H. González

Stabilization of dielectric liquid bridges by electric fields in the absence of gravity

The stability of liquid bridges in zero gravity conditions under the influence of an a.c. electric field tangential to the interface is examined in this paper. For the theoretical study, a static analysis was carried out to find the bifurcation surfaces as a function of the three relevant non-dimensional parameters: Λ, the slenderness or ratio of height to diameter of the cylindrical bridge; β 0 , the ratio of dielectric constants of the two fluids used and Ξ, a non-dimensional quantity proportional to the applied voltage. Stable and unstable regions of Λ−β o −Ξ space were distinguished. Results indicate a strong stabilizing effect for higher values of β 0 . The experimental study, using silicone and ricinus oil to approximate zero gravity conditions fully confirmed quantitatively the theoretical results.

The measurement of growth rates in capillary jets

The growth of perturbations on a capillary jet issuing from a circular nozzle in the Rayleigh regime is experimentally investigated. Electrohydrodynamic sinusoidal stimulation is employed to this end, along with two independent methods to obtain growth rates of the linear regime with the best accuracy so far. The first method exploits the correlation between the stimulation voltage and the breakup time measured with the help of stroboscopic images of the jet. The second method is an analysis of the spatial evolution of perturbations through a local jet-shadow-width photometry, with careful avoidance of the initial transient and the final nonlinear stages. Experiments conducted with ink allow the application of both methods, as the liquid is opaque. They give consistent results, with very small statistical errors, with respect to the expected theoretical dispersion relation, once the dynamic surface tension is adjusted. The adjusted value is in accordance with an estimate made from drop-dynamics experiments also reported here. By dealing with a simpler liquid (aqueous solution of NaNO 3 ), we are able to compare results from the first method against the theoretical predictions without adjustment of any parameter. The agreement is again excellent. Possible sources of systematic errors in this kind of measurements are identified and procedures for avoiding them are designed.

EXPERIMENTS ON DIELECTRIC LIQUID BRIDGES SUBJECTED TO AXIAL ELECTRIC FIELDS

Experimental determination of the critical axial electric field needed to hold a nonconducting liquid bridge of given slenderness is presented. The Plateau tank technique is used to minimize gravity forces on earth. Improvement of previous data is achieved by determining the gravitational Bond number. The results are compared to numerical calculations of the stability limits, showing a good agreement.

The effect of residual axial gravity on the stability of liquid columns subjected to electric fields

The stability criterion for almost cylindrical dielectric liquid bridges subjected to axial electric fields in the presence of residual axial gravity is obtained. In its absence, a perfectly cylindrical equilibrium solution is allowed for all values of the relevant parameters, which are the slenderness of the liquid bridge, the electrical Bond number and the relative permittivity between the outer and inner media. This basic solution is unstable beyond a critical slenderness which varies with the electrical parameters (Gonzblez et al. 1989). The destabilization takes place axisymmetrically. The inclusion of the gravitational Bond number as a new, small parameter may be treated by means of the Lyapunov-Schmidt Method, a wellknown projection technique that gives the local bifurcation diagram relating the admissible equilibrium amplitudes for the liquid bridge and the aforementioned parameters. As in the absence of applied electric field, the gravitational Bond number breaks the pitchfork diagram into two isolated branches of axisymmetric equilibrium solutions. The stable one has a turning point whose location determines the new stability criterion. Quantitative results are presented after solving the resulting set of linear recursive problems by means of the method of lines.

Normal-mode linear analysis and initial conditions of capillary jets

The normal-mode linear analysis of an axisymmetric infinite capillary jet is generalized to account for arbitrary initial conditions. An exhaustive study of the dispersion relation reveals the parametric behaviour of all eigenvalues and their corresponding normal modes. The two capillary modes (dominant and subdominant) are found to be necessary and sufficient to describe any possible non-recirculating initial conditions. An infinite set of other modes accounts for initial conditions with recirculating velocity field. The predictions of the normal-mode analysis are contrasted against previous computations of the initial-value problem, previous experiments, and our own one-dimensional numerical simulations. Contrary to the claim of some authors, the normal-mode analysis accurately predicts the initial transient with non-exponential growth of the disturbance amplitude observed in previous works. Simple and accurate formulae for the duration of the initial transient are deduced, with emphasis on improving the growth-rate measurement.

Stability analysis of conducting jets under ac radial electric fields for arbitrary viscosity

A temporal linear modal stability analysis is presented for conducting viscous liquid jets flowing with nonzero velocity relative to an ambient gas and subjected to an ac radial electric field. Parametric resonance between natural dc frequencies and the frequency (or multiple) of the imposed ac field eventually leads to destabilization of the jet for perturbations with wave numbers in the stable domain. In this way, it is possible to obtain drops of smaller size. The main result is the extension of the stability analysis to liquids of arbitrary viscosity using a dynamical approach, instead of previous variational models valid for slightly viscous liquids. The effect of the outer gas in relative motion is taken into account in the framework of currently available semiempirical theories. A brief discussion of the dispersion relation for dc fields is included as the natural starting point for the discussion of the ac case. Use of the 1-D averaged model for axisymmetric perturbations, an alternative to the 3-...

Parametric instability of conducting, slightly viscous liquid jets under periodic electric fields

Abstract A temporal, linear, modal stability analysis is presented for conducting liquid jets in air subjected to time periodic electric fields. The field is originated by a mixed ac-dc potential difference between the jet and a long coaxial cylindrical electrode. As a result of the Lagrange function formalism a governing equation for the time dependent amplitude of deformation is obtained. Slightly viscous liquids may be also described by the model. The stability is obtained by inspection of the Floquet exponents of the solutions. We extend previous results for dc voltages with a discussion on the observability of parametric resonances arising in the small wavelength region of the spectrum, a region that would be stable under dc fields.

The effect of an axial electric field on the stability of a rotating dielectric cylindrical liquid bridge

The branching points of the shape families bifurcating from a cylindrical liquid bridge anchored on two plane‐parallel electrodes, when subjected to rotation and an electric potential difference, are determined. It is shown that the cylindrical shape may be destabilized through either an axisymmetric mode or a C mode. The stable region in the parameter space is always enlarged as the electric field is increased.

Influence of bounded geometry on the initial growth of electrocapillary instability for a liquid metal under electric field

Abstract The deformation of an initially plane liquid metal surface by a normal electric field is known and analyzed since the works of Tonks, Frenkel, Taylor, Melcher, etc. It has been established that until a critical value of the field no destabilization occurs (the surface remains flat) while above this onset a peak pattern with defined wavelength appears where wavelength and the critical field depend on physical values of the liquid. For higher fields a whole band of wavelengths is unstable and a linear analysis of the first stage of the peak growth can show which wavelength dominates. Nevertheless, these works deal with large horizontal geometries. The influence of bounded geometry lead to modifications of the onset values that can be found thanks to a static analysis. This means that they are independent of the viscosity and of the geometry of the bath walls. In this paper we show how the initial deformation evolves (dynamical analysis) in confined geometry. The chosen geometry is a cylindrical liquid bath with the liquid anchored at the circular contact line and with constant volume. Both these assumptions being necessary to allow the growth of a pattern. The liquid is supposed to be inviscid as most liquid metals are.

Stability of inviscid conducting liquid columns subjected to a.c. axial magnetic fields

The natural frequencies and stability criterion for cylinderical inviscid conducting liquid bridges and jets subjected to axial alternating magnetic fields in the absence of gravity are obtained. For typical conducting materials a frequency greater than 100 Hz is enough for a quasi-steady approximation to be valid. On the other hand, for frequencies greater than 105 Hz an inviscid model may not be justified owing to competition between viscous and magnetic forces in the vicinity of the free surface. The stability is governed by two independent parameters. One is the magnetic Bond number, which measures the relative influence of magnetic and capillary forces, and the other is the relative penetration length, which is given by the ratio of the penetration length of the magnetic field to the radius. The magnetic Bond number is proportional to the squared amplitude of the magnetic field and inversely proportional to the surface tension. The relative penetration length is inversely proportional to square root of the product of the frequency of the applied field and the electrical conductivity of the liquid. It is shown in this work that stability is enhanced by either increasing the magnetic Bond number or decreasing the relative penetration length.