Interfacial Relaxation Overstability in a Tangential Electric Field

Abstract

It is well known that electromechanical polarization surface waves propagate along the lines of electric field intensity imposed tangential to the interface between perfectly insulating fluids. These waves have a stiffening effect on electrohydrodynamic equilibria that is analogous to that of the Alfvén surface waves on hydromagnetic equilibria. An investigation is presented of the dynamical effects of charge relaxation on these waves. A self-consistent model represents the relaxation in terms of an Ohmic conduction process in the bulk of the fluids, with surface shears induced by the free interfacial charges placed in dynamic equilibrium by viscous stresses. The dominant effect of the charge relaxation is to produce overstability. Experiments are described where this instability appears as a spontaneous oscillation of the interface with wavenumbers directed along the lines of electric field intensity. Detailed analytical results are given for liquid-gas and liquid-liquid interfaces. The field required to produce incipient instability and the propagation direction of the observed instability are satisfactorily predicted. It is found that in this liquid-vapor case, relatively simple explicit expressions can be given for the incipient instability conditions. A discussion is given of the significance of this work for the dielectrophoretic orientation of liquids in the zero-gravity environments of space.

Convective and absolute electrokinetic instability with conductivity gradients

“…Electrohydrodynamic instability has been a subject of extensive research since Taylor and Melcher's pioneering leaky dielectric model (Melcher & Taylor 1969;Saville 1997). The core of the leaky dielectric model is the Ohmic model, and the essence of the electrohydrodynamic instability mechanism is charge accumulation at material interfaces and its coupling to fluid motion through electric body forces (see, for example, Melcher & Schwartz 1968;Hoburg & Melcher 1976). The natural velocity scale in this instability is the electroviscous velocity that results from a balance between the viscous and electric stresses (Melcher 1981).…”

Space-Charge Dynamics of Liquids

“…We have already introduced the convention of the total linear changes in the potential at the interfaces as given by (20) and (21).…”

“…We recognize (18) and (19) as linear constant-coefficient difference equations, for which we assume solutions of the form (20) n Yn = Yn xn = XXn (21) We define the parameter and substitute our assumed form of solution into (13) and (14) For non-trivial, solutions to (23) and (24), the determinant of the coefficients must be zero, for which we obtain …”

Interfacial instability in electrified plane Couette flow

“…They considered a constant electric field applied in the plane of the undisturbed interface and analyzed the linear stability of the twophase systems showing that the influence of the electric field is a dispersive regularization of short waves. Melcher & Schwarz (1968) also pointed out that the electric field produces net surface forces due to the polarization that tend to disrupt the interface and they studied the effect of an electric field on the linear stability separating two non-conducting dielectric fluids of infinite extent. They established that the electric field stabilizes and increases the propagation speed of surface waves.…”

“…The case of two superposed conducting or non-conducting fluids was examined by Melcher & Schwarz (1968). They considered a constant electric field applied in the plane of the undisturbed interface and analyzed the linear stability of the twophase systems showing that the influence of the electric field is a dispersive regularization of short waves.…”