(First received 26 October 1993; and in final form 28 January 1994)
Abstract--Planar phase Doppler system is a promising technique for simultaneous sizing and velocimetry of particles smaller than 10 #m in diameter, in particular submicron spherical particles. Some new features of this technique are highlighted herein, including the possibility of obtaining unambiguous measurements of drop sizes in the range of 0.2-1 #m using only two signal detectors. In situ measurements of submicron electrospray droplets covering a 4:1 range of liquid viscosity and a 20:1 range of electrical conductivity are reported. The results are compared with the existing theories and empirical correlations and used to classify the capillary-type electrosprays.
1. I N T R O D U C T I O N
Drop size measurements in a capillary-type electrospray are presented. The experimental results are supportive of a three-regime classification of the electrohydrodynamic at- omization process. These regimes may be referred to as fully random, fully organized and intermediate modes of atomization. The present results illustrate how a given spray switches from one regime to the other by changing the liquid properties, while operating with a fixed hydrostatic head. It has been possible to identify a departure from the fully organized single- filament mode by applying the principle of energy conservation to the filament.
The intermediate mode of electrospraying is important from a practical point of view, as it permits significantly larger volume flowrates as compared to the fully organized mode.
The above results were obtained using an advanced version of a phase Doppler anemometer, which is optimized for sizing and velocimetry of small drops, in particular submicron droplets. This measuring technique is described herein and compared with the standard phase Doppler system. The present experiments were conducted with solutions of 1-octanol and sulfuric acid in different proportions, providing a 20:1 variation in the electrical conductivity and 4:1 variation in the liquid viscosity. The results showed polydisperse droplet distributions, such that the standard deviation was 20-30% of the mean diameter. The mean value of the droplet diameter ranged from 0.3 to 0.85 #In for various solutions using a zero hydrostatic head at the capillary tip.
Although a rigorous theoretical model covering all three modes is not conceivable at present, some ideas concerning a theoretical description of the single-filament mode and its transition to a multi-filament mode are presented.
2. MEASURING TECHNIQUE
As shown by Naqwi and Ziema (1992) and Naqwi et al. (1992), a planar optical layout of a phase Doppler system, combined with the joint probability method for signal processing, enables accurate measurements of particles smaller than 10/~m. Results of validation experiments using monosize latex particles are presented in the above articles and show that an accuracy of 0.1 #m can be achieved using standard signal processors. Higher resolution is also possible with improved signal processing. The measuring device does not require any calibration as long as the refractive index of the particle material is known. Besides the refractive index, the conversion factor between phase signal and particle diameter depends upon the wavelength of laser light and geometry of the optical system. All these parameters are generally known with a high precision.
The planar layout used for the present measurements is illustrated in Fig. 1. A laser beam with a wavelength of 0.5145/~m was split into two beams, which were passed through two Bragg cells for frequency shifting. The Bragg cells were made of tellurium dioxide (TeO2) and served the purpose of shifting the light frequencies of the two beams by 79 and 80 MHz. As a result of frequency shifting through TeO2 crystals, the electric vectors of polarization were rotated by 90 °, so that they lay in the plane of the beams (i.e. horizontal plane) after frequency shifting.
The two laser beams were crossed at their focal points using a lens with 200 mm focal length. The beams intersected at an angle of 7 ° and produced an ellipsoidal region of interference with a diameter and length of 80 and 1.3 mm, respectively. Within this region, the light intensity was equal to, or larger than, 1/e 2 times the maximum intensity that existed at the center of the ellipsoid. An expanded view of the interference zone is given in Fig. 1. The interference fringes in the measuring volume were spaced at 4.2 #m and were moving perpendicular to the plane of fringes with a frequency of 1 MHz, which corresponded to the difference between the shift frequencies of the two Bragg cells.
The electrospray consisted of a vertical capillary, so that the droplet motion was predominantly perpendicular to the plane of laser beams and parallel to the interference fringes. Nevertheless, the motion of the fringes enabled several fringe crossings during the passage of the droplet through the measurement volume, so that the light scattered by each droplet consisted of oscillations in time that characterize LDV signals.
The scattered light was collected by three receivers that were located in the plane of the laser beams, such that their optical axes were oriented at angles of + 30 ° and 65 ° from the bisector of the laser beams. Scattered light was collected by the three receivers over cones with opening angles of 9 ° .
The electrical outputs of the detectors were digitized by a transient recorder (4-Channel LeCroy with a digitizing speed of 100 MHz) and transferred to a signal processor that consisted of transputer modules on a PC board. Phase shifts tk12 and tP23 between signals from detector pairs (D 1, D2) and (D 3, D2), respectively were recorded and compared with the theoretical response curves shown in Fig. 2. These curves are based on Mie scattering theory. The computational code is described in detail by Naqwi and Durst (1993).
M e a s u r e m e n t o f s u b m i c r o n d r o p l e t s 1203
180- - - P h a s e b e t w e e n D~ & D1 - - - P h a s e b e t w e e n D3 ~xDe
/
120 i ~ t~
\~ F 1 x l /
/ _ /
60- / a
/
- 6 0
- 1 2 0
R e f r a c t i v e I n d e x = 1.43 - 1 8 0 . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . . . ~
0 .0 0.5 1.0 1.5 2.0 Drop diameter, micron
Fig . 2. R e s p o n s e c u r v e s o f p l a n a r p h a s e D o p p l e r s y s t e m w i t h a b e n c h - t o p a s s e m b l y .
The response curves for individual detector pairs, as shown in Fig. 2, are nonmonotonic in general, i.e. a given value of phase may correspond to more than one value of particle diameter. In such a situation, it is required that each combination of the two phase difference signals (~b12, ¢23) should be related to a single particle diameter, so that the diameters could be measured unambiguously. If the above condition is met, then according to Naqwi and Ziema (1992), a joint probability function can be constructed using the measured pair of phase shifts and the known values of standard deviations of uncertainty in the phase measurements. The peak of the joint probability function corresponds to the best estimate of the particle diameter.
Since both the phase shifts ¢12 and ¢23 have comparable magnitudes, the measurement accuracy can be enhanced by a factor of about x/~ by combining them. A similar enhancement of accuracy cannot be achieved in standard phase Doppler systems, as one of the phase shifts is significantly smaller than the other. See Naqwi (1993) for further discussion of measurement accuracy in three-detector phase Doppler systems.
As mentioned above, a two-detector system may be used satisfactorily, if droplets are smaller than 1 gm. Such a device has been recently built in the author's laboratory, in order to continue investigations on electrosprays and other submicron atomizers. The new hardware is illustrated schematically in Fig. 3. As opposed to the previous setup, the present device is well packaged, using the components of Adaptive Phase/Doppler Velocimeter (APV) systems of TSI Inc. Hence, it is mechanically stable and permits traversing of large flow fields. Packaging is achieved by employing fiber optics in order to connect the compact transmitting and receiving probes to the modules containing opto-electronics and other bulky optical components.
The response curves of the packaged assembly for two different focal lengths of the transmitting lens are given in Fig. 4(a) and show a monotonic, though non-linear relation- ship between the phase shift and the droplet diameter. Figure 4(b) shows an equivalent standard system. Both the systems employ 50 mm beam spacing in the transmitting fiber probe. The receiving probes consist of semicircular front lenses and the associated optics for coupling the scattered light into multimode fibers. The front lenses have a focal length and a diameter of 310 and 80 mm, respectively.
The planar and standard systems, represented in Fig. 4(a) and (b), respectively, satisfy the requirement of comparable sensitivity given by Naqwi and Ziema (1992) in Equation (6) of their article. According to this equation, the receivers in a standard system should have the same elevation angles as the off-axis angle in order to achieve a sensitivity comparable to the corresponding planar system, provided that the beam angle in the transmitting probe is unchanged.
1204 A . A . NAQW1
I
i
I - III 7s a,g. I T r s u s m i t l i n g / 1 \
I /\\ 7s , ~
x\\ K
A P V R e e ~ e ~
Detection sad Down-Mixing As~mbly
Signal I Pr~emor
Fig . 3. Planar phase Doppler system based on APV technology.
r~
I
c~
3 0 - 3 0 -
P l a n a r p h a s e D o p p l e r 7 5 ° c o l l e c t i o n
O X
- 3 0
- 6 0 \ ~ \ \ .
\
\
- 9 0 \
\
- 1 2 0 . \ \ \
- - 2 5 0 m m focal l e n g t h - 1 5 0 - - 1 2 2 m m f o c a l l e n g t h
S t a n d a r d p h a s e D o p p l e r 7 5 ° c o l l e c t i o n
¢
i
i
I
2 5 0 r a m f o c a l l e n - - 1 2 2 m m f o c a l l e n
/ \ /
V / /
l
t /
/ /
t h t h
, ~ r i , , i r i i r , , , i , , r ~ 7
0 .5 1.0 Drop d i a m e t e r , m i c r o n
Fig . 4. Response curves for the packaged assembly. (a) Planar phase Doppler system; (b) standard phase Doppler system.
Although the average slope of the response curves for the standard phase Doppler system is comparable to the planar system, the phase-diameter relationship is highly nonmono- tonic in the former device. It is obvious from Fig. 4(b) that the standard geometry is not suitable for submicron sizing.
The major differences between the standard and planar phase Doppler systems can be explained using the geometrical theory of light scattering; however, this theory is not
Measurement of submicron droplets 1205
appropriate for a detailed description of scattering by particles with diameters approaching the laser wavelength. According to geometrical scattering, polarization should be parallel to the scattering planes for transparent droplets and the receivers should be located close to the Brewster angle, so that direct reflections from the drops are suppressed and refracted light is dominant in the scattered light signal.
There are at least four scattering planes (pertaining to two laser beams and two or more receivers) in a phase Doppler system. In a standard optical layout all these planes have different orientations in space and hence, the condition of parallel polarization is met only approximately. This does not pose any significant problem for sizing large droplets, e.g. those in the range of 10-200/zm. However, the beam angle and the receiver spacing need to be increased for sizing smaller particles, which leads to an increasing deviation from the condition of parallel polarization and contributes to fluctuations in the phase Doppler response curves as seen in Fig. 4(b).
The above problem is overcome in a planar optical layout by collapsing the scattering planes with the plane of the laser beams and by orienting the polarization vectors of the laser beams parallel to their plane of interference. The resulting arrangement is ideally suited for sizing fine droplets. However, the planar layout is usually inappropriate for large particles as the sizing sensitivity is too large and the size range is too small.
Considering large differences in the optical layouts of the phase Doppler technique for small and large droplets, is it now desirable to employ flexible hardware, which could be adapted to both the planar and the standard optical layouts. This need is satisfied by the newly developed APV technology.
3. THEORETICAL CONSIDERATIONS
It is now well-established that submicron droplets may be generated using capillary type electrohydrodynamic atomizers, see, e.g. Fernandez de la Mora et al. (1990). The capillary- based electrospraying process was first investigated by Zeleny (1915, 1917) and has since been examined by many other investigators, such as Burayev and Vereshchagin (1972) and Smith (1986). These authors have described various types of instabilities that are induced in the liquid meniscus at the tip of the capillary, as a result of an electrical field parallel to the capillary axis. Depending upon the liquid properties and the strength of the electrical field, many different phenomena may occur at the capillary tip, e.g. a corona discharge may take place without any flow or liquid may start dripping in the form of drops comparable in size to the capillary diameter. The present article is concerned with a special type of flow, in which the liquid stretches out of the capillary tip as an almost perfect cone whose tip is formed into one or more filaments. The liquid filaments break up into fine drops, which are smaller than the capillary diameter by several orders of magnitude. Usually there is no significant corona discharge in this mode of operation.
Before seeking theoretical models of capillary-type electrosprays, it is desirable to determine whether or not they are operating in the classical single-filament mode. In this mode, the entire volume of the liquid passes through the filament whose diameter is about half the droplet diameter. Hence, the kinetic energy of the liquid is highest in the filament and may be expressed as
r m a x = ½ p Q u 2 , (1)
where p, Q and u are the liquid density, volume flowrate and average flow velocity in the filament, respectively. Assuming the filament diameter to be 0.53 times the droplet diameter dp, u may be expressed in terms of Q and d r using the continuity relation. The resulting expression for kinetic energy is as follows:
lOpQ a Kmax ~ 4 (2)
dr
The above relationship, though approximate, highlights the inverse dependence of the largest kinetic energy on the fourth power of the droplet diameter. With decreasing droplet
1206 A.A. NAQW!
diameters, it becomes increasingly difficult to maintain the single-filament mode unless volume flow rates are reduced correspondingly.
By applying the principle of energy conservation to the electrospray, realizability conditions for the existence of a single-filament mode may be derived. The kinetic energy Kma x must be balanced by the absolute enthalpy of the liquid pQh combined with the electrical energy input VI, where V and I are the potential difference and the electrical current, respectively. Comparing the above two forms of energy with the maximum kinetic energy, the following non-dimensional groups are obtained:
10Q 2 N 1 - hd 4 (3)
and 10pQ 3
N2-- VId~ (4)
It is understood that neither the filament would freeze to absolute zero temperature, nor would the entire energy of the electrical field probably be spent on accelerating the fluid. Hence, both N~ and N 2 are expected to be substantially smaller than 1 in the single-filament mode of atomization.
Another realizability condition--which should be satisfied by any electrospray--is the upper limit on the electric current, which follows from the Rayleigh limit for charge of the individual drops. Assuming that each drop carries the largest possible charge, the maximum current is given as
I = 2 4 0 ( ~°~']1''2 (5) . . . . \ 2 d ~ ] '
where e o and y are the permittivity of the free space and the surface tension of the liquid, respectively. Equation (5) follows from the well-known expression of Rayleigh charge limit, see, e.g. Bailey 0988).
4. FLOW FACILITY AND F L U I D P R O P E R T I E S
The flow facility consisted of the classical arrangement for electrohydrodynamic at- omization. As shown in Fig. 5, atomization occurred at the tip of a capillary whose inner diameter was 0.4 mm. A grounded copper plate of 30 mm diameter was located 20 mm below the capillary tip and a potential difference of 6-7 kV was applied between the plate and the capillary. Droplet size measurements were taken 10 mm below the capillary tip along a horizontal line, which is represented by the dashed line in Fig. 5. Various size distributions presented in the next section were taken at point B, which was located 5 mm off-axis.
The present tests were conducted with l-octanol blended with 1-10% sulfuric acid. Various physical properties of the octanol-sulfuric acid solutions are listed in Table 1. These properties were measured using standard analytical instruments. By varying the amount of sulfuric acid, a range of about 20:1 in electrical conductivity and 4:1 in viscosity was covered.
The liquid was allowed to flow from a constant head container. The free surface of the liquid was maintained either at the same level as the capillary tip or raised 4 cm above it. The volume flowrate was estimated using the laminar pressure drop through a tubing of known length and diameter. Without an electrical field, there was no flow through the capillary due to surface tension. The flow induced by the electrical field was found to be 0.1 ml h - 1 for zero head and 0.11 ml h-1 for the hydrostatic head of 4 cm.
The overall electrical current was measured by connecting an ammeter between the metallic capillary and the ground plate and was found to be about 1 #A, which reached the least count of the ammeter. The uncertainty in this reading is estimated to be 25%. The author did not get an opportunity to obtain a more precise measurement; however, the current was found to be fairly invariant with the changes in liquid properties and the hydrostatic head.
Measurement of submicron droplets 1207
C a p i l l a r y
L i q u i d Cone~/./: :: :: ..~.~, ~ - Spray D r o p l e t s
l../i i i i i i i i ~ iii i i i :y~ / - G r o u n d P la te
_J_
Fig. 5. Schematic diagram of the eleetrospray.
Table 1. Properties of 1-octanol/sulfuric acid solution used for electrospraying
Solution No. 1 No. 2 No. 3 No. 4 No. 5 No. 6
H2SO 4 concentration 1% 2% 3% 4% 5% 10% Conductivity (f~- l m - 1) 0.0055 0.0185 0.0316 0.0437 0.0533 0.1079 Viscosity (m 2 s - 1) x 106 11.77 12.87 15.12 18.50 25.29 45.46 Surface tension (N m - 1) x 103 26.0 26.0 26.0 25.9 25.9 25.5 Density (kg m - a) 850 855 860 865 870 880 Viscos./cond. 2 (kg. m.O 2 s - 1) 330.73 32.15 13.02 8.379 7.745 3.436 Refractive index 1.427 1.428 1.429 1.430 1.430 1.432
5. E X P E R I M E N T A L RESULTS AND D I S C U S S I O N
The liquid used in the present electrospray is very volatile and prohibits droplet measurements using off-line devices, such as a differential mobility analyzer and an inertial impactor. The measurements involving sampling are also affected adversely by the high charge density of the drops. These difficulties are obviated by the phase Doppler technique, which enables in situ measurements and provides accurate estimates of droplet sizes and velocities. Furthermore, the measurement has a high spatial resolution, so that local concentrations of droplets, as well as their migration trends, can be examined. This capability of the phase Doppler technique was demonstrated in this preliminary study by examining the variation of mean drop size with off-axis location y. Starting at point A (see Fig. 5), a horizontal distance of 10 mm was covered. As shown in Fig. 6, the mean drop diameter decreases with increasing distance from the spray axis. Apparently, the repulsive forces between drops of like charges have a stronger influence on the smaller drops and they are progressively moved outwards.
The mean diameters in Fig. 6 and in other diagrams are based on 1000 signals collected at each location. In Fig. 6, the mean diameters are consistently smaller than 1 #m.
According to equation (5), a drop diameter of 1/zm corresponds to a maximum current of 800 #A, suggesting that the measured current of 1 #A is realizable.
During the present studies, entire drop size distributions could be measured. Typical results are shown in Fig. 7. These histograms are truly representative of droplet population for sizes larger than 0.2/zm. Droplets in the range 0-0.2/zm are identified, if detected, but a specific diameter cannot be assigned to them by the present instrument. Rather arbitrarily, all such drops were assigned a value of 0.1/zm by the signal processing code. This resulted in an artificial secondary peak in one of the histograms. In fact, each measured distribution had a single strong peak, i.e. the distinction between the main drops and the satellites was found to diminish for such fine drops.
1208 A.A. NAQWI
1 , 2
r. 1.0 0
0
O.8
£
2 o9 0.6
"tJ
c~0.4 0
0 2
0 0
- - l z H z S 0 4 - 2 g H 2 S 0 4
7
o 2 4 6 8 1o Distance y (ram)
Fig. 6. Mean size vs off-axis location.
_ _ S o l u t i o n ~ 1 z e r o h e a d S o l u t i o n ~61 4 c m h e a d
The polydispersity oI the droplets is quantitatively represented in Fig. 8, which shows the mean and the root-mean-square diameters of droplets for the two cases of hydrostatic pressures and six different concentrations of sulfuric acid in octanol.
In Fig. 8, drop sizes are plotted as a function of # /a z where/~ and a denote the liquid viscosity and electrical conductivity, respectively. Evidently, the drop size increases with increasing viscosity and decreasing conductivity. However, the relationship between the mean drop size and t~/a or ]//0 "3/2 is not monotonic. A monotonic change in the mean drop diameter occurs with l~/a2; hence, this parameter is used for plotting the results.
Applying the realizability criteria for single-filament mode to the present spray, it can be shown that N 1 as given by equation (3), varies from 0.05 to 3 for zero head and 0.03 to 1 for the hydrostatic head of 4 cm, respectively. The above estimates are based on mean droplet diameters for the six solutions and a constant specific heat of 1 kJ kg- 1 K - 1. The value of N2 was about the same as N 1 in the present experiments.
The sudden change in the dp vs i~/a 2 relationship in Fig. 8 pertains to N 1 of 0.15 and 0.066 for the hydrostatic heads of zero and 4 cm, respectively. These values suggest that the sudden changes in the curves of Fig. 8 are caused by a transition of the flow from the single-filament mode to the multi-filament mode. Earlier experimental results on submicron droplets, reported by Fernandez de la Mora et al. (1990), also indicate that the value of N1 for single- filament mode is O (10-2).
v i scos i ty / conduc t iv i ty 2, k g m . O h m 2 / s
Fig. 8. Drop size as a function of liquid properties.
The above authors have also found a non-dimensional group of parameters that is somewhat invariant in single-filament mode. This group is given as
X = [271r2a3/pQ 2] 1/3, (6)
where a is the radius of the filament. Based on several previous experimental results, x varies from 0.33 to 0.87. According to the present results, assuming a ratio of 1.9 between the drop diameter and the filament diameter, x is 0.21 and 0.24 for Solution No. 1 (i.e. the right-most points in Fig. 8) operating under hydrostatic heads of 0 and 4 cm, respectively. It is hard to anticipate the origin of discrepancy but the somewhat lower values of the above parameter may have been caused by shrinkage of drops due to evaporation, prior to their measure- ments.
The parameter x decreases further with increasing concentrations of sulfuric acid in the solution. Nevertheless, there is a slow variation of drop size with viscosity and conductivity for Solution Nos 1, 2 and 3 (the last three points in Fig. 8), which is in agreement with equation (6). This equation pertains to single-filament mode and does not include the effects of viscosity and conductivity.
Evidently, the spray was operating in the multi-filament mode for Solution Nos 4, 5 and 6, where the operation with a constant head results in an almost linear relationship between mean droplet diameter and ~/O "2. The detailed nature of the atomization process is not known for the above cases. However, a conical body of liquid at the capillary tip could be seen. Furthermore, almost regular fluctuations with a frequency of about 1 kHz were observed by pointing a laser beam to the tip of the cone and collecting the light scattered therefrom. This organized structure disappeared in the case of the smallest drop diameters.
Apparently, the spray under consideration switches from the highly organized single- filament mode to a completely random process that has been considered by Kelly (1976, 1978), who has suggested the following correlation between the mean drop size, flowrate and electric current, expressed in/~m, m 3 s- 1 and A, respectively.
d r ~ 80~/Q- (7)
According to the above relationship, the mean drop diameter should be 0.42 and 0.44 for the heads of 0 and 4 cm, respectively. For these values of hydrostatic head, the measured diameters corresponding to Solution No. 6 were 0.31 and 0.40/~m, respectively. It may be pointed out that in the past, the validity of equation (7) has been proven only for droplets larger than 1/~m. The smaller values of measured drop diameters are consistent with the previous observations reported by Kelly (1978).
Finally, it may be remarked that, owing to randomization of liquid breakup near the cone tip, about 100 times larger flowrate is handled by the spray of Solution No. 6. This increase in flowrate occurs at the expense of a moderate dispersion in the size distribution.
1210 A.A. NAQWI
6. F I N A L REMARKS
The electrospray measurements based on a planar phase Doppler system have clearly emphasized the need for further experimental, as well as theoretical, work to understand the nature of the pertinent phenomena. It appears that the process of electrohydrodynamic atomization may be classified into three regimes, i.e. completely random, completely organized and intermediate. The third type is evidently more complicated than the others but may be important from a practical point of view.
Further experimental work is needed to establish the conditions under which a transition from one regime to the other takes place. The future analytical work would focus on the individual regimes. The random atomization process is satisfactorily described by the equilibrium analyses of Kelly (1976, 1978).
The classical single-filament mode of atomization is known to be controlled by interfacial shear stresses, at least for liquids of low electrical conductivity. The shear stresses induce a vortical flow inside the liquid cone as reported by Hayati et al. (1986). The vortical motion is not observed for high conductivity liquids. Hence, it is desirable to gradually increase the conductivity in an electrospray and examine the transition from a large scale vortical motion to an insignificant flow recirculation. It may be speculated that the recirculation zone shrinks towards the tip of the liquid cone due to domination of conduction over convection of charges. However, the convective mode eventually prevails as charges finally cease to move by conduction and are carried by the liquid drops. Hence, the interfacial shear stresses may be playing an important role even if the associated recirculation zone is not observable.
Barrero (1991) and colleagues have used a rather simple model of interfacial shear stress to demonstrate that the associated hollow-cone boundary layer matches asymptotically with an inviscid vortex in the core of the liquid cone. Furthermore, the thinning rate of the boundary layer towards the tip of the cone is slower than linear with the streamwise distance and results in a collapse of the hollow-cone layer into a continuous body of liquid just before it reaches the cone tip. Assuming that the liquid filament d iameter - -and hence the droplet d iameter- -would scale with the thickness of the boundary layer at the point of collapse, the order of magnitude of the drop size is estimated as la2/p?. This parameter is 4.5 ktm for Solution No. 1 and increases gradually to 71.3/~m for Solution No. 6.
Considering that the measured drop diameter is about 1/~m for Solution No. 1, the above theory gives reasonable results as long as the single-filament mode prevails. Remarkably enough, this theory reproduces the empirical correlation of equation (6) as well. It should be further pointed out that the electrical conductivity of Solution No. 1 is about four orders of magnitude larger than that of the liquid used by Hayati et al. (1986). Hence, it is not expected that a large vortex occupying the entire liquid cone existed in the present experiments. However, a small recirculation zone near the cone tip may have been present, so that the model of Barrero et al. (1991) was applicable.
In the above scenario, the emergence of a multi-filament mode would mark the inception of boundary layer instabilities due to increasingly large interfacial shear stresses. The experimental results presented herein will be useful in validating such theoretical descrip- tions.
Acknowledoements The experimental part of this work was done at Laboratory of Fluid Mechanics (LSTM), University of Erlangen. The author is grateful to Dr M. Ziema for his assistance in taking the measurements. Thanks are also due to the director of LSTM, Prof. F. Durst for his support and encouragement. The author is indebted to Prof. J. Fernandez de la Mora for his suggestion of the spray fluid and other valuable advice.
R E F E R E N C E S
Bailey, A. G. (1988) Electrostatic Spraying of Liquids, Chap. 3. Wiley, New York. Barrero, A. (1991) Private Communication Dept. Ingenieria Energrtica y Mecanica de Fluidos, Univ. of Seville, Av.
Reina Mercedes s/n, 41012 Seville, Spain. Burayev, T. K. and Vereshchagin, I. P. (1972) Physical processes during electrostatic atomization of liquids. Fluid
Mechanics--Soviet Research 1, 56. Fernandez de la Mora, J., Navascues, J., Fernandez, F. and Rosell-Llompart, J. ~1990) Generation of submicron
monodisperse aerosols in electrosprays. J. Aerosol Sci. 21 (Suppl. 1), $673.
Measurement of submicron droplets 1211
Hayati, I., Bailey, A. I. and Tadros, Th. F. (1986) Mechanism of stable jet formation in electrohydrodynamic atomization. Nature 319, 41.
Kelly, A. J. (1976) Electrostatic metallic spray theory. J. appl. Phys. 47, 5264. Kelly, A. J. (1978) Electrostatic spray theory. J. appl. Phys. 49, 2621. Naqwi, A. (1993) Innovative phase Doppler systems and their applications. Proceedings of 3rd International
Congress on Optical Particle Sizing, Plenary Lecture, p, 245, Yokohama, Japan. Naqwi, A. and Durst, F. (1993) Analysis of laser light scattering interferometric devices for in-line diagnostics of
moving particles. Appl. Optics 32, 4003. Naqwi, A. and Ziema, M. (1992) Extended phase Doppler anemometer for sizing particles smaller than 10 #m. d.
Aerosol Sci. 23, 613. Naqwi, A. Ziema, M., Liu, X., Hohmann, S. and Durst, F. (1992) Droplet and particle sizing using the dual
cylindrical wave and the planar phase Doppler optical systems combined with a transputer based signal processor. Proceedings of Sixth International Syrup. Applications of Laser Techniques to Fluid Mechanics, Paper 15.3, Lisbon, Portugal.
Smith, D. P. H. (1986) The electrohydrodynamic atomization of liquids. IEEE Trans. Ind. Applic. IA-22, 527. Zeleny, J. (1915) On the condition of instability of electrified drops, with applications to the electrical discharge from
liquid points. Proc. Camb. Phil. Soc. 18, 71. Zeleny, J. (1917) Instability of electrified liquid surfaces. The Physical Review X, 1.
