F. J. García

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.

On the breakup of slender liquid bridges: Experiments and a 1-D numerical analysis

Abstract Slender axisymmetric dielectric liquid bridges are made stable by the action of an axial electric field. In this paper, the subsequent dynamics of a slender liquid bridge after turning off the electric field is considered. The evolution in time of the bridge profile is investigated both theoretically and experimentally. A one-dimensional model is used to simulate the dynamic response of the system. Experiments are performed applying an axial electric field to a liquid bridge of 1 mm of diameter, and turning-off the electric field. The evolution of the liquid bridge is recorded using a video camera, and the digitized images are analysed. Good agreement between computations and experiments is found.

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.

Dynamics and deformation of a drop in a DC electric field

We consider a single conducting drop in suspension in a poorly conducting liquid between two horizontal electrodes. When a DC field is applied to the electrodes, the drop charges and rises within the liquid, then falls down as its charge leaks away, due to the finite electric relaxation time of the liquid. The drop keeps bouncing as long as the high voltage applied remains above a minimum threshold. We focus our study on the dynamics and the deformation of a water drop before the lift-off and during its motion. Electrodes of different materials are used in order to illustrate the role of interfacial energy between the electrode and the water.

Pattern imaging of primary and secondary electrohydrodynamic instabilities

A little known electrohydrodynamic instability, which we call a rose window, is observed in air/liquid interfaces in electric fields with unipolar space charge distributions. Depending on the liquid properties, the rose window may appear from an initial rest state (primary instability) or on top of another instability, the classical unipolar-injection-induced instability, destroying its pattern (secondary instability). After imaging of the rose window, we use an edge-detection filter to find the instability threshold and study the characteristic pattern as a function of the liquid properties. Results show that the specific properties of the electric field, due to charge injection, are the cause of the rose-window and that the primary and secondary rose windows are essentially different instabilities.

Perpendicular-field EHD instabilities visualized in a tip-plane configuration

EHD interfacial instabilities can be induced by corona discharge from a tip electrode onto a liquid-air interface. The corona current charges the liquid surface and instabilities may appear depending on the applied voltage and the liquid properties. We present a technique to detect the onset of instability based on image processing. To establish the instability threshold we apply an edge-detection algorithm to images of the liquid surface acquired through a video camera.

Dynamics of slender viscous dielectric liquid bridges subjected to axial AC fields

Abstract An analysis of slender axisymmetric liquid bridges is performed on the basis of one-dimensional models recently derived, and generalized here to include the effect of dielectric forces at the interface. The natural frequencies and stability criteria in the absence of gravity are obtained. In the inviscid case, results are compared with the known exact linear solutions of the corresponding three-dimensional problem.

Spatial modes in one-dimensional models for capillary jets

One-dimensional (1D) models are widely employed to simplify the analysis of axisymmetric capillary jets. These models postulate that, for slender deformations of the free surface, the radial profile of the axial velocity can be approximated as uniform (viscous slice, averaged, and Cosserat models) or parabolic (parabolic model). In classical works on spatial stability analysis with 1D models, considerable misinterpretation was generated about the modes yielded by each model. The already existing physical analysis of three-dimensional (3D) axisymmetric spatial modes enables us to relate these 1D spatial modes to the exact 3D counterparts. To do so, we address the surface stimulation problem, which can be treated as linear, by considering the effect of normal and tangential stresses to perturb the jet. A Greens function for a spatially local stimulation having a harmonic time dependence provides the general formalism to describe any time-periodic stimulation. The Greens function of this signaling problem is known to be a superposition of the spatial modes, but in fact these modes are of fundamental nature, i.e., not restricted to the surface stimulation problem. The smallness of the wave number associated with each mode is the criterion to validate or invalidate the 1D approaches. The proposed axial-velocity profiles (planar or parabolic) also have a remarkable influence on the outcomes of each 1D model. We also compare with the classical 3D results for (i) conditions for absolute instability, and (ii) the amplitude of the unstable mode resulting from both normal and tangential surface stress stimulation. Incidentally, as a previous task, we need to re-deduce 1D models in order to include eventual stresses of various possible origins (electrohydrodynamic, thermocapillary, etc.) applied on the free surface, which were not considered in the previous general formulations.

The breakup length of harmonically stimulated capillary jets

A simple transfer function that can predict the breakup length of a pressure-modulated capillary jet is rigorously deduced from first principles. In this paper, the initial velocity modulation of a stimulated jet is given in terms of its pressure amplitude by means of a generalized Bernoulli equation, which in turn is connected to the breakup time through a two-mode linear analysis. The predicted breakup length is compared against experimental results with water jets emerging from a thin 1 mm-diameter orifice for different pressure modulations. These experiments agree better with the presented theoretical prediction than with a previously established model.

Stability of insulating viscous jets under axial electric fields

Abstract The stability spectrum for a jet of perfectly insulating, viscous liquid subjected to a longitudinal electric field is obtained for axisymmetric perturbations. Both dielectric forces at the interface and viscous dissipation produce lower growth factors for all the range of unstable wavelengths. If the imposed field is time varying, parametric resonances are possible but they are easily suppressed, even by a small viscosity, and the r.m.s. value of the dielectric pressure dominates over the pulsating part.