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.
The small-amplitude motions of a plane interface between two fluids stressed by an initially perpendicular electric field are investigated. The fluids are modeled as Ohmic conductors and the convection of the surface charge caused by the dynamic interplay of interfacial electric shear stresses and the viscous stresses is highlighted. The influence of viscosity on instability growth rates in the zero-shear stress limits of perfectly conducting and perfectly insulating interfaces is described and compared to cases involving electrical shear stresses. Detailed attention is given to the instability of an interface between fluids having electrical relaxation times long compared to times of interest. It is shown that, for many common liquids, even a slight amount of surface charge makes the interface unstable at a considerably lower voltage than would be expected from theories based on the dielectrophoretic limit of no interfacial free charge. Experiments, performed using high-frequency ac stresses, gradually increased dc fields, and abruptly applied dc fields, support the theoretical model. In the general case, the electric Hartmann number is identified as an index to the dominance of the electric shear stresses over the viscous shear stresses in determining the interfacial convection of free charge.
investigated using quasi-one-dimensional models f o r the imposed f i e l d s i n which either a perpendicular o r a tangential imposed f i e l d varies i n a direction perpendicular t o t h e interface. Three experiments are reported which support t h e t h e o r e t i . c a l models and emphasize t h e i n t e r f a c i a l dynamics as w e l l as t h e s t a b i l i z i n g e f f e c t s of a t a n g e n t i a l magnetic f i e l d .surface waves are measured as a function of magnetization w i t h fields imposed first The effects of nonuniform f i e l d s areThe resonance frequencies of ferrohydrodynamic perpendicular, and second t a n g e n t i a l , t o t h e unperturbed interface. In a t h i r d experiment, t h e second configuration i s augmented by a gradient i n the imposed magnetic f i e l d t o demonstrate the s t a b i l i z a t i o n of a f e r r o f l u i d surface supported against gravity over a i r ; t h e ferromagnetic s t a b i l i z a t i o n ofARayleigh-Taylor i n s t a b i l i t y . a
The interface between two miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium tangential electric field is studied experimentally and theoretically. A bulk-coupled electrohydrodynamic instability associated with the diffusive distribution of fluid conductivity at the interface is experimentally observed.The configuration is modelled using a layer of exponentially varying conductivity spliced on each surface to a constant-conductivity fluid half-space. Over-stable (propagating) modes are discovered and characterized in terms of the complex growth rate and fastest growing wavenumber, with the conductivity ratio and an inertia-viscosity time-constant ratio as parameters. In the low inertia limit, growth rates are governed by the electric-viscous time τ = η/εE2. Instability is found also with the layer of varying conductivity bounded by rigid equipotential walls. A physical mechanism leading to theoretically determined fluid streamlines in the form of propagating cells is described.At relatively high electric fields, large-scale mixing of the fluid components is observed. Photocell measurements of distributions of average fluid properties demonstrate evolution in time on a scale determined by τ.
If a temperature gradient is imposed on a slightly conducting liquid, a gradient in natural electrical conductivity generally results. It is shown that if the liquid is then subjected to a wave of electric field traveling perpendicular to the temperature and conductivity gradients, charges are induced in the liquid bulk. These charges relax to form a traveling wave which interacts with the imposed field to pump the liquid. The sign of the conductivity gradient determines whether the liquid is pumped in the same direction or a direction opposite to that of the traveling wave. Equations are given for the velocity profile in plane flow, showing the effect of fluid properties as well as of the frequency, wavelength, and potential of the traveling wave. Experiments support the significance of the theory. Observations of a type of bulk Rayleigh-Taylor instability are discussed.
An electrohydrodynamic traveling-wave induction interaction is shown to pump slightly conducting liquids [electrical conductivities 10−5 to 10−15 (Ω·m)−1] without electrical contact with the flow. A gradient in fluid conductivity perpendicular to the direction of flow is required. Here, this is provided by a liquid interface, which is exposed to a traveling potential wave imposed by means of a segmented electrode parallel to the interface. Induced charges relax through the liquid to form a traveling wave of surface charge on the interface which lags the wave of image surface charges on the electrode. Hence, a time-average electrical surface traction is produced tending to make the fluid move with the traveling wave. Expressions for the fields, the time-average electric traction and the fluid velocity (in plane flow) are derived and discussed. Experiments illustrate the validity of these equations and tend to support the model used for the interfacial conduction process.
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