Electrohydrodynamic Rayleigh-Taylor Instability Research Articles

Influence of boundary roughness on the saturation of electrohydrodynamic Rayleigh-Taylor instability in two superposed fluids in the presence of nanostructured porous layer

Using linear stability analysis, the influence of boundary roughness on electro-hydrodynamic Rayleigh-Taylor instability (EHRTI), in a poorly electrically conducting fluid film of finite thickness, is studied. It is a theoretical study, based on the assumption of densely packed porous lining, prepared with smart material of nanostructure, that permits the use of modified Darcy equation with Saffman-slip condition at the interface. Modify means the addition of Lorentz forces due to magnetic and electric fields. A dispersion that accounts for the growth rate of perturbed waves is derived and stability discussed theoretically. The effects of electromagnetic fields, surface tension, boundary roughness, and porous layer are demonstrated using Stokes and lubrication approximations and shown graphically for the above-said physical parameters on the stability of the system. The strength of electromagnetic fields, porous layer and boundary roughness decreases the unstable growth rate for finitely conducting fluids, while surface tension stabilizes the system for a lower Bond number.

Electrohydrodynamic Rayleigh-Taylor instability in leaky dielectric fluids

In this paper, an analysis is presented of the influence of electric field on the Rayleigh-Taylor instability (RTI) of two leaky dielectric fluids. A numerical model is developed based on the coupled solution of the governing equations of the electric field (i.e., Poisson equation) and the fluid flow (i.e., Navier-Stokes equation), where the leaky dielectric model is employed to take into account the free charges in the fluids. These equations are formulated within the framework of phase field and solved simultaneously. The numerical model, after validated with existing data, is applied to study the effect of the electric field on interfacial morphology associated with the RTI. Different from the perfect dielectric model, the free charges originating from the conductivity in a leaky dielectric fluid plays an important role in the evolution of the RTI under the influence of an applied field. Various interfacial morphologies have been observed in the electrohydrodynamic RTI, suggesting that the electric field has a significant influence on the RTI. An electric field (horizontal or vertical) may suppress or aggravate the instability depending on the system parameters the permittivity ratio and the conductivity ratio of the two leaky dielectric fluids.

Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

Non-linear study of electrohydrodynamic Rayleigh–Taylor instability in a composite fluid–porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams–Bashforth predictor and Adams–Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.

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

The nonlinear analysis of the electrohydrodynamic Rayleigh–Taylor instability of a cylindrical interface separating two conducting fluids of circular cross section is investigated in the absence of gravity. The fluids are assumed to be stressed by a uniform axial electric field. The analysis is based on the method of multiple scale perturbation. The linear dispersion relation, nonlinear Schrödinger equations and a nonlinear Klein–Gordon equation are obtained. The stability conditions of the perturbed system are discussed both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in terms of various parameters of the problem. Regions of stability and instability are identified.

Parametric Third-Subharmonic Resonance in Nonlinear Electrohydrodynamic Rayleigh-Taylor Instability with Mass and Heat Transfer

The nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer is investigated. The fluids are stressed by a periodic acceleration and a normal electric field. Based on the method of multiple scales, a parametric nonlinear Schrodinger equation with complex coefficients is derived in the third-subharmonic resonance case. A standard nonlinear Schrodinger equation with complex coefficients is obtained in the non-resonance case. A temporal solution is carried out for the parametric nonlinear Schrodinger equation. Necessary and sufficient conditions for stability are obtained. Numerical calculations show that the thickness of the fluid, the normal electric field, and the coefficient of mass and heat transfer have destabilizing effect. It is found that the external frequency plays a dual role in the stability criteria.

Nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer subject to a vertical oscillating force and a horizontal electric field

Weakly nonlinear stability of interfacial waves propagating between two electrified inviscid fluids influenced by a vertical periodic forcing and a constant horizontal electric field is studied. Based on the method of multiple-scale expansion for a small-amplitude periodic force, two parametric nonlinear Schrodinger equations with complex coefficients are derived in the resonance cases. A standard nonlinear Schrodinger equation with complex coefficients is derived in the nonresonance case. A temporal solution is carried out for the parametric nonlinear Schrodinger equation. The stability analysis is discussed both analytically and numerically.

Nonlinear electrohydrodynamic Rayleigh–Taylor instability with mass and heat transfer: effect of a normal field

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids with interfacial transfer of mass and heat is presented for layers of finite thickness. The fluids are subjected to a normal electric field in the absence of surface charges. Using a technique based on the method of multiple scales it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. When the mass and heat transfer are neglected, the cubic nonlinear Schrödinger equation is obtained. Further, it is shown that, near the marginal state, a nonlinear diffusion equation is obtained in the presence of mass and heat transfer. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.

Nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer. Effect of a tangential field

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids with interfacial transfer of mass and heat transfer is presented for layers of finite thickness. The fluids are subjected to a tangential electric field. The method of multiple scale perturbations is used to obtain a dispersion relation for the first order and a Ginzburg-Landau equation, for the higher orders, describing the behaviour of the disturbed system. The stability criterion is expressible in terms of various competing parameters representing the equilibrium heat flux, latent heat of evaporation, gravity, surface tension, densities of the fluids, dielectric constants of the fluids, thickness of the layers and thermal properties of the fluids. The stability of this perturbed system is discussed both analytically and numerically near the marginal state according to the nonlinear diffusion equation and the stability diagrams are obtained.

Intervals of electrohydrodynamic Rayleigh-Taylor instability: A normal periodic field producing surface charge

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

Intervals of electrohydrodynamic Rayleigh-Taylor instability: effect of a normal periodic field

The intervals of electrohydrodynamic Rayleigh-Taylor instability influenced by a periodic normal field are considered. It is shown that a linear model of the interface is governed by Hill’s differential equation. Characteristic values and intervals of stability are discussed. The special case of Mathieu differential equation type is obtained.

Intervals of electrohydrodynamic Rayleigh–Taylor instability. I. Effect of a tangential periodic field

The intervals of electrohydrodynamic Rayleigh—Taylor instability influenced by a periodic tangential field are considered. It is shown that a linear model of the interface is governed by Hill’s differential equation. Characteristic values and intervals of stability are discussed. The special case of the Mathieu differential equation type is obtained.

Nonlinear electrohydrodynamic Rayleigh–Taylor instability. II. A perpendicular field producing surface charge

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids is studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method of multiple scale perturbations is used to obtain two nonlinear Schrödinger equations describing the behavior of the disturbed system. The stability of the perturbed system is discussed both analytically and numerically and stability diagrams are obtained. The electric field plays a dual role in the sense that it can stabilize the system for relatively large values of wavenumbers and small values of the density ratio and vice versa. The stabilizing range of the electric field for some given density ratios is tabulated. The analogy with hydromagnetic stability is established. Expressions for the surface elevation and the cutoff wavenumber separating stable and unstable disturbances are also obtained.

Nonlinear electrohydrodynamic Rayleigh–Taylor instability. Part 1. A perpendicular field in the absence of surface charges

Nonlinear electrohydrodynamic Rayleigh-Taylor instability is investigated. A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal electric field is subjected to nonlinear deformations. We use the method of multiple-scale perturbations in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable from unstable flows. We obtain two nonlinear Schrödinger equations by means of which we can deduce the cutoff wavenumber and analyse the stability of the system. It is found that if a finite-amplitude wave exists then its small modulation is stable. We also obtain the surface elevation for such waves. The electric field plays a dual role in the stability criterion and the dielectric constant plays a distinctive role in this analysis. If the dielectric constant of the upper fluid is smaller than that of the lower fluid the field has a destabilizing effect for large wavenumbers. For relatively smaller wavenumbers the electric field stabilizes considerable parts of the first and second subharmonic regions in the stability diagrams; a result which is in contrast with the linear theory. If the dielectric constant of the upper fluid is larger than that of the lower fluid, then the field is stabilizing for larger values of the wavenumber K′ when ρ is small (ρ is the density ratio) and destabilizing for smaller values of K′.

Electrohydrodynamic Rayleigh-Taylor instabilities of a plane circular interface

The electrohydrodynamic Rayleigh-Taylor instability for two dielectric fluids confined in an infinite rigid cylinder and having a circular horizontal interface is investigated. It is found that the vertical electric field has a destabilizing effect for a set of restricted wave numbers satisfying an eigenvalue equation. The special case when one of the two fluids is a perfect conductor is discussed in some detail. A feed-back mechanism has been introduced to control such instabilities.