Antonio Barrero

Current and droplet size in the electrospraying of liquids. Scaling laws

Measurements of the current and size of the primary droplets of sprays generated by electrostatic atomization of a variety of liquids with different electrical conductivities, permittivities, liquid-gas surface tensions, densities and viscosities have been carried out. Scaling laws of the spray current as well as the charge and size of the droplets have been obtained from a theoretical model of the charge transport. Comparisons between experimental and theoretical results are good. We have found that there are two different behaviours strongly related to the viscosity and electrical conductivity of the liquid. The separation between both behaviours is governed by the dimensionless parameter δμδ1/3=[ɛ02γ3/(K2μ3Q)]1/3; Q, μ, K, γ, and ɛ0 are the flow rate, viscosity, electrical conductivity, surface tension of the gas-liquid interface and vacuum permittivity, respectively. For liquids with high enough conductivities and viscosities (δμδ1/3 ≪ 1), the spray current and droplet size are approximately given by I/I0 = 6.2[Q/(β-1)1/2Q0]1/2 - 2.0 and d/(β-1)1/3d0 = 1.6[Q/ (β - 1)1/2Q0]1/3 - 1.0, where βɛ0 is the liquid permittivity and I0 = (ɛ0γ2/ρ)1/2,d0 = [γɛ02/(ρK2)]1/3 and Q0 = γɛ0/ρK are a reference intensity, droplet size and flow rate, respectively. In the opposite limit, we have found I/I0= 11.0(Q/Q0)1/4 - 5.0 and d/d0 = 1.2(Q/Q0)1/2 -0.3. Comparisons with experimental data reported in the literature are also satisfactory

Coaxial jets generated from electrified Taylor cones. Scaling laws

Abstract An experimental investigation on the electrified co-axial jets of two immiscible liquids issuing from a structured Taylor cone (Science 295 (5560) (2002) 1695) has been carried out. The structure of these almost conical electrified menisci consists of an outer meniscus surrounding an inner one. The liquid threads which issue from the vertex of each one of the menisci give rise to a two-concentric layered jet whose eventual breakup results in an aerosol of relatively monodisperse compound droplets with the outer liquid encapsulating the inner one. The effect of the flow rates of both liquids on the current transported by these coaxial jets and on the size of the compound droplets has been investigated. Several couples of liquids have been used to explore the influence on the spraying process of the properties of the liquids: i.e. the electrical conductivity K , dielectric constant β , interfacial tension of the liquid couple γ , viscosity μ , etc. We have found that the measurements of the current emitted through the coaxial jet when they are made dimensionless fit satisfactorily the current scaling law of regular electrosprays. Data of the mean diameter of the compound droplets have been obtained using a non-intrusive laser system. As expected the breakup process and therefore the droplet size are strongly dependent on the liquid viscosities and on the ratio of the liquid flow rates.

THE ELECTROSTATIC SPRAY EMITTED FROM AN ELECTRIFIED CONICAL MENISCUS

Abstract The electrostatic spray emitted from an electrified almost conical meniscus is analyzed in this work by means of a Lagrangian model using particle dynamics. Instead of solving the classical Poisson problem for the spray, we follow each one of the emitted particles and their mutual electrostatic interaction. The spray is shown to be dilute, allowing for essential simplifications on the particle aerodynamics. Computer simulations yield as many detailed spatial and statistical characterizations of the spray as one needs once the model is validated by actual experiments using laser-doppler anemometry and particle size analyzers also presented here. The experiments show that the theoretical model can predict not only the mean, but also the RMS of desired quantities such as droplet velocity and size at a certain point.

Zeroth-order, electrohydrostatic solution for electrospraying in cone-jet mode

Abstract Liquid and charge emissions in steady regime from an electrified meniscus take place when its shape develops an almost conical point. A very thin and remarkably stable capillary jet emerging from the conical vertex eventually breaks up into droplets, forming the so-called electrospray . The emission process is an extremely complicated electrohydrodynamic phenomenon which may be solved by performing a perturbation analysis which requires the knowledge of an electrostatic, zeroth-order solution for the shape of the electrified meniscus with a conical tip. In this work, the shape of these tip-ended, axisymmetric, electrified menisci is solved for the first time assuming negligible space charge. The solution of this first-order, electrostatic problem yields not only the backbone result on a further perturbation scheme to solve the liquid and charge emission process, but also the old problem of that value of the potential difference at which the liquid is to be connected in order to achieve a tip-ended shape, necessary to have electrostatic atomization, as a function of the liquid properties and boundary geometry.

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.

A novel pneumatic technique to generate steady capillary microjets

Abstract We report a novel technique to generate steady capillary microjets with diameters in the range of micrometric size. The microjet is driven by the aerodynamic suction of a highly accelerated coflowing gas stream. After undergoing capillary instability and breakup, these jets eventually yield remarkably monodispersed size aerosols in the micrometric range. Aerosol generators of this kind may have a wide range of applications in science and technology.

THE ROLE OF THE ELECTRICAL CONDUCTIVITY AND VISCOSITY ON THE MOTIONS INSIDE TAYLOR CONES

Abstract The role of the electrical conductivity and viscosity on the liquid motions inside Taylor cones has been investigated. The electrical conductivity plays an essential role since it determines the electric tangential stresses acting on the cone surface. Flow visualization shows that two different patterns of the liquid motion can be distinguished. One, for liquids with sufficiently high values of the electrical conductivity and viscosity which corresponds to small values of the Reynolds number and the other for less viscous and less conducting liquids for which the characteristic Reynolds number of the flow is larger than unity. Some theoretical models of the liquid motions are given and compared to the flow patterns observed in the laboratory.

Whipping instability characterization of an electrified visco-capillary jet

The charged liquid micro-jet issued from a Taylor cone may develop a special type of non-axisymmetric instability, usually referred to in the literature as a whipping mode. This instability usually manifests itself as a series of fast and violent lashes of the charged jet, which makes its characterization in the laboratory difficult. Recently, we have found that this instability may also develop when the host medium surrounding the Taylor cone and the jet is a dielectric liquid instead of air. When the oscillations of the jet occur inside a dielectric liquid, their frequency and amplitude are much lower than those of the oscillations taking place in air. Taking advantage of this fact, we have performed a detailed experimental characterization of the whipping instability of a charged micro-jet within a dielectric liquid by recording the jet motion with a high-speed camera. Appropriate image processing yields the frequency and wavelength, among the other important characteristics, of the jet whipping as a function of the governing parameters of the experimental set-up (flow rate and applied electric field) and liquid properties. Alternatively, the results can be also written as a function of three dimensionless numbers: the capillary and electrical Bond numbers and the ratio between an electrical relaxation and residence time.

Striking features of fluid flows in taylor cones related to electrosprays

Abstract For fluid flows inside and outside the Taylor conical meniscus related to electrosprays we adopt here a simplified model where the velocity field varies as 1/ r ; r is the distance from the cone apex. Such a dependence corresponds to the conical similarity class of exact solutions of the Navier-Stokes equations. This allows a detailed analysis of the problem and discovery of a number of striking features: (i) collapse—appearance of strong near-axis bipolar jets due to a cumulative effect of motion converging to the apex near the surface, (ii) vortex dynamo—generation of swirl as a result of bifurcation, (iii) vortex breakdown—internal separation of the swirling flow, (iv) splitting of the diverging flow into a few branches due to azimuthal instability, and (v) hysteretic transitions between regimes. The conical similarity can be, in particular, due to the electric Marangoni effect or Lorenz electromagnetic forces. We believe that the predictions of the similarity model can be also qualitatively valid for real flows in Taylor menisci because the above features are related to physical mechanisms that act as well in more general cases. So, in studying electrosprays, it is useful to keep in mind a possibility of the above effects.

Solution breakdown in a family of self-similar nearly inviscid axisymmetric vortices

Many axisymmetric vortex cores are found to have an external azimuthal velocity v, which diverges with a negative power of the distance r to their axis of symmetry. This singularity can be regularized through a near-axis boundary layer approximation to the Navier-Stokes equations, as first done by Long for the case of a vortex with potential swirl, v ∼r -1 . The present work considers the more general situation of a family of self-similar inviscid vortices for which v ∼r m-2 , where m is in the range 0 < m < 2. This includes Longs vortex for the case m = 1. The corresponding solutions also exhibit self-similar structure, and have the interesting property of losing existence when the ratio of the inviscid near-axis swirl to axial velocity (the swirl parameter) is either larger (when 1 < m < 2) or smaller (when 0 < m < 1) than an m-dependent critical value. This behaviour shows that viscosity plays a key role in the existence or lack of existence of these particular nearly inviscid vortices, and supports the theory proposed by Hall and others on vortex breakdown.