J. Fernandez de la Mora

The current emitted by highly conducting Taylor cones

When a liquid meniscus held at the exit of a metallic capillary tube is charged to a high voltage V , the free surface often takes the form of a cone whose apex emits a steady microjet, and thus injects a certain charge I and liquid volume Q per unit time into the surrounding gas. This work deals with liquids with relatively large conductivities K , for which the jet diameter d j is much smaller than the diameter d n of the capillary tube. In the limit d j / d n → 0, the structure of the jet ( d j and I , in particular) becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the measured current is given approximately by I = f (e) (γ QK /e) ½ for a wide variety of liquids and conditions (e, and γ are, respectively, the dielectric constant of the liquid and the coefficient of interfacial tension; f (e) is shown in figure 11). The following explanation is proposed for this behaviour. Convection associated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distribution slightly at distances r from the apex large compared to a certain charge relaxation length λ, but substantially when r ∼ λ. When the fluid motion is modelled as a sink flow, λ is of the order of r * = ( Q ee 0 / K )

Generation of monodisperse droplets 0.3 to 4 μm in diameter from electrified cone-jets of highly conducting and viscous liquids

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Source of heavy molecular ions based on Taylor cones of ionic liquids operating in the pure ion evaporation regime

(e 0 is the electrical permittivity of vacuum). If, in addition, the surface charge density is described through Taylors theory, the corresponding surface current convected towards the apex scales as I s ∼ (γ QK /e) ½ , as observed for the spray current. The sink flow hypothesis is shown to be realistic for sufficiently small jet Reynolds numbers. In a few photographs of ethylene glycol cone jets, we find the rough scaling d j ∼ 0.4 r * for the jet diameter, which shows that the jet forms as soon as charge relaxation effects set in. In the limit e [Gt ] 1, an upper bound is found for the convected current at the virtual cone apex, which accounts for only one-quarter of the total measured spray current. The rest of the charge must accordingly reach the head of the jet by conduction through the bulk.

The effect of charge emission from electrified liquid cones

The size distributions of droplets emitted from Taylor cones operating in the cone-jet regime are measured by sampling their electrosprays into an aerodynamic size spectrometer (APIs Aerosizer). The sizing scheme is not affected by the large charge on the un-neutralized droplets in the range of diameters d explored, 0.3 μm < d < 4 μm. The diameters of the droplets electrosprayed from highly conducting liquids are found to be relatively insensitive to electrostatic variables, depending for a given liquid mostly on the flow rate Q pushed through the jet. At fixed Q, the size distributions consist of one or several fairly monodisperse classes of droplets with diameters di(Q); i = 1, 2, …, N(Q). Near the minimum flow rate Qmin at which the cone is stable, the spray tends to consist of “primary” and “satellite” droplets only, with N = 2. However, at larger flows, the modality of the distributions (N) increases. The largest size mode bifurcates into two branches at a critical flow rate Q1, coinciding with the onset of lateral oscillations of the jet. The diameter d1 of the largest drops scales approximately with r∗=(Qτ)13, where τ is the electrical relaxation time of the fluid. Surprisingly, all the other size classes have diameters di (i ≠ l) nearly independent of flow rate, which scale as dmin = (γτ2/ρ)13 (γ= coefficient of surface tension; ρ=liquid density). Although the jet diameter dj appears to be unaffected by viscosity, its breakup mechanism, and thus the diameters di of all the droplet classes, do depend on the viscous parameters Πμ (μ = coefficient of viscosity of the liquid). The diameters of the smaller droplets are given by functions didmin=Gi(Πμ) (i ≠ 1), which depend steeply on Πμ for values of this parameter below 0.06, but appear to level off above Πμ=0.15. An inviscid asymptote, in which d1r∗=F(η), is approached also for d1 for sufficiently large values of Πμ where η2=ρQγτ. F is nearly constant below the bifurcation, and seems to tend to the asymptote F=0.43 η23 at large η, in qualitative agreement with the behavior of dj(Qτ)13 given by Fernandez de la Mora and Loscertales (J. Fluid Mech. 260, 155–184, 1994). It follows from the scaling laws found that, by varying the electrical conductivity of a given liquid, it should be possible to generate monodisperse droplets with initial diameters of the order of dmin, which may span the whole range between 100 μm down to a few nanometers. The flow rate must, however, be between Qmin and its value at the bifurcation, which requires that η ∼ 1.

Sizing nanoparticles and ions with a short differential mobility analyzer

The full spray emitted by Taylor cones of the ionic liquid 1-ethyl-3-methyl imidazolium tetrafluoroborate (EMI+BF4−) held in a vacuum is investigated at room temperature by time of flight mass spectrometry. The current is composed mainly of ions under most conditions studied, but contains a small component of nanometer drops that tends to dominate the emitted mass flow. Exceptionally, drop ejection vanishes close to the smallest flow rate at which the Taylor cone is steady. The present discovery of a stable strictly ionic regime in Taylor cones of substances other than liquid metals owes much to earlier observations with sulfuric acid, where most but not all the current was ionic. Most striking is the fact that this purely ionic regime is obtained at an electrical conductivity K of only 1.3 S/m, much smaller than that of sulfuric acid, and smaller than that at which formamide electrolytes with K>2 S/m do still emit substantial drop currents. The ion emission includes primarily the dimer (EMI–BF4)EMI+, acc...

Differential mobility analysis of molecular ions and nanometer particles

The formation of stable cones in electrified liquid interfaces was explained by Taylor as a balance between electrical and capillary tensions, where the electrostatic potential varies as ϕ ∼ r½ with the distance r from the cone tip. Although Taylors predictions for the dependence of the onset voltage for cone formation on the liquid surface tension γ and the cone dimensions agree with observed trends, his conclusion that the cone semiangle α can only take the value α = αT = 49.3° does not. A more general theory free from this paradox is constructed for highly conducting fluids by accounting for the space charge of the droplets emanating from the cone apex, whose potential has the remarkable property of also obeying Taylors r½ law. In this formulation, where the apex of a conical meniscus of semiangle α emits an angularly uniform opposed coaxial conical spray of semiangle π—β, both β and the spray current I turn out to be fixed as functions of α; namely, β = β(α), and I = 2πγKqG(α), where Kq and q are the droplets electrical mobility and total charge, respectively. In experiments with 5% H2SO4 in 1-octanol, the observed sprays are approximately conical with an apex nearly touching the meniscus tip. The measured and predicted β(α) relations are in reasonable agreement in the range 46° > α > 32°, where the liquid cone is stable and the spray is visible, though the data fall clearly below the theoretical curve. The predicted spray current I is also in rough agreement with preliminary experiments. The analysis applies neither to sprays of large droplets with significant inertia, nor to liquid cones in vacuo.

Aerodynamic focusing of particles in a carrier gas

An analysis of the effects of diffusion in differential mobility analyzers (DMAs) at high Peclet number (Pe) shows that the associated peak broadening may be greatly reduced when the axial separation between entrance and exit slits is comparable to the inter-electrode gap. This prediction is verified in a shortened version of Reischls DMA using molecular ions from an electrospray source. Gaussian peaks with relative full width at half maximum as small as 0.066 are observed at a DMA Reynolds number of 1190 in the mobility spectra of (butyl) 4 N + ions in air (Pe = 10 4 ). After correcting for the broadening effect of the aerosol flow rate and the sampling slit width, the predicted diffusive peak widths agree well with those observed, but only at the highest resolutions. The DMA described here is the first one able to measure with excellent resolution the mobilities of particles down to 1 nm in diameter, and even of molecular ions.

Direct measurement of ion evaporation kinetics from electrified liquid surfaces

Abstract Differential mobility analyzers (DMAs) can classify a steady and narrowly monomobile stream of charged particles from a continuum spectrum of electrical mobilities. This feature has been widely exploited in aerosol research involving particles larger than some 10 nm. But high losses and low resolution due to Brownian diffusion have traditionally impaired DMA use for smaller particle sizes. These aerosol instruments have thus been poor competitors with time of flight drift tubes for mobility-based analysis of molecular ions and clusters. Recently, however, these problems have been overcome. Specially designed and run DMAs can now supply a pure and steady stream of molecular ions or clusters in a gas by classification from a complex ion mixture. The potential of such devices for investigations involving ions and nanoparticles is illustrated through various examples of recent work.

Experiments on the kinetics of field evaporation of small ions from droplets

The problem of whether a stream of microscopic particles may be concentrated into a focal point by entrainment within a carrier gas is considered for dilute particles linearly coupled to the velocity field of an incompressible gas. Typically, the dynamical behaviour of the particles is governed by a so-called Stokes number S , the product of their relaxation time and a characteristic value of the velocity gradient in the suspending fluid. An inequality due to Robinson (1956) is used to illustrate the natural tendency of potential flows to concentrate the particles. For geometries with planar or axial symmetry, with errors cubic in their initial distance to the axis, the trajectories of identical particles originating near an axis of symmetry are shown to cross it at a common focal point provided they have some initial convergence and their Stokes number is larger than a critical value S *. The position of the focal point of supercritical particles depends on their Stokes number, tending to infinity as S approaches S *. Particle trajectories originating far from the axis of symmetry are seen to cross the centreline at defocused positions, in analogy with the optical geometric aberration effect. The focusing phenomenon is illustrated numerically for two-dimensional potential flows through nozzles of several geometries and also analysed in the proximity of the axis of symmetry. For these examples, the threshold value S * of the Stokes number for focusing is of order one, over an order of magnitude larger than typical values of the familiar critical Stokes number marking the onset of particle impaction on solid surfaces. The focal width may be made over two orders of magnitude smaller than the nozzle diameter by restricting the region where particles are seeded to a moderate angle away from the axis. This angle may be higher than ¼π for the case of a jet exiting through a slit in an infinitely thin plate. There is also some discussion of the use of high-resolution focusing instruments.

Hypersonic impaction of ultrafine particles

When concentrated solutions of NaI in formamide with electrical conductivities K larger than 1.1 S/m are electrosprayed from a Taylor cone-jet in a vacuum, ions are evaporated at substantial rates from the surface of the meniscus and the drops. This constitutes a new source of ions and nanoparticles, where the relative importance of these two contributions is adjustable. The currents of ions are measured independently from those associated with drops by a combination of stopping voltage analysis and preferential scattering in a gas background. The magnitude E of the electric field at the surface of the drops and at the apex of the cone-jet is controlled through the electrical conductivity K of the liquid and its flow rate Q through the jet. E is related through available scaling laws for Taylor cone-jets to the ratios K/Q or I/Q, where I is the current of drops emitted by the jet. Ion currents are very small or null at typical K/Q values used in the past. A relatively small initial ion current is attribut...