Galal M. Moatimid

Electrohydrodynamic stability of two cylindrical interfaces under the influence of a tangential periodic electric field

The electrohydrodynamic stability of two cylindrical interfaces influenced by a periodic tangential field is studied. The model allows for general forms of deformations of the interfaces. Two simultaneous ordinary differential equations of the Mathieu type are obtained. The coupled equations are solved by the method of multiple scales and stability conditions are discussed. It is found that the constant tangential field has a stabilizing effect while the tangential periodic field has a stabilizing influence except at resonance points. Graphs are drawn to illustrate the resonance regions in a parameter space. It is also found that the thickness of the jet plays a role in the stability criterion. The frequency of the modulated field can be used to control the position of the resonance regions. The special cases of large modulation and small modulation are also examined. It is found that for large modulation the electric field exhibits an enhanced destabilizing influence.

The effect of an axial electric field on the stability of cylindrical flows in the presence of mass and heat transfer and absence of gravity

The effect of an axial electric field on the Kelvin-Helmholtz instability of a cylindrical interface, which admits mass and heat transfer, between two fluids is studied. The fluids are in the form of coaxial cylindrical shells of different thicknesses. The gravitational effects are neglected. A dispersion relation that accounts for the growth of asymmetric waves is derived. It is found that the uniform axial electric field has a strong stabilizing influence on the cylindrical interface for all short and long wavelengths in all symmetric and asymmetric modes of perturbation. In contrast, the streaming shows a strong destabilizing influence. It is also found that the surface tension may be stabilized or destabilized according to certain conditions. The present analysis indicates that the instability criterion of the system is independent of the mass and heat transfer coefficient, but it is different from that in the same problem without mass and heat transfer: A comparison of the results, in the two cases, shows the destabilizing effect of the mass and heat transfer. In the absence of mass and heat transfer, it is demonstrated that there is a critical Weber number, below which the nonaxisymmetric disturbance becomes unstable. The Weber number, herein, is defined as the ratio of surface tension force to the inertial force. The critical Weber number depends on the wavelength of the disturbances, the density ratio between the two fluids and the Alfven wave velocity.

Rivlin-Ericksen Fluid in Tube of Varying Cross-section with Mass and Heat Transfer

In this paper, the problem of heat and mass transfer due to the steady motion of a Rivlin- Ericksen fluid in tubes of varying cross-section is considered. Suction at tube walls is taken into account. Under the assumption that the deformations of the boundaries are small, the equations of motion have been solved by using a perturbation technique. The temperature and concentration distributions are obtained. The effects of various physical parameters are discussed. The Nusselt and Sherwood numbers are obtained. A set of figures for a quantitative illustration is presented.

Stability conditions of an electrified miscible viscous fluid sheet

The Kelvin-Helmholtz problem of viscous fluids under the influence of a normal periodic electric field in the absence of surface charges is studied. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming finite dielectric fluids. The interfaces permit mass and heat transfer. Because of the complexity of the considered system, a mathematical simplification is adopted. The weak viscous effects are taken into account so that their contributions are incorporated into the boundary conditions. Therefore, the equations of motion are solved in the absence of viscous effects. The boundary value problem leads to two simultaneous Mathieu equations of damped terms having complex coefficients. The symmetric and antisymmetric deformations reduced the coupled Mathieu equations to a single Mathieu equation. The classical stability criterion is found to be substantially modified due to the effect of mass and heat transfer. The analytical results are numerically confirmed. It is found that the sheet thickness and mass and heat transfer parameters have a dual influence on the stability criteria. It is also found that the field frequency has a stabilizing influence especially at small values of the wave number. In contrast to the case of a pure inviscid fluid, it is found that the uniform normal electric field plays a dual role in the stability criteria. This role depends on the choice of the numerical values of the physical parameters of the system under consideration.

Non-linear electrorheological instability of two streaming cylindrical fluids

A weakly non-linear instability of surface waves propagating through two viscoelastic cylindrical dielectric fluids is investigated. The examination is conducted in the presence of a tangential electric field and uniform axial relative streaming. The influence of the surface tension is taken into account, while the gravitational forces are ignored. Weak viscoelastic effects on the interface are considered, so that their contributions are demonstrated through the boundary conditions. Therefore, the equations of motion are solved in the absence of the viscoelastic effects. The solutions of the linearized equations of motion under the non-linear boundary conditions lead to derivation of a non-linear equation governing the interfacial displacement. This characteristic equation has damping terms and complex coefficients, where the nonlinearity is kept up to the third order. The linear state leads to a dispersion relation, where the stability is analysed. Taylors theory is adopted to expand the governing non-linear equation in the light of the multiple scale technique, to impose the well-known Schrodinger equation. Several special cases are reported upon appropriate data choices. The stability criteria are discussed theoretically and illustrated graphically in which stability diagrams are obtained. Regions of stability and instability are identified for the electric field intensity versus the wave number for the wave train of the disturbance.

Nonlinear dynamics and stability of two streaming magnetic fluids

Abstract This paper concerns the linear and nonlinear instability of Kelvin–Helmholtz flows in magnetic fluids under external driving. The fluids are subjected to an oblique magnetic field. With the use of the method of multiple scaling, a generalized derivation of the amplitude equation is obtained in marginally unstable regions of parameter space. A Melnikov function is formulated for such an instability and it is shown that there exist transverse homoclinic orbits leading to chaos.

Electrohydrodynamic instability of two superposed viscous miscible streaming fluids

Abstract The linear stability of two dielectric viscous fluids separated by a horizontal interface is investigated. The interface admits heat and mass transfer. The system is stressed by a normal periodic electric field producing surface charges at the interface. The effect of surface tension, small viscosity, velocity streaming and gravity on the critical surface charges density and on corresponding electric field are analyzed. The contribution of viscosity with the existence of surface charges and streaming are discussed. The investigation includes the stability analysis of the presence of the periodic electric field as well as the constant one. It is found that the presence of the surface charges made by the normal electric field play a dual role in the stability criterion, which shows some analogy with the nonlinear theory of stability. Some previous studies are compared using appropriate data. The marginal state of stability is also considered. It is found that the surface charges vanish under certain conditions. This study shows that the mass and heat transfer parameter has a destabilizing effect whether the electric field is static or periodic. Parametric excitation of the electrohydrodynamic (EHD) surface waves is analyzed in the case of Rayleigh–Taylor (R–T) instability. The transition curves are obtained by means of Whittakers technique. The analytical results are numerically confirmed.

Kelvin-Helmholtz Instability of Miscible Ferrofluids

We study the stability of an interface between two inviscid magnetic fluids of different densities flowing parallel to each other in an oscillatory manner. The system is pervaded by a uniform oblique magnetic field distribution. The analysis allows for mass and heat transfer across the interface. A general eigenvalue relation is derived and discussed analytically. The classical stability criterion is found to be substantially modified due to the effect of the oblique magnetic field with mass and heat transfer. Some previous studies are reported for appropriate data choices. The longitudinal magnetic field has a strong stabilizing influence on all wavelengths, which can be used to suppress the destabilizing influence of the mass and heat transfer. We conclude with a discussion of the stability of unsteady shear layers on the basis of the results. The parametric excitation of the surface waves is analyzed by means of the multiple-time-scales method. The transition curves are obtained analytically.

On the stability of a rotating electrified liquid jet. Effect of an axial electric field

The electrohydrodynamic stability of a liquid cylinder subject to surface tension and subjected to periodic rotation has been elaborated for all axisymmetric perturbations. The dielectric fluids are assumed to be stressed by a uniform axial electric field. The analysis is based on the method of multiple time scales. The zeroth-order perturbation yields a transcendental dispersion relation. The axial electric field plays a stabilizing role and can be used to suppress the instability of the constant rotation. It is observed in the case of constant rotation that if the outer surrounding medium is rotating faster than the inner liquid jet it makes the system more stable. The problem to first order in the perturbation is solved analytically. The solvability condition is obtained. The transition curves are examined. The frequency of the rotation can be used to control the position of the resonance regions. The analytical results show that the increase of the amplitude of the angular velocity has a destabilizing effect. The axial electric field plays a dual role in the stability criterion, a stabilizing influence in the nonresonance case and a destabilizing role at the resonance case.

Effects of an unsteady rotation on the electrohydrodynamic stability of a cylindrical interface

Abstract The effect of a periodic rotation on two dielectric inviscid fluids separated by a cylindrical interface is studied. The system is influenced by a constant perpendicular electric field. The model allows for general forms of deformations of the interface. The standard normal modes approach is utilized. The amplitude of the periodic rotation is considered as a smallness parameter. The method of multiple time scales is used to achieve the stability of the problem. Fourier series approach is used to solve the equations of motion. The solutions are obtained in terms of modified Bessel functions. A transcendental dispersion relation is obtained in zero-order perturbations. Several special cases are discussed. A generalization to Rayleighs theorem is obtained. The solvability condition, in first order perturbations, is derived. It is found that the resonance regions may appear due to the periodicity of the rotation. According to the periodicity the electric field has change its mechanism at the resonance case.