Electrohydrodynamic Waves Research Articles

The Dynamics of Periodic Traveling Interfacial Electrohydrodynamic Waves: Bifurcation and Secondary Bifurcation

The Dynamics of Periodic Traveling Interfacial Electrohydrodynamic Waves: Bifurcation and Secondary Bifurcation

Nonlinear wave interactions on the surface of a conducting fluid under vertical electric fields

In this paper, we are concerned with capillary–gravity waves propagating on a two-dimensional conducting fluid under the effect of an electric field imposed in the direction perpendicular to the undisturbed free surface. This work aims to investigate the impact of the electric fields on the nonlinear wave interactions in this context. The full system is mathematically difficult to solve since it is a nonlinear, two-layered, free boundary problem, and the interface dynamics results from the strong coupling between the Euler equations for the lower fluid layer and an electric contribution from the upper gas layer. To investigate electrohydrodynamic wave interactions, we propose a novel numerical scheme based on a time-dependent conformal map and an interpolation technique to conduct unsteady simulations of the fully nonlinear electrified Euler equations of the two-layered problem. To gain analytical insights, we first derive weakly nonlinear envelope equations based on the method of multiple scales for the resonant triad, long-short wave interaction, and modulation of a single-mode wavetrain (a special case of resonant quartet interaction). Summative remarks are made to illustrate the transition from 3-wave interactions to 4-wave interactions and vice versa, occurring when the coefficients of the associated nonlinear Schrödinger equation become singular. The fully nonlinear results obtained by the prescribed numerical method are compared with the predictions by the weakly nonlinear theories, and good agreement is achieved.

A priori estimates of the electrohydrodynamic waves with vorticity: horizontal electric field

ABSTRACT In this paper, we are concerned with an incompressible and inviscid conducting fluid in the presence of surface tension and horizontal electric field. It is obtained the local-in-time estimates on the interface in and the velocity fields in by using the method introduced by Shatah and Zeng [A priori estimates for fluid interface problems. Commun Pure Appl Math. 2008;61(6):848–876]. The estimates of a horizontal electric field can be obtained from the estimates of the interface and elliptic estimates.

A priori estimates of the electrohydrodynamic waves with vorticity: Vertical electric field

We consider an incompressible and inviscid conducting fluid in the presence of surface tension and vertical electric field. We will reduce the system to the equations on the interface and the velocity fields. By the reduced equations, it is obtained the local-in-time estimates on the interface in H3k+1 and the velocity fields in H3k by using the method introduced by Shatah and Zeng [20]. The estimates of a vertical electric field can be obtained from the estimates of the interface and elliptic estimates.

Faraday waves under perpendicular electric field and their application to the walking droplet phenomenon

Vertically oscillating fluid surfaces have been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic waves in similar configurations. In the present work, the unification of both effects and their consequences on the stability of the surface. Given the versatility of electromagnetic fields, application to the phenomenon of walking droplets is suggested; the dispersion relation and bouncing regimes of and the force on the droplets are revisited, and feasible experimental configurations are proposed.

Well-posedness of electrohydrodynamic waves under vertical electric field

This paper is devoted to the problem of wave propagation on a perfect conducting fluid under a vertical electric field, a kind of electrohydrodynamic waves. Three competing restoring forces resulting from gravity, surface tension, and normal electric field are taken into account. There are many numerical and experimental results on electrohydrodynamic waves, but the system’s well-posedness, which is a fundamental problem, has not been investigated in the past. We shall show the system considered is locally well posed based on energy estimates in proper Sobolev spaces and careful examinations of the Dirichlet–Neumann operators.

Local bifurcation of electrohydrodynamic waves on a conducting fluid

We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.

Research of the performance of pulse electrohydrodynamics in blockage removal

In line with contemporary trends and seeking to develop new methods and technologies, a new, original technology was explored and designed based on a non-conventional process of electrical pulse discharge in a water chamber, referred to as 'Pulse Electrohydrodynamic Technology' (PELHYDT). The application of the PELHYDT in sewer blockage removal is presented in this paper. Existing machinery can remove two blockages of gully pot connections per hour. Three blockages of pipe conduits are generally removed during an 8-h working day. Applying PELHYDT technology, which allows for high rates of removal of mechanical obstructions, it is possible to achieve operating fluid pressures in the order of 10(3)-10(4) bars, a velocity of 100 m/s, a deformation acceleration of the model material structure of 10(6)-10(7) m/s2, and high-frequency hydraulic shock waves with a frequency of 10(3)-10(4) Hz. The applicability of this efficient technology in sewer blockage removal was proven under laboratory conditions at operating fluid pressures from 50 to 160 bars, which are standard for sewer maintenance. Water velocities generally achieved in sewers using existing flushing technologies range between 1 and 3 m/s and usually do not exceed 9 m/s. PELHYDT creates waves whose velocity is at least 100 m/s, and is therefore about ten times more efficient than existing technologies. PELHYDT generates an electrohydrodynamic wave very quickly, virtually in the form of an explosion. It was proven under laboratory conditions that the application of this technology for blockage removal in practice will not result in any sewer damage.

Nonlinear stability, excitation and soliton solutions in electrified dispersive systems

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated in (2+1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. A three-wave resonant interaction for nonlinear excitations created from electrohydrodynamic capillary-gravity waves is observed to be possible in a dispersive medium with a self-focusing cubic nonlinearity. Under suitable conditions, the nonlinear envelope equations for the resonant interaction are derived by using multiple scales and inverse scattering methods, and an explicit three-wave soliton solution is discussed. Both the dynamic properties and the modulational instability of finite amplitude electrohydrodynamic wave are studied for the cubic nonlinear Schrödinger equation by means of linearized stability analysis and the nonlinear interaction coefficient. We show that the trajectories in phase space exhibit different behavior with the increase of nonlinear perturbations, and we determine the electric field and wavenumber ranges at which the original point is elliptic or hyperbolic, respectively. It is found also that the presence of the electric field in the equation modifies the nature of wave stability and soliton structures, and that the amplitude and width of the soliton are decreased and increased, respectively, when the electric field value increases.

Axisymmetric waves in electrohydrodynamic flows

The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollow cylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal.

Modulation instability of electrohydrodynamic waves on liquid jet

An analytical study of slow modulation has been made of cylindrical interface between two inviscid streaming fluids, in the presence of a relaxation of electrical charges at the interface, and stressed by an axial electric field. A new technique based on the perturbation theory, to derive the non-linear evolution equations has been introduced. These equations are combined to yield a non-linear Ginzburg–Landau equation and a non-linear modified Schrödinger equation describing the evolution of wave packets. The linear analysis showed that the streaming has a destabilizing effect and the electric field has stabilizing influence associated with parameters condition involving the electric conductivity and permittivity of the fluids. While the non-linear approach indicated that the streaming may become unstable for sufficiently high velocities, with a new condition on the material properties, involving weak electric relaxation times in both fluids.

Nonlinear waves on the surface of a dielectric liquid in a strong tangential electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope angles. It is established that the equation can be solved for liquids with sufficiently high values of the permittivity. This makes it possible to describe the interaction of the counter-propagating waves.

Resonant absorption of shear instabilities in flow systems with energy dissipation

It is shown that hydrodynamic and electrohydrodynamic waves excited in two-layer dissipative systems due to shear instabilities experience resonant absorption of two types: at the rotational frequency of particles of the medium and the frequency of their collision with the lattice.

Generation of electrohydrodynamic waves at the liquid-vacuum interface

The linear electrodynamic problem of the stability of a viscous liquid surface at the liquid-air interface is studied in view of the surface charge kinetics. The electric field critical intensities which break the stability of the plane interface are determined. Conditions for generating sustained waves at the interface are found.

Waveguide propagation of internal electrohydrodynamic waves in heterojunctions

We analyze the propagation of internal electrohydrodynamic waves, which were predicted for impurity semiconductors with a free-carrier density gradient, in an isotypic n-n+ heterojunction.

Interaction of contact electrohydrodynamic waves in current-carrying semiconductors

It is shown that contact electrohydrodynamic waves similar to the waves on an interface between two immiscible liquids can exist on an interface between two identical semiconductors with different concentrations of free charge carriers. When a current flows, instabilities of such waves, particularly an analog of the Kelvin-Helmholtz hydrodynamic instability, appear in one of the layers. The possibility of practical utilization of contact waves interacting with currents is discussed.

On the stability of shock waves in a continuous medium with a space charge

The stability of shock waves is discussed for a hydrodynamic model of motion of a continuous medium with a space electrical charge. The correctness of a mixed problem obtained by linearization of the hydrodynamic model and the equations of a strong discontinuity for electrohydrodynamic shock waves is proved. As is known, this indicates stability of this type of strong discontinuity in the model of a continuous medium considered.

Contact electrohydrodynamic waves of free charge carriers at the interface of two semiconductor layers

It is shown that electrohydrodynamic waves similar to gravity waves at the interface of two liquids can propagate in a semiconductor structure composed of two semiconductor layers with different charge carrier densities and placed in a transverse electric field. The conditions for existence of such waves are specified. The linear and nonlinear modes of wave propagation are studied.

Electrodynamics of midlatitude spread F 3. Electrohydrodynamic waves? A new look at the role of electric fields in thermospheric wave dynamics

The study of atmospheric tides has long recognized the importance of electrodynamic or ohmic losses, in the form of forces, on the strength of winds in the Earth's upper atmosphere. Now, recent observations of ionospheric and atmospheric phenomena (particularly, but not exclusively, at midlatitudes) are suggesting that electrodynamic processes may also be important for atmospheric buoyancy waves with periods as short as a few hours. During the daytime, passive ohmic losses may be responsible for a strong azimuthal filtering of buoyancy waves which limits their propagation in the upper atmosphere to near equatorward where there is a minimum of the drag. At night, the active development of plasma instabilities, whose growth rate is also strongly azimuthally dependent, may not only minimize ion drag but may also feed energy into particular buoyancy waves to counteract the nighttime's enhanced molecular and thermal dissipation, thus creating a strong equatorward and westward orientation to observed traveling ionospheric disturbances. In all, the strength of the apparent coupling between buoyancy waves and ionospheric electrodynamics in the upper atmosphere may suggest the classification and study of a new form of electrohydrodynamic waves.

Nonlinear electrohydrodynamic waves on films falling down an inclined plane.

The stability of a perfectly conducting viscous film, falling down an inclined plane, is considered for the case of an applied uniform normal electric field. A highly nonlinear evolution equation for the deformation of the free surface of the film is derived. The study of the linear stability of the system shows the destabilizing effect of the electric forces. A weakly nonlinear analysis leads to a Ginsburg-Landau equation, which predicts that the destabilization induced by the electric field in an otherwise stable film occurs in the form of traveling waves of finite amplitude.