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The linear stability analysis has been analyzed for an electrified liquid sheet confined between two symmetric dielectric movable ambient gas. The present study aims to estimate the planer jet systems response when applying a tangential electric field. The dispersion relations for varicose and sinuous modes have been formulated. The electrical Euler number and some flow parameters have been tested for their influence on the electrified liquid sheet instability. In other words, the effects of electric field on the dominant wave number, and instability range (cutoff wave number) are discussed. The results clarify that the tangential electric field has a stabilizing effect for sinuous mode over the whole range of gas velocity ratio. On the other hand, for varicose mode, the electric field slightly improves the system stability to a certain limit, but it has a great role in stability for higher values of gas velocity ratio.

The present work deals with temporal electro-aerodynamics instability properties of an inviscid confined planar jet in a zero gravity environment and the existence of electric field. The considered system is composed of a horizontal liquid sheet surrounded by two identical moving layers of fluid. The electric field acts uniformly normal to the interfaces. The governing equations with the boundary conditions are solved for fluid dynamics and electric fields. The dispersion relation and the integrated solution for the model are obtained for both varicose and sinuous modes. The influence of different parameters governing the flow on instability behavior of the system such as the confinement, basic velocity ratio, and electric voltage is discussed in detail. We conclude that increasing the thickness of the outer fluids for small range of unstable wave numbers decreases the disturbance growth rate and increases the number of saddle points. In addition, when the basic velocity ratio is less than one the electric field has a stabilizing effects, but when it exceeds one it has a destabilizing effect.

We study the linear stability of a three-layer flow of immiscible liquids located in a periodic normal electric field. We consider certain porous media assumed to be uniform, homogeneous, and isotropic. We analytically and numerically simulate the system of linear evolution equations of such a medium. The linearized problem leads to a system of two Mathieu equations with complex coefficients of the damping terms. We study the effects of the streaming velocity, permeability of the porous medium, and the electrical properties of the flow of a thin layer (film) of liquid on the flow instability. We consider several special cases of such systems. As a special case, we consider a uniform electric field and solve the transition curve equations up to the second order in a small dimensionless parameter. We show that the dielectric constant ratio and also the electric field play a destabilizing role in the stability criteria, while the porosity has a dual effect on the wave motion. In the case of an alternating electric field and a periodic velocity, we use the method of multiple time scales to calculate approximate solutions and analyze the stability criteria in the nonresonance and resonance cases; we also obtain transition curves in these cases. We show that an increase in the velocity and the electric field promote oscillations and hence have a destabilizing effect.

The present work deals with temporal stability properties of a falling liquid film down an inclined plane in the presence of constant electromagnetic field. Using the Karman approximation, the problem is reduced to the study of the evolution equation for the free surface of the liquid film derived through a long-wave approximation. A linear stability analysis of the base flow is performed. Also, the solutions of stationary waves and Shkadov waves are introduced and discussed analytically by analyzing the linearized instability of the fixed points and Hopf bifurcation.

The present work deals with temporal stability properties of a falling liquid film down an inclined plane in the presence of a parallel subsonic gas flow. The waves are described by evolution equation previously derived as a generalization of the model for the Newtonian liquid. We confirm linear stability results of the basic flow using the Orr–Sommerfeld analysis to that obtained by long wave approximation analysis. The non-linear stability criteria of the model are discussed analytically and stability branches are obtained. Finally, the solitary wave solutions at the liquid–gas interface are discussed, using specially envelope transform and direct ansatz approach to Ginzburg–Landau equation. The influence of different parameters governing the flow on the stability behavior of the system is discussed in detail.

The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity. After studying the linear conditions, a generalized nonlinear kinematic model is then derived to present the physical system. Applying the boundary conditions, analytical solutions are obtained using the long-wave perturbation method. In the first step, the normal mode method is used to characterize the linear behaviors. In the second step, the nonlinear film flow model is solved by using the method of multiple scales, to obtain Ginzburg-Landau equation. The influence of some physical parameters is discussed in both linear and nonlinear steps of the problem, and the results are displayed in many plots showing the stability criteria in various parameter planes.

The present work deals with the stability properties of an immersed annulus swirling jet in a zero gravity environment. The considered system is composed of two streaming coaxial fluid cylinders, embedded in a third streaming fluid, where the intermediate one (annulus) has a uniform swirl speed. The fluids are immiscible, inviscid, and incompressible. The linear stability criteria of the model are discussed analytically and stability diagrams are obtained. We conclude that the radii ratio, the Weber number and the swirl number play a significant role in determining the dynamics of the developing interfacial patterns.