Electrostatic spraying of liquids in cone-jet mode

Journal of Electrostatics, 22 (1989) 135-159 Elsevier Science Publishers B,V., Amsterdam - - Printed in The Netherlands

135

ELECTROSTATIC S P R A Y I N G OF LIQUIDS IN CONE-JET MODE

M. CLOUPEAU and B. PRUNET-FOCH

Laboratoire d'Adrothermique du CNRS, 4ter Route des Gardes, 92190 Meudon (France) {Received November 29, 1988; accepted December 12, 1988)

Summary Electrostatic spraying from a capillary is investigated in the case in which the droplets are formed by the breakup of a permanent jet extending from a volume of liquid in conical form. Domains of operation in this cone-jet mode have been determined after achieving good reproducibility of phenomena, which requires the effective control of multiple parameters. For a liquid of given conductivity, the jet diameter varies with the volume flow rate and the applied voltage, but only within a limited range whose extent depends in particular on the geometry of the capillary. Jet diameter and drop emission frequency measurements show that the energy minimization principle cannot be applied to this type of atomization; the ratio of the drop charge to Rayleigh limit charge varies greatly, depending on conditions. Several methods are indicated for reducing the droplet size differences, which are particularly noticeable when kink instabilities occur.

I.Introduction Electrostatic spraying can be observed by means of very simple apparatus. One needs only to apply a potential difference of a few thousand volts between a plate and the end of a capillary supplied with liquid under a pressure near zero (Fig. 1 ). Electrical forces exerted on the charges induced by influence on

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© 1989 Elsevier Science Publishers B.V.

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the meniscus at the end of the capillary cause the emission of charged droplets. These droplets may be neutralized if necessary by different methods. In ambient air, such a system is capable of furnishing droplets varying in size, depending on the conditions, from the millimetre to the submicron range. These spraying phenomena were described in 1915 by Zeleny [ 1,2 ], and after having been rediscovered by Vonnegut and Neubauer in 1952 [3], they have since been investigated by various authors in connection with different applications [4]. In vacuum, in which the electrical field on the surface of the liquid is not limited by the appearance of corona discharges, it is possible to produce very small droplets; for liquid metals, the system can even operate as an atomic or polyatomic ion emitter [5-8 ]. Many parameters are involved in this spraying process and, depending on their values, different modes of operation are obtained which correspond to the production of aerosols of different characteristics. In spite of considerable research, many difficulties remain in controlling the reproducibility of phenomena and the particle sizes of aerosols which are often polydispersed. Droplets of uniform size have been obtained regularly using "dripping" [9] and "harmonic spraying" [10] modes. However, the diameter of the droplets thus produced is greater than about 30 ~m. Similar results can nevertheless also be obtained by running the liquid under pressure through a very small orifice to form a jet whose rupture into droplets is regularized by means of mechanical vibrations; this method is used in ink-jet printers and for the production of standard aerosols. One of the objectives of our experimental study was to obtain, by electrostatic spraying, droplets having as uniform a size as possible and a diameter smaller than about 20 pm. The functioning mode offering the greatest possibility with respect to droplet dimensions and production frequencies is the one in which the meniscus takes the form of a cone extended at its apex by a jet whose breakup produces the droplets. The present paper deals with the conditions for obtaining this mode in ambient air, the phenomena that are detrimental to the regularity of drop emission, the characteristics of the drops produced, and the means of reducing the droplet size variations. 2. G e n e r a l

2.1 Earlier investigations At the end of the 19th century, Lord Rayleigh [11] calculated the electric charge beyond which a drop is no longer stable. This critical charge qR is reached when the electrostatic pressure PE directed outward balances the capillary pressure Pc directed inward. If ~D is the diameter of a spherical drop, 7 the surface tension of the liquid, e the dielectric constant of the ambient medium, we have:

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(c,d). qa = 2n (2E7~))1/2

(1)

Lord Rayleigh observed that the instability of a drop resulted in the emission of a liquid jet. The continuous production of drops by the breakup of a permanent jet extending from a meniscus in conical form (Fig. 2a) was investigated for the first time by Zeleny [1,2]. Vonnegut and Neubauer surely obtained the same mode during their first experiments [3 ] on liquids such as distilled water and alcohol. Assuming that the emitted droplets all have the same size, and that their surface and electrical energies are distributed so that they have a minimum sum, these authors established the following relationship between the chargeto-volume ratio q/v of a droplet and its diameter ~D:

q / v = 6 ( 2e?~g~ ) 1/2

(2)

The charge qv, or Vonnegut charge, deduced from this expression is equal to half the critical Rayleigh charge, qR. This theory was subsequently developed [ 12] by adding considerations of statistical mechanics to account for the distributions of sizes and charges in groups of droplets obtained under different conditions. However, the applicability of the energy minimization principle was contested by Krohn [ 13 ]. This question will be examined later (§5.1.2) in connection with the spraying method considered here.

2.2 Terminology. Conditions o[ existence Taylor [ 14 ] was the first to try to demonstrate theoretically, in a very special case, the existence of conical menisci; for this reason, the expression "Taylor cone" is often used. Other theoretical investigations have since been carried out on this subject [15-18]. The spraying mode associated with this particular form of meniscus was investigated by various authors [ 19-24 ] who gave it several designations. Mutoh et al. [22] used the expression "convergent jets", while Hayati et al. [24]

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spoke of "stable jet mode". For Smith [23], it is only to this mode that we should apply the term "electrohydrodynamic", a term often used in a more general sense [4,25]. In the absence of consensus, we shall use the compound word "cone-jet" which simply denotes the aspect of the meniscus without prejudging as to the stability of the jet and the way this configuration is maintained (cf.§4.1). Several authors have noted that this mode can be obtained in air only if the conductivity K of the liquid is between certain limits. For the lower limit, estimates generally vary between 10-s and 10-11 S/m. Much greater differences appear with respect to the upper limit. According to Mutoh et al. [22] the jet is no longer permanent, but simply intermittent, above 10 -~ S/m. Conversely, Smith [23] feels that there is no upper limit of conductivity, but that above 10-1 S/m, the produced droplets are so small that the light-scattering is too weak to be seen. According to our tests, the cone-jet mode can be effectively observed in air for a conductivity of 10-1 S / m when the liquid has a low surface tension. However, to our knowledge, there have been no experiments proving the absence of an upper limit of K. For Burayev and Vereshchagin [26], the most important parameter is the surface tension ~ of the liquid: if its value is too high, a triggering of corona discharges prevents electrostatic atomization. According to Smith [23], a liquid cannot be atomized in the cone-jet mode if its surface tension is greater than about 0.05 N / m . The limit is in fact higher. The cone-jet mode was obtained by several authors [2,20] with pure glycerin (y--0.063 N / m ) ; it may also be observed, though with more difficulty, with pure water (y=0.073 N / m). The differences mentioned above as examples stem especially from the fact that the limits of each parameter cannot be set independently of the values of all the other parameters. As it is not possible to explore all the combinations, differences are inevitably observed between the results obtained by each author under slightly different experimental conditions. 2.3 Variants When the potential difference between the capillary and the plate is gradually increased, variants of the cone-jet regime can be observed if the initiation of corona discharges does not lower the electric field on the surface of the meniscus or produce disordered movements of this surface. The jet begins by shifting laterally, with the meniscus losing its axial symmetry (Fig. 2b) or the jet splits up, with the meniscus forming two emissive cusps (Fig. 2c). Several emitting sites are then established around the end of the capillary (Fig. 2d). Their number increases with the applied voltage. This type of phenomenon makes it possible to obtain simultaneously a large number of jets on long circular or linear edges.

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In this multijet mode, it is difficult to obtain equal splitting up of the total volume flow between all the jets. This is an additional cause of the differences in droplet size. We shall be dealing here only with the case of a single jet coming from a capillary. 3. Experimental conditions and techniques

3.1 Droplet production Most of the tests were conducted with stainless steel capillaries having an outer diameter of 0.3-1 mm. Certain tubes were hot-drawn up to rupture; for an initial outer diameter of 0.3 mm, the diameter of the outlet section was then reduced to about 0.12 m m (Fig. 3). These capillaries were connected (Fig. 1 ): either to a special syringe pump, imposing known, perfectly constant volume flow rates, or to a tank supplying liquid under constant pressure. In the latter case, the volume flow rate depends on the applied pressure and pressure losses between the tank and the end of the capillary, which themselves are dependent on the liquid chosen and on its temperature. This volume flow rate also depends on the applied voltage, since the electrostatic pressure on the meniscus produces a suction effect. The flow rate consequently must be measured with each test. A potential difference varying from 0 to 20 kV is applied between the capillary and an electrode, which will be called "plate" although it can be of any form. Corona discharges are initiated less easily when the polarity of the capillary is positive; all the results presented here were obtained with this polarity. The value of the applied potential is the only electrical information given in certain publications. However, the resulting electric field on the liquid varies according to the dimensions of the capillary and the parts to which it is connected, the shape and dimensions of the plate and the surrounding elements, the distance between the plate and the end of the capillary and, finally, the b

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012 !ii!iiiiii mm I-t° 'm -I Fig. 3. Form of capillary ends.

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position of the grounded point in the circuit. The voltage consequently has only a comparative value in experiments in which these characteristics remain unchanged. The value of the current in the high-voltage circuit is more appropriate information for comparing tests conducted under different conditions. It should be pointed out, however, that the measured current is equal to the current transported by the jet (and thus by the drops) only in the absence of corona discharges. Water and various organic products were used in the pure state or in mixtures. Only the results concerning liquids of low viscosity will be given. Low-field d.c. conductivities K varied between 10-1 and 10 -9 S/m, and volume flow rates 5 between 10 -3 and 10 mm3/s. These limits correspond to what is regarded here as "high" and "low" values of conductivities and flow rates.

3.2 Observation of meniscus and spraying The phenomena were observed by optical systems with a long working distance: a Zeiss stereomicroscope with a working distance of about 10 cm and maximum magnification of 100, and a Bausch and Lomb microscope with a working distance of 12 mm for the maximum magnification of 1,000. Both apparatus are equipped with a Polaroid camera system. Lighting may be continuous or pulsed. To have single-instant photos, two pulsed light sources were used: a Nanolite spark lamp from Impulsphysik whose flash time is about 20 ns and, for some control experiments, a B.M. Industries double-frequency YAG laser whose impulse time is only a few nanoseconds. Also, image sequences were taken with an Imacon 790 electronic camera from Hadland Photonics Ltd. to study the evolution of phenomena in the case of atomization into droplets with diameters greater than about 10 ~m. 3.3 Particle size measurements 3.3.1 Measurements by light scattering A laser granulometer of the CERT (Toulouse) was used for the study of aerosols made up of fine water droplets. The instrument (Fig. 4) consists essentially of a series of mirrors arranged on an elliptical arc. The aerosol, located at focal point F1, is illuminated by a laser beam and the scattered light is reflected towards focal point F2. A rotating mirror located at F2 successively sends the light beams coming from the different mirrors to a photomultiplier. A computer program based upon the complete Mie theory is used to determine the droplet size distribution from the intensity of the different beams. 3.3.2 Direct measurements Direct measurements of drop diameters were carried out using 1-hexadecanol, whose melting point is about 49 ° C. The product, possibly doped in order

141

Fig. 4. Diagram of granulometer. (1) Laser beam; (2) Aerosol; (3) Flat mirrors; (4) Filter; (5) Rotating mirror sending scattered light to a photomultiplier.

Fig. 5. Apparatus for investigating the atomization of products which are solid at ambient temperature but liquid at higher temperature. {1 ) Supply syringe; (2) Hot-air inlet; (3) To heated storage tank; (4) Capillary; (5) Charged droplets; (6) Metallic disk; (7) Window; (8) Heated plate; {9 ) Plate receiving the sample of solidified droplets; (10) Motor; ( 11 ) Sliding contact. to increase its conductivity, is h o t sprayed; t h e droplets solidify during their t r a j e c t o r y in t h e a m b i e n t air before reaching a receiving plate. T h e d i a m e t e r s of t h e solid spheres collected are t h e n m e a s u r e d u n d e r the microscope. T h e a p p a r a t u s (Fig. 5) is designed so t h a t the electric field on the capillary r e m a i n s c o n s t a n t during the test. T h e " p l a t e " consists of a r o t a t i n g metallic

142

disk. During adjustments, the disk is still. The solidified droplets go through a circular opening and are collected on a heated plate from which the re-liquified product flows by gravity. During the experiment, the disk describes a complete rotation during which a limited number of droplets are deposited on a glass plate embedded in the disk. The outside of this plate is covered with a transparent conducting deposit connected to the disk. The plate is then removed for examination under the microscope. The same device was also used for some measurements on liquid drops, covering the receiving plate: either with a film of magnesium oxide, in which the drops create impressions having dimensions near their own when their diameter is greater than 15 pm, or a product of the same density as the atomized liquid and immiscible with it, in which the trapped drops remain spherical.

3.4 Drop emission frequency Drop photodetection, allowing the determination of the emission frequency, was carried out as follows (Fig. 6): The zone located just ahead of the formation of the drops is illuminated by the suitably focused beam from a 30 mW laser, and its image is formed in the plane of a slit perpendicular to the axis of the capillary. The light scattered by the drops is received by a photomultiplier. The signals are stored on a storage oscilloscope. Whenever a drop passes in front of the slit a peak is produced. The spacing and amplitudes of the peaks give an idea of the regularity of the atomization. The average frequency f is deduced from the number of peaks observed on a scan of a given duration. The smallest pulses, corresponding to very small satellite drops, are not taken into account. The volume and charge of these satellite drops represent only a practically negligible part of the volume and charge of all the drops.

Fig. 6. Apparatus used to observe atomization a n d m e a s u r e the droplet emission frequency. (1) Aerosol; (2) Laser; (3) Microscope; (4) Slit; (5) Photomultiplier; (6) Source of continuous or pulsed light; (7) Removable frosted glass.

143

3.5 Functioning domains The functioning domains in the cone-jet mode were determined according to the following procedure. For a given configuration of the capillary-plate system and for a liquid of known physical properties, a volume flow rate 5 is imposed. The phenomena at the outlet of the capillary are observed under the microscope with continuous or pulsed lighting, while the voltage U is gradually increased. One thus determines the value of U between which there is stable cone-jet functioning. The same tests are conducted for different volume flow rates. For certain values of U and 5 allowing the cone-jet mode, the following parameters were measured: current i, frequency f of droplet production and diameter IZ/j of the jet at the end of its permanent continuous part. This diameter often determines the average size of the emitted drops (cf. §5.1 ). 4. E x p e r i m e n t a l results on cone-jet mode

4.1 Origin of cone-jet configuration The theoretical investigations of Joffre et al. [17,18] on electrified menisci show that stable conical menisci of perfectly conducting liquids may exist when a release of charges (due for example to a corona discharge ) exerts a regulating effect on the electric field in the vicinity of the apex. At each point of the surface there is then an equilibrium between the capillary, hydrostatic and electrostatic pressures. The creation of a permanent jet, for its part, requires a penetration of the field lines in the liquid, so that the liquid must not be a perfect conductor. Only this penetration will allow the appearance of a component of the electric field tangent to the surface, which, by acting on the surface charges, creates a force driving the liquid and an acceleration of the jet downstream [ 23,24,27 ]. For liquids with relatively high conductivities, the jet formation zone is limited to the apex of the meniscus. The remaining surface is practically equipotential and an almost static equilibrium of forces exists at each point. The cone

a

b

c

Fig. 7. Different forms of meniscus in cone-jet mode.

d

144

may then have a practically straight generatrix (Fig. 7a) or exhibit a shape as in Fig. 7b. For decreasing conductivities, the acceleration zone extends further towards the base of the cone. In the limit, it begins at the outlet of the capillary. There is then no longer a clear distinction between meniscus and jet. However, the profile of the liquid at the capillary outlet often remains similar to that of a more or less open cone (Figs. 7c and d). By extension, the name of cone-jet can still be applied. These different conical configurations (Fig. 7) make it possible to obtain very fine jets from capillaries of sufficiently large diameter to avoid the problems of obstruction raised by tubes with very small diameter. The conical appearance ultimately disappears when the liquid has a very low conductivity and the volume flow rate is high; the smaller the diameter of the capillary, the sooner will this occur. For currently used capillaries having an outer diameter greater than 100 ~m, these conditions correspond generally to the production of large drops; they are not considered here.

4.2 Problems of reproducibility Experiments on electrostatic atomization usually reveal reproducibility problems. Thus, this method is often considered to yield aerosols of irregular characteristics. These problems, which may suggest random phenomena, have multiple causes. They stem in particular from variations in the electrical conductivity of the liquid, a parameter which has a significant effect on the atomization behaviour. Thus, the ageing of the product results in an increase in conductivity which, for example, is very fast in the case of ultra-pure water; this makes it necessary to measure and to set K before each series of experiments. Similarly, in the case of a volatile liquid, evaporation at the end of the capillary between two tests sometimes produces a significant modification of K; it is then necessary to purge the old liquid before the start of a new experiment. Other reproducibility faults may arise from modifications, even very small, in the geometry or the wettability of the capillary, and from hysteresis phenomena. Examples of the latter effects are given below.

4.3 Functioning domain Taking into account the preceding remarks, it is possible to obtain sufficient reproducibility for determining functioning domains using the procedure described in §3.5. Figure 8 corresponds to the following conditions: the liquid is p-dioxane to which is added a small amount of formamide to reach a conductivity K of 3.2 X 10 -7 S/m, the positive high voltage is applied to the capillary, with the plate connected to the ground,

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145

- the capillary, placed horizontally, is cylindrical; its diameter is 0.5 mm; it is coated with a non-wettable product except on its outlet section, - the plate, measuring 10 × 10 mm, is placed 10 mm from the end of the capillary; this porous plate of sintered metal is drained to avoid the accumulation of liquid which could modify the geometry during the test. When, for a given rate 5, the voltage is gradually increased (top diagram in Fig. 8), pulsating modes are first observed. The stable cone-jet mode is established above a value UA of the voltage and continues up to a value Us, beyond which instabilities or multiple-jet regime appear. When the volume flow rate is varied, points A and B describe curves a and b, limits between which there --

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146

is cone-jet functioning. We see here that this mode does not appear for flow rates below 0.05 mm3/s. The other three diagrams in Fig. 8 give the corresponding limit values of the current i, the diameter ~ j of the jet and the emission frequency 7
4.4 Influence of conductivity Figure 9 allows a comparison of the cone-jet functioning domains when conductivity changes from 3.2 × 10 -7 to 3 × 10 -6 and then to 3.6 × 10 -5 S / m - all other conditions remaining equal to those of the example dealt with in the preceding paragraph. When conductivity increases, the boundaries of the domain move towards lower flow rates. This is accompanied by a reduction in jet diameter.

4.5 Influence of capillary geometry For a given conductivity, the range of possible volume flow rates varies according to the geometry of the capillary used.

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Example 1. For a liquid of 3.2 × 10 -7 S / m conductivity and a capillary with an outer diameter of 0.5 m m (domain 1, Fig. 9), the lower limit of the flow rate is 0.05 mm3/s; with a capillary twice that diameter, the cone-jet mode is observed only for flow rates higher than 0.5 mm3/s. Example 2. For a liquid of 3.6 × 10 -~ S / m conductivity and a capillary of 0.5 mm (domain 3, Fig. 9), the upper limit of the flow rates is about 0.3 mm3/s. Figure 10 shows that, if a finer capillary is used (Fig. 3b), the upper limit of the flow rates for which a stable cone-jet exists (zone 1) is at least four times higher. Beyond 1 mm3/s, the meniscus gradually loses its conical appearance and the jet becomes irregular (zone 2, in which the voltage limits are not specified). Above 6 mm3/s (zone 3), the speed of the liquid at the outlet of the capillary is sufficient to produce a jet even in the absence of an electric field; in this zone, the application of a voltage has the effect of simply accelerating the jet that is already established. 4.6 Influence of capillary wettability Functioning regularity is sometimes disrupted by the following phenomenon. Liquid rises on the capillary and accumulates near the outlet section, forming a ridge over the entire periphery or on a small part only. This ridge sporadically emits a jet of fine droplets, or finally detaches into a large drop

148

and the cycle begins again. During the growth of the ridge, the flow rate of the atomized liquid is lower than the total rate; furthermore, the electric field on the meniscus decreases owing to the apparent increase in the section of the capillary. There is consequently no stable functioning. A treatment lowering the wettability of the capillary surface can have a favourable effect by preventing the appearance of these phenomena. Such is the case for the domain shown in Fig. 10 obtained with a non-wettable capillary and in which the minimum flow rate is below 0.01 mm3/s. If, all other conditions remaining equal, the capillary is not treated, the stable cone-jet mode is obtained only above 0.1 mm3/s.

4.7 Effects of corona discharges When corona discharges are initiated at the outlet of the capillary, they reduce the electric field and generally constitute a spurious phenomenon. In fact: if they occur before the critical field initiating the cone-jet regime is reached, they prevent the establishment of this mode; this phenomenon occurs especially with liquids having a high surface tension and requiring high fields to offset the capillary pressure; if they occur once the regime has been established, fluctuations in the discharge current often prevent the conservation of steady state conditions. Conversely, corona discharges can favour stability by allowing a reduction in the density of the surface charge of the jet (cf. §5.2) or by reducing the electric field near the outlet of the capillary. The latter effect is observed in zone 5 of Fig. 10. The broken line (curve d) corresponds to the limit of the voltages beyond which the corona discharges appear. Below this line (zone 4 ) an irregular multi-jet regime exits. Above this line {zone 5) there is often a single stable jet; if the corona discharge is eliminated by increasing the dielectric strength of the surrounding medium (for instance by adding freon 12 ), the stable jet disappears and the same functioning mode as in zone 4 prevails. -

-

4.8 Hysteresis phenomena In the preceding examples, the limits of the domains were always determined by gradually increasing the voltage. When the cone-jet mode is initiated, it is sometimes possible to maintain it even if the voltage is reduced down to values much lower than the initiation voltage. Figure 11 illustrates this hysteresis phenomenon for conditions identical to those of domain 3 Fig. 9. Operating at decreasing voltage, the domain is broadened down to curve c. The same type of phenomenon exists upon the passing of the border b, but it is practically negligible. Wettability or corona discharge phenomena can also give rise to other cases of hysteresis.

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4.9 General tendencies The few examples given above show to what extent the electrostatic atomization phenomena in the cone-jet mode are sensitive to any modification, even tiny, in one of the experimental conditions. The tests however make it possible to set forth some general rules concerning the volume flow rates 5 and the diameters ~ j of the jets, parameters which determine to a great extent the average size and the emission frequency of droplets. (1) The possible domains of 5 and ~ j depend to a great extent on the conductivity K of the liquid. For a given K, these domains are more or less narrow (or even nonexistent) depending on experimental conditions. They can be displaced or enlarged on one side or the other by suitably choosing certain parameters, and in particular the geometry of the capillary. It is, however, important to note that these displacements or extensions in the functioning domains are limited. For instance, it is not possible to obtain very fine jets with liquids of low conductivity (unless special methods are used, such as the ion injection system [25,28], which allows the atomization of insulating liquids). (2) Within each domain (i.e., for a given K), ~ j decreases as 5 decreases or as U increases. (3) On the average, the possible values of ~ j and 5 become smaller as K increases; only fine jets and low flow rates can be obtained in the cone-jet mode for liquids with high conductivity. 4.10 Discussion Other relations between various parameters can be deduced from observations, but the diversity of the parameters and phenomena calls for great care concerning the generalization of results. Even though this observation may cause some irritation, it must be acknowledged that there are few rules for which exceptions cannot be found. For example it is altogether common to note that current increases with voltage and it is generally observed that an increase

150 in voltage causes a reduction in average droplet size. There are however cases in which these two rules do not apply: Figure 12, corresponding to conditions identical to those of Fig. 8 but with a slender capillary, shows that for rates lower than 0.15 mm3/s the variation of i and ~ j with U is reversed. The present findings and the works already cited (in particular Refs. [2224 ] ) indicate approximately the conditions under which the cone-jet mode can be obtained; however, for each particular atomization problem, it will always be necessary to look experimentally for the most favourable conditions. The modification of certain parameters sometimes enables the desired results to be approached. Thus, the conductivity of a given liquid can often be considerably increased by addition of small amounts of suitable additives. On the other hand, it cannot drop below a certain value whatever the degree of purity of the liquid. This limits the possibilities of increasing the size of droplets produced in the cone-jet mode for certain liquids, and in particular for water, which is not kept easily at a level of conductivity lower than 10 -4 S/m. The surface tension of water is higher than that of organic liquids and this constitutes another disadvantage for the cone-jet mode owing to the initiation of corona discharges. It can be lowered by adding surfactants, but for dynamic phenomena such as electrostatic atomization, there is less actual decrease than for the values measured in static equilibrium.

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151 The appearance of corona discharges may be delayed or favoured using gases such as freon 12 or argon whose dielectric strengths are respectively higher and lower t h a n that of air. Another method consists in lowering or increasing the temperature of the ambient air. 5. Breakup of electrified jets into drops As in the preceding chapter, we shall consider here only the case of liquids with a low viscosity, i.e. of the order of the 1 m P a s. 5.1 Usual case of varicose instabilities 5.1.1 Droplet size If the distance ;t between two consecutive breakups of a jet is equal to k times the diameter IZIj, the resulting droplet has a diameter ~ D such that: ~ D / ~ J = (3k/2)1/3

(3)

For jets without an electric charge, of low viscosity liquids, the conventional Rayleigh theory shows that the most probable value of k is about 4.5, leading to a ratio i2iD//~ J of about 1.89. In practice, the distance between two successive breakups varies each time and small satellite drops can be created at the

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152

moment of the breakups so that one obtains a mixture of droplets of different sizes (Fig. 13). The influence of jet electrification [29,30] on the most probable value of ~ D / ~ J (or of k) could be determined, in the case of electrostatic atomisation, by comparing the diameter of the jet to the most probable size of the droplets given by the particle size measurements. In our experiments, the latter measurements covered essentially the very fine droplets from jets whose diameters were too small to be accurately measured. We consequently studied the ratio ~D,m/~J, in which ~D,m is the volume median diameter of drops. This diameter is obtained from the emission frequency f of the main drops and the volume flow rate 5: (4)

Z)D.m = ( 65/z~f) 1/3

The values of ~D,m/~J as a function of ~ j given in Fig. 14 correspond to points located on the lower and upper limits of domain 1 in Figure 9. The differences observed between the experimental points and the curve of slope 1.89 are not greater than the measurement errors. The average value of k can thus be considered near 4.5 in all cases. Measurements carried out under dif-

i

J

•

8O

E ::k E d

G 6o

E

c 40 E E >

2O

0

,

I

~

I

,

20

Jet

diameter

I

*

I

l

40

(Z)j (/~m)

Fig. 14. D r o p volume m e d i a n d i a m e t e r as a f u n c t i o n o f jet diameter. C o m p a r i s o n w i t h t h e line o f slope 1.89. T h e e x p e r i m e n t a l p o i n t s c o r r e s p o n d to p o i n t s located o n t h e lower a n d u p p e r limits o f d o m a i n 1 in Fig. 9.

153

ferent experimental conditions for droplets of ~D,rn>I 3 l~m give the same result, as long as the charge of the jet is not too high (cf. §5.2 ). This is in agreement with theoretical [30] and experimental [22 ] data showing that the value of k varies little with the charge of the jet. Concerning the distribution of drop sizes, particle size measurements show that its width varies greatly with test conditions. The solid-line histogram in Fig. 15 is an example of a very narrow distribution. It was obtained by laser granulometry for distilled water to which a surfactant was added. The average diameter of the droplets is 1 pro, and the emission frequency is higher than 18 million droplets per second. About 99.8% of the volume of liquid sprayed is contained in drops of diameters ranging from 0.94 to 1.1 }~m. Such uniformity is also observable for larger drops, but it remains exceptional. Small variations in one or the other of the parameters leads to wider distributions such as the one shown with broken lines in Fig. 15. A phenomenon favourable to the uniformity of sizes is observed in the sequence of images in Fig. 16: each satellite drop created upon the breakup of the jet is caught and absorbed by the drop which follows it. However, in general, satellite drops remain and move away, faster than the main drops, from the axis of the jet.

I L 3 I I I I I I

2O

fi ¢15

', ,,

,

tl

E

'

L- I

>o

,, 1

1l

10

" L.

5

. . . . . . . . . . .

-

o

0.4

....

i

r1,2

I

[,,_ 2.8

2

Droplet diameter

"-1 I

( prn}

Fig. 15. Distribution of drop diameters. Solid line: Distilled water +0.5% surfactant ( K = 1.5 X 10 -3 S/m; t)= 10 -2 mm3/s; i=40 hA); Broken line: pure water ( K = 5 X 10 -4 S/m; z)= 10 -2 mm3/s; i=30 nA).

154

T

3

4

5

7

9 °

•

6

.

8

200 /~m I r Fig. 16. Coalescence of satellite drops with following drop. Liquid: dioxane + water; K = 10-; S / m; ~= 1 mm:~/s; i = 14 nA. Time interval between two photos: 5/~s.

To systematically obtain droplets of the same size, it is necessary - as in the case of non-charged jets - to produce the breakup of the jet at regular intervals by disturbances having a frequency near the average spontaneous breakup frequency. Such regularizations were achieved under special conditions by means of mechanical or electrical disturbances. Droplets of the same size, with a diameter greater than or equal to 5 ~tm, were produced in this manner at a frequency lower than or equal to 2 × 105 s - 1 [31 ].

5.1.2 Droplet charge The charge-to-volume ratio q/v of the drops as a function of their size is often compared to that obtained by Vonnegut and Neubauer [3] by applying the energy minimization principle. The following considerations show that this principle is not applicable to electrostatic atomization in the cone-jet mode. In all the examples presented till now (except in zone 5 of Fig. 10 ), atomizing is not accompanied by corona discharges, so that the current i measured in the high-voltage circuit is equal to the current transported by the drops. Under these conditions, the ratio of the total charge of the drops to their total volume is equal to the ratio i/5 and eqn. (2) becomes: i/ ~ = 6 ( 2 ~ 3

) 1/2

(5)

which gives, for the drops, a "Vonnegut diameter" ~D,V equal to: ~D,V

=

[6(2eT)z/20/i] 2/3

(6)

The latter can be compared with the drop volume median diameter ~D,m obtained from the measurements of the emission frequency. Figure 17 gives, as a function of flow rate, the values of the ratio ~ D , J ~ D , V corresponding to the

155

1

9 (mm3/s)

10

Fig. 17. Variations in ratio of drop volume median diameter to “Vonnegut diameter” as a function of flow rate. Curves I and II correspond respectively to the lower limits of domain 1 in Fig. 9 and zone 1 in Fig. 10. At points M, N, 0 and P, the values of &,, are about 5,120,4 and 26 pm.

lower limits of domain 1 in Fig. 9 and zone 1 in Fig. 10. It is seen that this ratio varies, depending on conditions, from 0.5 to 1.4 approximately and is only exceptionally near unity. Let us consider in detail the case in which On,,/&,v differs most from unity, i.e. the point M where this ratio is equal to 0.5. It corresponds to an experiment with a mixture of dioxane and formamide in which: K= 3.2 x 10m7 S/m; dielectric constant of liquid measured at 100 Hz= 38x lo-” F/m; y=O.O35 N/m; ti=52~10-‘~ m3/s; i=7.8x10mgA; @J=2.6~10-6 m. The charge relaxation time is about 400 times greater than the material transit time referred to the jet diameter, so that at the location of the measurement of /25,, the total current i is only a convection current. The charge q of a drop formed by an element of the jet with a length of lzOJ is equal to the volume of this element multiplied by the charge-to-volume ratio i/C of the jet: q = nk@; i/4ti

(7)

In order for the resulting

drop, of diameter

On, to have the Vonnegut

qv =x(2cy@&)“2 it would be necessary k=48(ti2/i2)&;3

charge: (8)

that q = qv, which gives, considering

eqn. (3): (9)

It is found that, to obtain droplets having the Vonnegut charge, the distance between two breakups of the jet should be equal to about 36 times the diameter of the jet, which is obviously unrealistic. Also at point M (Fig. 17)) the drops formed by the breakup of an element of

156

the jet with a length of 4.5 ~ j have a low relative charge level q/qR: it is less than 18% of the Rayleigh limit charge. On the other hand, at point P the charge of certain drops is near the Rayleigh limit charge (cf. §5.2). In general, the drop charge level depends greatly on production conditions. Drops of the same diameter but obtained under different experimental conditions can have very different charge levels. These results are not in agreement with the conclusions drawn from the energy minimization principle. The charge and size of drops can probably be predicted only from a detailed theoretical study of the jet acceleration mechanism which should take into account in particular the respective values of the conduction and convection currents throughout the jet. 5.2 Special case of kink instabilities When the charge-to-volume ratio of the jet is very high, at least three types of phenomena can be observed: (1) The production of drops too heavily charged to be stable; these give rise in turn to jets which are resolved into fine droplets (Fig. 18a). (2) The appearance of lateral kink-type instabilities (Fig. 18b). (3) The creation of multiple branches on the jet (Fig. 18c). These branches, which are observed only for relatively high flow rates, will not be commented upon here. The first phenomenon can occur if the drop charge becomes equal to or greater than the Rayleigh limit charge. It begins to appear, for example, for experimental conditions relative to point P in Fig. 17 (or Fig. 10). In fact, the Rayleigh limit charge is not quite reached by drops whose diameter is near ~D.m, but it is exceeded by the largest drops which correspond to values of k clearly higher than the average value (about 4.5). The fact that, just after their detachment, the drops are not yet spherical also favours jet formation. The second phenomenon, i.e. the appearance of kink instabilities, occurs with slightly higher charge-to-volume ratio of the jet. For example, these instabilities are well established for experimental conditions relative to point P' a

b

c

.i .~.° Fig. 18. Different phenomena observed with highly charged jets.

157 in Fig. 10. In general, they appear only for volume flow rates which increase as the conductivity of the liquid decreases. W h e n these kink instabilities exist, the conduction current is still high at the end of the permanent part of the jet. Beyond the zone in which they appear, the charge continues to increase, thereby amplifying the instabilities. The jet stretches out into disordered winding threads and is thinned out very irregularly. This leads to the production of droplets of very different sizes. As kink instabilities and also the emission of jets by drops are due to an excessive liquid surface charge, they can be reduced or even eliminated by reducing the charges. This reduction occurs sometimes as a result of the spontaneous initiation of corona discharges. This effect can be amplified by lowering the dielectric strength of the gas surrounding the jet. Another method of reducing the charges is to produce ions having a polarity opposite to that of the jet by means of corona discharges on a needle placed in the vicinity of the capillary. Part of these ions is picked up by the jet which is thus partially neutralized. The effectiveness of these two methods has been checked in several cases. The breakup into drops, instead of occurring according to Fig. 18b, takes place according to the diagram of Fig. 13. Droplets are not as fine as those produced in the presence of kink instabilities, but their sizes are much more uniform. 5.3 General tendencies Certain rules were derived (§4.9) regarding the domains of the cone-jet regime and the diameter of the jets obtained. They can be completed by information relative to drop size and production rate. In general, the average drop size increases and the emission frequency decreases as the conductivity of the liquid or the applied tension decreases, or as the flow rate increases. This however remains true only if the charge density of the jet is not too high. Above a certain flow rate (which increases as the conductivity of the liquid decreases) kink instabilities appear. In spite of an increase in flow rate, the drops then have an average size smaller than that obtained just before the appearance of these instabilities, and their emission frequency is higher. 6. Conclusions

Electrostatic atomization from a capillary was investigated in the case of drops formed by the breakup of a permanent jet extending from a conical volume of liquid. For liquids of relatively high conductivity, the conical form of the meniscus results from a static equilibrium between capillary, hydrostatic and electrostatic pressures; the jet formation and acceleration zone is limited to the end of the meniscus. When conductivity is low, this acceleration zone can begin at the outlet of the capillary and the conical form is more or less

158 marked depending on the flow rate of the fluid, the size of the capillary and the applied voltage. Cone-jet mode domains were determined after obtaining good reproducibility of phenomena, requiring the effective control of multiple parameters. For a liquid of a given conductivity, the jet diameter varies with the volume flow rate and the applied voltage, but only within a limited range whose extent depends in particular on the geometry of the capillary. In general, the higher the conductivity of the liquid and the applied voltage, and the lower the volume flow rate, the finer will the jet be. The breakup into droplets takes place in a manner similar to that of a neutral jet as long as the surface charge of the jet is not too high. Jet diameter measurements, combined with drop emission frequency measurements, show that the energy minimization principle cannot be applied to the process of electrostatic atomization in the cone-jet mode. Unlike what is predicted by that principle, the ratio of drop charge to Rayleigh limit charge varies greatly, depending on production conditions. When the surface charge of the jet is very high, kink instabilities appear. These lateral instabilities lead to the production of drops of very different sizes. They can be eliminated by partial neutralization of the jet. Even in the absence of such instabilities, the droplets produced exhibit size variations owing to the natural variations in the distances between the successive breakups of the jet and the formation of satellite droplets. The direct formation of droplets of uniform size was achieved by causing the breakup of the jet at regular time intervals by mechanical or electrical disturbances. These results show that, in spite of certain difficulties and limitations inherent to the method, electrostatic atomization can be controlled within a range that is difficult to attain with other atomization methods.

Acknowledgements The authors express their appreciation to Mme. D. Bisch for her precious technical assistance and for completing the figures in this article. This work was supported in part by a contract from the Direction des Recherches Etudes et Techniques du Minist~re de la D~fense.

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