Electrohydrodynamic Kelvin Research Articles

Electrohydrodynamic Kelvin–Helmholtz instability in a power-law fluid layer bounded above by a porous layer

The numerical study of two immiscible, electrically conducting, non-viscous, superposed, and counter-streaming power-law fluid Kelvin–Helmholtz instability (KHI) is discussed in the present work. This instability is because, in the presence of an electric field, the upper fluid layer is heavier than the lower fluid layer. To comprehend how physical parameters such as the electric field, power-law fluid, layer thickness, porous parameter, and Bond number related to streaming fluids affect the evolution of an unsteady approach to perturbation affecting the physical system, the so-obtained dispersion relation has been investigated by applying both linear theory and the normal mode method. It has been observed that the system is stabilized by the electric field, the power-law fluid, and the porosity parameter; nevertheless, the layer thickness and Bond number of the counter-streaming fluids have a destabilizing effect on neutral stability.

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

Electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer: Effect of perpendicular electric field

In this paper, we investigate the effect of perpendicular electric field on the linear analysis of Kelvin–Helmholtz instability of a plane interface between two viscous and dielectric fluids, when the fluids are subjected to constant normal electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of relative velocity as well as applied electric field. It is observed that heat transfer and perpendicular electric field both have destabilizing effect while vapor fraction stabilizes the interface.

Three-Dimensional Viscous Potential Electrohydrodynamic Kelvin–Helmholtz Instability Through Vertical Cylindrical Porous Inclusions With Permeable Boundaries

In this paper, the electrohydrodynamic three-dimensional Kelvin–Helmholtz instability of a cylindrical interface with heat and mass transfer between liquid and vapor phases is studied. The liquid and the vapor are saturated, two coaxial cylindrical porous layers, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. The dispersion relation is derived and the stability analysis is discussed for various parameters. It is found that the streaming velocity has a destabilizing effect, while the axial electric field has a stabilizing one. The suction for both the liquid and the steam has a destabilizing effect in contrast with the injection at both boundaries. The flow through porous structure is more stable than the pure flow. The case of the axisymmetric (for zero value of the azimuthal wave number m) and asymmetric (for nonzero value of the azimuthal wave number m) disturbances at large wavelength (at the wave number k→0) are always stable. Meanwhile, it is the same dispersion relation for the plane geometry at large wave number. Finally, our results are corroborated by comparing them with the previous published results.

Electrohydrodynamic Kelvin - Helmholtz Instability of Cylindrical Interface through Porous Media

Electrohydrodynamic Kelvin - Helmholtz Instability of Cylindrical Interface through Porous Media

Viscous potential flow of electrohydrodynamic Kelvin–Helmholtz instability through two porous layers with suction/injection effect

The linear electrohydrodynamic Kelvin–Helmholtz instability of an interface between two dielectric fluids fully saturated porous media with heat and mass transfer in the presence of a horizontal electric field is investigated. The lighter fluid is above the heavier one, so that in the absence of both motion and electric fields, the arrangement is stable where the interface is flat. It also taken into account the existence of a constant suction/injection velocities at porous boundaries. The effects of the various parameters on the stability of the interface are presented and illustrated through some sets of figures. These parameters such as the Darcy’s coefficients, suction/injection velocities at the boundaries, dielectric constants, heat and mass transfer coefficient, the relative streaming velocity and the thickness of the fluid layers. It was found that the Darcy’s coefficient for the porous layers plays a stabilizing role in the stability picture. Also, It was found that the thickness of the lighter fluid has stabilizing effect, and vise versa occurs for the heavier fluid. The injection of the fluids at both boundaries have stabilizing effect, in contrast with the suction at both boundaries.

Viscous potential flow analysis of electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer

Viscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer in presence of a horizontal electric field has been carried out. Stability criterion is given by a critical value of relative velocity of two fluids as well as critical value of the applied electric field. Various graphs with respect to physical parameters, such as wave-number, viscosity ratio, ratio of dielectric constants of two fluids, heat transfer coefficients have been drawn and effect of various parameters have been described.

Electrohydrodynamic Kelvin–Helmholtz instability of two superposed Rivlin–Ericksen viscoelastic dielectric fluid-particle mixtures in porous medium

The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed Rivlin–Ericksen viscoelastic dielectric fluid-particle mixtures in porous medium is investigated. The considered system is influenced by a uniform horizontal electric field. Perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially stable configuration as long as perturbations in the direction of streaming are ignored, and the system remains stable in this case. For the potentially unstable configuration, the system is found to be stable or unstable for a certain wavenumber range depending on acceleration due to gravity, surface tension, and fluid velocities. For perturbations in all other directions, there exists instability for a certain wavenumber range, and the instability of the system can be delayed by the applied electric field. Numerical results show that Stokes' drag coefficient, electric field, kinematic viscosity have stabilizing effects; and mass density of the particles, porosity of the porous medium, kinematic viscoelasticity, fluid velocity, number density of the particles have destabilizing effects; while permeability of the medium has a dual role in the stability of the considered system, and the porosity of the porous medium has no effect on the stability for large wavenumbers. The limiting case of Rayleigh–Taylor instability is also discussed, and stability conditions are obtained.

Electrohydrodynamic instability of two superposed Walters B´ viscoelastic fluids in relative motion through porous medium

The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B´ model) dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration, as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally, it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions. Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics.

Electrohydrodynamic Kelvin–Helmholtz InstabilityConditions of a Vortex Sheet in Uniform Shear Flow

The electrohydrodynamic Kelvin–Helmholtz instability of avortex sheet under the effect of background vorticity and a tangentialelectric field is described theoretically by an inviscid linearstability analysis. An eigenvalue equation for the complex wavevelocity is obtained from which we can obtain the stabilityconditions. It is found, when the electric field is absent, that thebackground vorticity increases the growth rate of the deformed vortexsheet whose vorticity is of the same sign as the background vorticity.In the presence of a tangential electric field, it is found that theelectric field has a stabilizing effect and the vortex sheet isneutrally stable if the wavenumber and the electric field values areless than some critical values depending on the backgroundvorticity.

Effect of normal electric fields on Kelvin–Helmholtz instability for porous media with Darcian and Forchheimer flows

The linear electrohydrodynamic Kelvin–Helmholtz instability of the interface between two dielectric fully saturated porous media under the effect of normal electric fields is considered. The lighter fluid is above the heavier one so that in the absence of both motion and electric fields, the arrangement is stable and the interface is flat. It is shown that when the fluids are moving parallel to each other at different velocities, the interface may become unstable, and the normal electric fields have usually destabilizing effect. The corresponding conditions for marginal stability are derived for Darcian and Forchheimer flows. In both the cases, the velocities, and the electric fields should exceed some critical values in order for the instability to manifest itself. In the case of Darcy’s flow, however, an additional condition, involving the fluids viscosities, their density ratios and the electric field values is required.

Nonlinear electrohydrodynamic Kelvin-Helmholtz instability conditions of a cylindrical interface under the influence of an axial electric field

The electrohydrodynamic Kelvin–Helmholtz instability of a cylindrical interface separating two dielectric streaming fluids, stressed by an axial electric field in the absence of surface charges on the interface, is studied. We have used the method of multiple scales. Two nonlinear Schrodinger equations are obtained, one of them leads to the determination of the cut-off wavenumber and the cut–off electric field. The other Schrodinger equation is used to analyze the stability of the system. The stability conditions of the perturbed system is discussed analytically and numerically. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein—Gordon equation. The various stability criteria are derived from this equation.

Intervals of Electrohydrodynamic Kelvin–Helmholtz Instability: A Normal Periodic Field Producing Surface Charges

The intervals of electrohydrodynamic (EHD) KELVIN-HELMHOLTZ instability influenced by a periodic normal electric field producing surface charges is considered. It is shown that a linear model of the interface is governed by Hill's differential equation. Characteristic values and intervals of stability arB discussed. The special case of Mathieu differential equation type is obtained

Nonlinear electrohydrodynamic Kelvin–Helmholtz instability conditions of an interface between two fluids under the effect of a normal periodic electric field

The electrohydrodynamic Kelvin–Helmholtz instability conditions of an interface separating two dielectric streaming fluids, stressed by a normal electric field in absence of surface charges on the interface, are studied. We use the method of multiple scales to solve nonlinear equations. In the first-order problem we obtained Mathieu's differential equation. For the second-order problem, we obtain the nonhomogeneous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third-order problem, we obtain the second-order differential equation of periodic coefficients; we also obtain a formula for surface elevation, and we determine the instability conditions.

Electrohydrodynamic solitons in Kelvin-Helmholtz flow: the case of a normal field in the absence of surface charges

Nonlinear electrohydrodynamic Kelvin—Helmholtz instability conditions are investigated. A charge-free surface separating two semi-infinite dielectric streaming fluids influenced by a normal electric field is subjected to nonlinear deformations. The method of multiple-scale perturbations is used in order to obtain two nonlinear Schrödinger (NLS) equations describing the behavior of the disturbed system. The stability and instability conditions of the perturbed system are discussed analytically. One of the two NLS equations is used to obtain the electrohydrodynamic (EHD) nonlinear cutoff wave number separating stable and unstable disturbances while the other equation is used to describe analytically the necessary condition for stability and instability for the system. For unstable cases, the solution starting with a solitary wave degenerates into a finite number of EHD solitons.