Alfonso M. Ganan-Calvo

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

THE SURFACE CHARGE IN ELECTROSPRAYING : ITS NATURE AND ITS UNIVERSAL SCALING LAWS

Abstract The electrospraying of liquids in steady cone-jet mode follows a well-defined EHD mechanism described and quantified in this work using a hybrid experimental–numerical technique: a collection of emitted microjet shapes corresponding to several liquids and different flow rates have been digitized and introduced in a quasi-one-dimensional analytical model. A universal value of the surface charge on the liquid microjet and the resulting charged droplets, independent of their size and of the liquid permittivity, has been found. The surface charge is shown to be always in equilibrium, being the liquid bulk quasi-neutral. From these findings, we finally present a consistent general scaling of all EHD variables involved which is experimentally verified. In this scaling, the electric current I and the characteristic microjet radius Ro are both proportional to the square root of the emitted flow rate, Q1/2, and independent of the liquid permittivity ei.

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.

On the theory of electrohydrodynamically driven capillary jets

Electrohydrodynamically (EHD) driven capillary jets are analysed in this work in the parametrical limit of negligible charge relaxation effects, i.e. when the electric relaxation time of the liquid is small compared to the hydrodynamic times. This regime can be found in the electrospraying of liquids when Taylors charged capillary jets are formed in a steady regime. A quasi-one-dimensional EHD model comprising temporal balance equations of mass, momentum, charge, the capillary balance across the surface, and the inner and outer electric fields equations is presented. The steady forms of the temporal equations take into account surface charge convection as well as Ohmic bulk conduction, inner and outer electric field equations, momentum and pressure balances. Other existing models are also compared. The propagation speed of surface disturbances is obtained using classical techniques. It is shown here that, in contrast with previous models, surface charge convection provokes a difference between the upstream and the downstream wave speed values, the upstream wave speed, to some extent, being delayed. Subcritical, supercritical and convectively unstable regions are then identified. The supercritical nature of the microjets emitted from Taylors cones is highlighted, and the point where the jet switches from a stable to a convectively unstable regime (i.e. where the propagation speed of perturbations become zero) is identified. The electric current carried by those jets is an eigenvalue of the problem, almost independent of the boundary conditions downstream, in an analogous way to the gas flow in convergent–divergent nozzles exiting into very low pressure. The EHD model is applied to an experiment and the relevant physical quantities of the phenomenon are obtained. The EHD hypotheses of the model are then checked and confirmed within the limits of the one-dimensional assumptions.

A new device for the generation of microbubbles

In this paper we present a new method for the production of bubble-liquid suspensions (from now on BLS) composed of micron-sized bubbles and with gas to liquid volume ratios larger than unity. We show that the BLS gas fraction λ=Qg/Ql, being Qg and Ql the flow rates of gas and liquid, respectively, is controlled by a dimensionless parameter which accounts for the ratio of the gas pressure inside the device to the liquid viscous pressure drop from the orifices where the liquid is injected to the exit, where the BLS is obtained. This parameter permits the correct scaling of the BLS gas volume fraction of all the experiments presented.

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.

On the general scaling theory for electrospraying

A systematic dimensional rationale is proposed here to analyse the electrohydrodynamic equations governing liquid electrospraying phenomena in the well-known steady cone-jet mode with no ambient discharges. As a result, a general, unified description of the complete parametrical space for the emitted current and droplet size is given. Four main distinct subspaces, their relevant boundaries and corresponding scaling laws are identified. Laws already proposed fit in their appropriate region, and previously unknown laws are found

ONE-DIMENSIONAL SIMULATION OF THE BREAKUP OF CAPILLARY JETS OF CONDUCTING LIQUIDS. APPLICATION TO E.H.D. SPRAYING

Nonlinear breakup of charged liquid jets is numerically analyzed in this work in the limit of a very small electrical Strouhal number Te/Tb≪1 (i.e. negligible charge relaxation effects, applicable to highly conducting liquids), where Te is the electric relaxation time of charges, and Tb is the breakup time in a Lagrangian framework following the liquid jet at its average axial velocity. The influence of the electrical Bond’s number and viscosity on (i) the capillary Rayleigh’s most probable breakup length, (ii) the breakup time, (iii) the volume of the satellite, and (iv) the charge of both main drop and satellite, are analyzed. The model is related to the microjet break-up phenomena in the electrospraying of liquids in steady cone-jet mode, and its range of applicability to those particular problems discussed. Previous experimental results [Mutoh et al., 1979, Convergence and disintegration of liquid jets induced by an electrostatic field. J. Appl. Phys. 50, 3174–3179; Clopeau and Prunet-Foch, 1989, Electrostatic spraying of liquids in cone-jet mode. J. Electrostatics 22, 135–159.] support our numerical finding that the influence of the electrical Bond’s number on Rayleigh’s length is small within the usual parametrical limits of stability of a steady Taylor cone-jet at atmospheric pressure.

Enhanced liquid atomization: From flow-focusing to flow-blurring

This letter describes the generation of small turbulence scales in connection with a singular back-flow pattern leading to efficient atomization. A simple pneumatic atomizer configuration results, with a tenfold efficiency increase over available plain-jet air-blast atomizers. Back-flow atomization derives from a global bifurcation of the liquid-gas flow pattern; the bifurcation is triggered by a single geometrical parameter of the atomizer. The extremely simple geometry involved can be implemented down to the micrometric scale, thus opening the door to the improvement of current atomizers and to unprecedented designs.

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.