are linearized, as are Maxwell’s equations in quasi-static approximation and the suitable boundary conditions at the interface. The method of normal modes has been used to obtain a quadratic characteristic equation in frequency with complex coefficients describing the interaction between viscoelstic Walters B conducting fluids and the electric field. In light of linear stability theory, the Routh–Hurwitz criteria are used to govern the structure’s stability. Several special cases are recoverd under suitable data choices. The stability analysis is conferred in detail via the behaviors of the applied electric field and the imaginary growth rate part with the wavenumbers. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through two sets of figures. Our results demonstrate that kinematic viscosities, kinematic viscoelasticities, and medium porosity improve stability, whereas medium permeability, heat and mass transfer coefficients, and fluid velocities decrease it. Finally, electrical conductivity has a critical influence on the structure’s stability.

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“…This effect is relatively stronger when the dielectric constant and the depth of the upper fluid is the greater at the same time and depth of the low fluid is low. Nonlinear electrohydrodynamic Kelvin-Helmholtz instability conditions of a cylindrical interface under the influence of an axial electric field have been studied by Othman [11] and Elhefnawy et al [12]. Dhiman at el.…”

Section: Introductionmentioning

confidence: 99%

Electrohydrodynamic Kelvin - Helmholtz Instability of Cylindrical Interface through Porous Media

Dhiman

Awasthi

Singh³

2013

Inter J Fluid Mech Res

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The effect of pressure correction on the linear analysis of Kelvin-Helmholtz instability of cylindrical interface in presence of saturated porous bed structure has been carried out, considering viscous potential flow theory. In the viscous potential flow theory, viscosity enters through normal stress balance and tangential stresses are not considered. The assume fluids in the system are considered to be viscous and incompressible with different kinematic viscosities. The fluids are subjected to be uniform electric field which is acting in the axial direction. A dispersion relation that accounts for the axisymmetric waves has been obtained and stability criterion has been given in terms of relative velocity. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of Kelvin-Helmholtz instability. The difference graphs have been drawn, to show the effect of various physical parameters such as porosity and permeability of medium, viscosity ratio, upper fluid fraction on the stability of the system. By the observation of the graphs, that axial electric field has stabilizing effect while porous media has destabilizing effect on the stability of the system.

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Nonlinear electrohydrodynamic stability of a finitely conducting jet under an axial electric field

Cited by 27 publications

References 22 publications

Instability of a viscous coflowing jet in a radial electric field

Instability of a viscous coflowing jet in a radial electric field

Electroviscoelstic Stability Analysis of Cylindrical Structures in Walters B Conducting Fluids Streaming through Porous Medium

Electrohydrodynamic Kelvin - Helmholtz Instability of Cylindrical Interface through Porous Media

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