James R. Melcher

Dynamics and stability of ferrofluids, surface interactions

The non-linear magnetization characteristics of recently developed ferrofluids complicate studies of wave dynamics and stability. A general formulation of the incompressible ferrohydrodynamics of a ferrofluid with non-linear magnetization characteristics is presented, which distinguishes clearly between effects of inhomogeneities in the fluid properties and saturation effects from non-uniform fields. The formulation makes it clear that, with uniform and non-uniform fields, the magnetic coupling with homogeneous fluids is confined to interfaces; hence, it is a convenient representation for surface interactions. Detailed attention is given to waves and instabilities on a planar interface between ferrofluids stressed by an arbitrarily directed magnetic field. The close connexion with related work in electrohydrodynamics is cited, and the effect of the non-linear magnetization characteristics on oscillation frequencies and conditions for instability is emphasized. The effects of non-uniform fields are investigated using quasi-one-dimensional models for the imposed fields in which either a perpendicular or a tangential imposed field varies in a direction perpendicular to the interface. Three experiments are reported which support the theoretical models and emphasize the interfacial dynamics as well as the stabilizing effects of a tangential magnetic field. The resonance frequencies of ferrohydrodynamic surface waves are measured as a function of magnetization, with fields imposed first perpendicular, and second tangential, to the unperturbed interface. In a third experiment the second configuration is augmented by a gradient in the imposed magnetic field to demonstrate the stabilization of a ferrofluid surface supported against gravity over air; the ferromagnetic stabilization of a Rayleigh-Taylor instability.

Traveling‐Wave Induced Electroconvection

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.

ELECTROHYDRODYNAMIC CHARGE RELAXATION AND INTERFACIAL PERPENDICULAR FIELD INSTABILITY.

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 i...

Traveling‐Wave Bulk Electroconvection Induced across a Temperature Gradient

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.

Continuum properties from interdigital electrode dielectrometry

Using a modal approach, a model is derived that makes the interdigital electrode microdielectrometer developed by S. D. Senturia et al. (J. Adhesion, vol.15, p.69-90, 1982) applicable to measuring continuum parameters in a wide range of heterogeneous media. In this so-called imposed omega -k technique, the medium is excited at the temporal (angular) frequency omega by means of an interdigital electrode structure having a spatial periodicity length lambda =2 pi /k and hence a dominant wavenumber k. Given the surface capacitance density C( omega , k) of any linear system having property gradients perpendicular to the plane of the electrodes, the model predicts the complex gain, taking into account the properties, geometry, and terminal configuration of the interdigital electrode structure. This capability can then be used with an appropriate parameter estimation strategy to determine the continuum properties and/or geometry of the medium. Examples illustrating the application of the technique are presented. >

INTERFACIAL RELAXATION OVERSTABILITY IN A TANGENTIAL ELECTRIC FIELD.

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 Alfven 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...

Electrohydrodynamics of a current-carrying semi-insulating jet

A quasi-one-dimensional non-linear model is developed for the axisymmetric dynamics. Streaming is coaxial with a cylindrical ‘wall’ supporting a potential having a linear axial dependence. In addition to a tangential field due to an axial current, the stream surface supports charges in proportion to the stream-wall potential difference; hence it is driven by normal and shear electric stresses. Free charge and polarization waves compete with the destabilizing effect of capillarity. With supercritical steady flow (the local jet velocity exceeds the wave velocity), it is found that the stream accelerates or decelerates in accordance with whether an equivalent longitudinal force density is respectively positive or negative. With subcritical flow, the effect of the force is reversed. Experiments demonstrate accelerating and decelerating flow regimes. Model and experiment are in agreement with regard to choking at a critical radius, and the dependence of radius and potential on position. Hysteretic switching between flow regimes is obtained by adjustment of stream and wall potentials, and is explained in terms of the model.

Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients

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/e E 2 . 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.

Electrohydrodynamic and Magnetohydrodynamic Surface Waves and Instabilities

Low‐frequency dynamics of a plane fluid interface stressed by tangential or perpendicular electric or magnetic fields is studied emphasizing the duality of the magnetic and electric cases. Both configurations are shown to be controlled by an effective Alfven velocity for the magnetic cases, and by an electrohydrodynamic dual to this velocity for the electric cases. A wavelength and threshold for instability are predicted for a surface stressed by a perpendicular field, and correlated with experimental results. This makes possible a critical experiment to determine the nature of interfacial electrostriction in dielectrics. A dielectric interface stressed by a tangential electric field supports incompressible electrohydrodynamic transverse waves that propagate along the lines of electric field intensity at a velocity strongly influenced by interfacial electrostriction. Experimental results indicate the existence of such waves.

Fluid electrification measurements of transformer pressboard/oil insulation in a Couette charger

A Couette charger (CC) facility has been built to simulate flow electrification processes in transformers where transformer oil fills the annulus between coaxial cylindrical electrodes. Transient measurements with a step change in temperature have shown the charge density to change from an initial value to a new steady-state value, including cases of polarity reversal, both values dependent on the equilibrium moisture levels in oil and pressboard. Through a model that accounts for diffusion of charge from the paper-oil interface into the bulk of the oil, these measurements are used to deduce the equilibrium wall charge density. To help understand the effects of energization and to scale laboratory measurements at low voltages and low frequencies to operating transformers, a charge injection model was refined to examine the migration of double layer and injected charge in the imposed sinusoidally time-varying electric field. Good fits between this model and measurements are achieved. >