48 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 25, NO. 1, JANUARYIFEBRUARY 1989

Experimental Study on the Breakup of Charged Liquid Droplets

Abstract-Charged droplets of water were formed at the tip of a capillary tube raised to high potential and subjected to external electric fields. The nozzle characteristics were tested to identify the different ejection modes. Under some conditions of electric field at the nozzle tip, breakup of the ejected droplets resulted. These droplets were collected on water-sensitive paper and then examined to verify the validity of the analytical model previously introduced by the authors. The results of these experiments showed good agreement with the model and support the validity of the concept of tree-like secondary breakups introduced in the model.

INTRODUCTION

T IS well known that an electrically charged liquid drop I becomes unstable when the electrical force of repulsion exerted by the charges exceeds the surface tension force [l]. The drop then emits one or more highly charged droplets [2]- [4] and thereby loses both mass and charge. In order to understand this phenomenon, many investigators have carried out both theoretical and experimental studies [5]-[9].

A mathematical model has been introduced by the authors to predict the final state for both single [lo] and multisibling breakup [ 1 11. In these studies the role of external forces on the breakup process and on forced disintegration of the drop below its Rayleigh limit was discussed. The demarcation between the modes of single and multisibling breakup has also been clarified. It was assumed that the main force driving the breakup process is the repulsion forces exerted by the droplet charge and that the multisibling case followed a sequence of tree-like secondary breakups. The results of this model allowed the final number of siblings to be estimated in terms of sibling mass ratios. (The sibling mass ratio was defined as the ratio of the total mass of all the siblings to the initial drop mass.) In particular, it was predicted that for the case of charge, and that the multisibling case followed a sequence of sibling mass ratios greater than 11.1 percent, single-sibling breakup occurred. For sibling mass ratios greater than 11.1 percent, multisibling breakup was predicted, so that for certain ranges of the sibling mass ratio a number of siblings was estimated (Fig. 6 in [l 11). In the present study, the validity of these analytical models has been examined experimentally.

Paper IUSD 86-121, approved by the Electrostatic Processes Committee of the IEEE Industry Applications Society for presentation at the 1986 Industry Applications Society Annual Meeting, Denver, CO, September 28-October 3. This work supported by the National Science and Research Council of Canada. Manuscript released for publication June 10, 1988.

H. M. A. Elghazaly is with the Department of Electrical Engineering, Faculty of Engineering Science, Cairo University, Giza, Egypt.

G. S. P. Castle is with the Department of Electrical Engineering, Faculty of Engineering Science, The University of Western Ontario, London, ON, Canada N6A 5B9.

IEEE Log Number 8823827.

TO ELECTROMETER AND

OSCILLOSCOPE

TO V A R I A B L E D.C. POWER SUPPLY

I

TO 'ELECTROMETER AND OSCILLOSCOPE Fig. 1. Schematic diagram of experimental setup.

GENERAL DESCRIPTION OF THE APPARATUS

The experimental setup used is shown schematically in Fig. 1. It consisted of a stainless-steel hypodermic capillary tube of 150-pm inside diameter and 450-pm outside diameter. Tap water colored with dye was fed from the reservoir to the capillary tube. The height of the reservoir was varied in order to control hydrostatic pressure, which in this experiment was established to be very close to zero, i.e., no dripping for uncharged liquid. A high-voltage power supply was connected to the liquid reservoir to charge the water by conduction. Two identical copper rings, 3.8-cm inner diameter and 1.3-cm height, were mounted and separated by a vertical distance of 1.5 cm. The upper edge bf the first ring (detection ring) was aligned with the capillary tube tip. This ring was grounded through an electrometer set to its current mode. The electro- meter measurement was amplified and traced on an oscillo- scope to sense any dripping and breakup of the water drops. Another dc power supply was connected to the second ring (field ring). This ring allowed the fine adjustment of the electric field around the end of the capillary tube. It also served the purpose of centering the droplets to be captured by a double-shielded Faraday cage located 6.2 cm below the capillary tip. The Faraday cage was also grounded through a

0093-9994/89/0100-0048$01 .OO O 1989 IEEE

ELGHAZALY AND CASTLE: BREAKUP OF CHARGED LIQUID DROPLETS 49

similar electrometer, and its signals were traced on the second channel of the oscilloscope, allowing the number of droplets entering the cage to be counted.

To reduce external electrical noise, mainly from the 60-Hz pickup, the capillary tube, the two rings, and the Faraday cage were mounted in an electrically shielded chamber. A band reject filter (40-100 Hz) was connected in the detection circuit between the electrometer and the oscilloscope to minimize the 60-Hz noise.

DETERMINATION OF NOZZLE CHARACTERISTICS Some preliminary experiments were carried out to deter-

mine the characteristics of the drops ejected from the nozzle under different charging and ring voltages, i.e., different fields around the nozzle tip. In each of these experiments either the charging or ring voltage was kept constant and the other was changed in steps to cover a broad range of drop sizes.

During the experiments, drops which formed at the nozzle tip became charged and then fell through the ring system into the Faraday cage. The second channel of the oscilloscope was used to sense the arrival of a drop in the cage and to estimate the time between two consecutive drips. Droplet size was measured by collecting 60 samples of the ejected droplets at each combination of charging and ring voltages. Fifteen samples were collected on water-sensitive paper placed on the top of the Faraday cage, and 45 samples were collected in oil (nondrying immersion oil for microscopy type B). The oscilloscope signal detected by the upper ring was used simultaneously with the collecting process to check that the collected number of droplets for either single-sibling or multisibling breakups was equal for each sample. If any difference in droplet number occurred, the sample was considered to be faulty and rejected. A total of 60 acceptable samples was obtained for each of the 30 separate experiments carried out. Since the oscilloscope used had the capability of expanding the trace, all the measurements were stored originally at 2 ddivision and then the required part was enlarged to determine the number of siblings.

The collected droplets were examined under a microscope ( 6 . 4 ~ to 80x magnifications) to measure the drop size and spreading factor of the water-sensitive paper (w.s.P.). These experiments also served to check the reproducibility of the results and the measurement of the time between two consecutive drips. In the case of drop disintegration, the initial drop size was determined by measuring the diameter of each individual drop and calculating the total mass of these droplets. This allowed the calculation of the initial drop diameter.

Fig. 2 shows examples of typical oscilloscope traces measuring the detection ring current for the three different modes of drop formation, i.e., single drop, breakup, and spray.

The interpretation of these traces can be understood by recalling that the current (Z) can be represented as I = dQ/dt = (dQ/ds). (dddt), where Q represents charge, t represents

time, and s represents the distance between the drop and the detecting ring.

(C)

div). (b) Breakup ( I = 50 msldiv). (c) Spray ( t = 0.5 sldiv). Fig. 2. Oscilloscope traces from detection ring. (a) Single drop ( t = 50 msl

For the single-drop case, the current increases to a maximum as the drop separates from the nozzle and the velocity increases (labeled as segment A). The current then decreases as the flux component originating from the drop (dQ/ds) decreases, as the drop leaves the vicinity of the detection ring (labeled segment “B”). This trace is character- istic of a single drop with no disruption.

For some combinations of charging and ring voltages it was found that the droplet would undergo disruption after its formation. This condition can occur for a droplet with a charge close to its Rayleigh limit which is perturbed by an external force such as aerodynamic, gravitational, or electric (see discussion in [ 1 13).

The droplet disruption could be observed visually through the stereo microscope. Attempts to photograph the process were unsuccessful due to the lack of adequate high-speed flash equipment. However, the disruption was also observed indi- rectly on the oscilloscope traces for the detection ring current. Two typical examples are shown in Fig. 2. The disintegrations were interpreted as producing a sudden change in droplet velocity caused by the repulsion between the droplets. This then produces a sudden change in the current superimposed upon the normal decay. By comparison, between the oscillo-

50 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 25, NO. 1, JANUARYIFEBRUARY 1989

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CHARGING VOLTAGE ( k V ) Nozzle characteristics at zero ring voltage. Fig. 3.

scope traces and the droplets collected on the W.S.P. it was established that the number of siblings could be determined by counting the number of sudden increases in the current trace in segment B of the oscillograph. The numbered sections shown in Fig. 2(b) illustrate examples for five and three siblings, respectively.

At higher values of charging voltage, individual droplets were no longer formed and a spraying mode developed. This produced a characteristic repetitive signal of markedly higher frequency. A typical example of this condition is illustrated in Fig. 2(c).

These three regimes are also illustrated in the results of a typical nozzle characteristic experiment given in Fig. 3. This shows that for zero ring voltage the drop size reduced with increasing charging voltage. As the charging voltage was further increased, the drop started to disintegrate after its formation. In this breakup region, the number of collected droplets increased rapidly with increasing charging voltage. As the charging voltage approached a certain value, slightly higher than that required for drop disintegration, the breakup mode changed to the spraying mode. In the spraying mode the residual drop which remained attached to the needle suddenly became conical-shaped and very fine droplets were emitted from its tip. (In both the single drop and breakup mode, the original drops were ejected directly from the needle tip.) Fig. 3 also shows that the time between two consecutive drips decreased with increasing charging voltage.

In order to obtain better control in the breakup mode, the electric field at the capillary tip was varied in precise increments. This was accomplished by setting the charging voltage close to that required for breakup. The ring voltage was then varied in steps with either positive or negative polarity until breakup started. This fine adjustment of the ring voltage allowed a fairly wide range of control. The results show that the more positive the ring voltage (the less the electric field concentration at the tip), the larger the drop size.

Charg ing V o l t a g e ( k V )

oam 0 c\ll.ul

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R i n g V o l t a g e ( V I Fig. 4. Contours of equal size droplets.

The contours of equal size droplets for different charging and ring potentials are given in Fig. 4, which also shows the voltage combinations at which the breakup occurred. These contour lines represent the average results of approximately lo00 data points generated from 18 different conditions of voltage combinations.

The spreading factor of W.S.P. was also measured at each step by comparing the average drop diameter of those collected on W.S.P. with those collected in oil. For the drop sizes used in performing the breakup tests, the spreading factor was found to vary between 2.19 and 2.31, with an average of 2.25. Although the spreading factor showed a trend to increase with the increase of the drop size, for the narrow range of drop sizes used in the breakup tests it was decided to use the average spreading factor in measuring the drop sizes. The W.S.P. was much more convenient than the use of the oil

ELGHAZALY AND CASTLE: BREAKUP OF CHARGED LIQUID DROPLETS 5 1

in capturing the droplets, and it also offered an extra magnification of about 2.25, which made the measurement of the very fine droplets easier and more precise.

samples in which an oval shape of a drop appeared, the average diameter was calculated and the drop was counted as a single drop.

BREAKUP TESTS RESULTS

The objective of these experiments was to determine the number of siblings for different sibling mass ratio intervals and compare the results with theoretical predictions. Both the charging and ring voltage were changed within the range of values required to produce breakup, as shown in Fig. 4, to allow different disintegration conditions. Eleven different combinations of the charging and ring voltages were selected to cover conditions producing different numbers of siblings and a range of initial drop sizes between 200- and 350-pm diameter. In choosing these conditions, the time between two consecutive drips was restricted to be longer than 3 s. This restriction was the practical limit required to ensure the individual collection of drops.

The samples at each voltage combination were collected on W.S.P. The oscilloscope trace was simultaneously stored and examined to count the number of siblings ejected from the initial drop and to verify the collected sample. If any difference in droplet number showed up, the faulty sample was rejected. After the collection process, the individual sibling diameters and the residual diameter were measured for each sample using a microscope of 80x magnification, and the sibling mass ratio was calculated.

Of a total of 144 experimental samples collected, 34 samples were rejected because there was either an error in collecting the droplets or because the initial droplet did not disintegrate.

Although many attempts were made to eliminate the experimental errors, some sources of error could not be removed and are described below.

1) The presence of unpredictable space charge and external acoustic noise near the nozzle may introduce random fluctua- tions to the external force.

2) The error in measuring normal droplet diameters of about 50 pm using the graticule of the microscope with 80 x magnification ( k 5 pm resolution based on half a division) was in the range of k 10 percent. The error in measuring large drops, 200 pm or larger, was less than k 2 . 5 percent. The error translates to an error of about k 30 percent in calculating the mass of normal droplets and about k 7.5 percent for large drops. For small siblings, less than 50 pm the error in measuring their mass may be considerably higher (k 100 percent for 16-pm droplets). This error will dramatically affect the accuracy of sibling mass ratios, especially at the transition between the different ranges of sibling mass ratios.

Although using the average spreading factor of the W.S.P. was another source of error in calculating the drop mass (k 8 percent), it offered an extra magnification of 2.25. This magnification in turn reduced the total measuring error of the drop mass for a normal drop (50 pm) from rt 30 to about k 21 percent, while for a 16-pm drop the total measuring error reduced from k 100 to k 5 3 percent.

3) Capturing the drop before reaching its final stable condition could be another source of error. For the few

Fig. 5 shows some typical magnified collected samples. In each of these photographs a relatively large drop, the residual drop, can be observed. One or more smaller droplets (siblings) are in most cases distributed to one side of the residual drop. These photographs also show that all the breakups were asymmetric since none of the samples showed a disruption of the initial drop to n identical drops. This phenomenon supports the assumption of a tree-like disintegration used in the theoretical study [l 11.

Although in a few photographs the distance between the residual drop and some of the siblings was very small in comparison with the drop size, this does not contradict the catenary assumption used in calculating the breakup distance [lo]. Since the distance on the W.S.P. represents only the horizontal component of the separation, there could in fact have been considerably more vertical displacement.

Fig. 6 presents four histograms showing the distributions of experimental results of the number of siblings for different sibling mass ratios. The results of the analysis of these distributions are summarized in Table I. It is clear that the mode of each distribution always satisfies the theoretical prediction of the number of siblings. Table I also shows that more than 80 percent of the collected samples verify the theoretical estimate of the number of siblings for sibling mass ratios covering the range between 5 and 50 percent. For sibling mass ratios between 1 and 5 percent this percentage agreement with the theory drops to approximately 60 percent. This lower agreement with the theory is not unexpected. In the analysis the assumption was made that the external forces affect the minimum energy condition only for the primary, and not the secondary, breakup [ll]. It can also be related to the error in measuring the droplet mass due to small sibling sizes in the lower ranges of sibling mass ratios.

Fig. 7 presents a graphical representation of all the experimental results of the number of siblings collected in the breakup test as a function of the sibling mass ratio as well as the results of the theoretical prediction [ 1 I]. It is clear that the experimental results show good agreement with the theoretical prediction, especially in the high ranges of sibling mass ratios. This figure also presents the calculated maximum error in measuring sibling mass ratios for some typical cases of collected samples. It shows that as sibling mass ratio de- creases, maximum error increases. As stated earlier, this is because, for low sibling mass ratios, the error in measuring the masses of the small siblings increases considerably. For some of the samples which did not satisfy the theoretical predictions, the calculated maximum error was higher than the error for those samples that match the predictions. Although the theoretical analysis predicts no breakup which yields 4, 5 , 7, or 8 siblings, in some samples these numbers were observed. This may be due to capturing the drops before their final stability or to the effect of the external forces on secondary breakup, which may lead to more disintegrations.

5 2 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 25, NO. 1, IANUARYIFEBRUARY 1989

- Fig. 5. Samples of ma] ~nified collected droplets (contact prints). Distance between tick marks represents 200 pm.

M /M0=11.1%-50%

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1 2 3 4

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Fig. 6. Experimental results of distribution of number of siblings for different sibling mass ratios.

TABLE I SUMMARY OF THE EXPERIMENTAL RESULTS

Distribution of the Percentage Number of Siblings Agreement

Theoretical Sib I i n g Mass Ratio of for Number (percent) Samples of Siblings 1

Number Prediction with

2 3 4 5 6 I 8 Theory

- - - - 82 - - - 81

- 65 58 1

1 - 4 -

4 1 22

23

- 2 20 3 3 2 1 -

11.1-50.0 28 1 21 2

3 31 24 6 - - 1 4

5 .O- 1 1 . 1 2.0-5.0 1.0-2.0 2 14 2

ELGHAZALY AND CASTLE: BREAKUP OF CHARGED LIQUID DROPLETS 53

0 .

i t - f 35.8%

I

1 P

f 22.1% I J ? 17.8%

I I

1 2 3 4 5 6 7 8 9 1 0 20 30 40 P e r c e n t a g e S i b l i n g Mass R a t i o

Fig. 7. Experimental results of number of siblings at different sibling mass ratios.

Due to the extremely small sibling sizes involved there are no experimental observations for sibling mass ratios less than 1 percent. However, it is expected that the error in matching the theory would be much higher. This limits the practical use of the theoretical prediction of the number of siblings to cover the range of sibling mass ratios between 1 and 50 percent. This range is quite wide for most of the electrostatic applications where the charge of the drop can be considered the main force driving the breakup process.

CONCLUSION

The experimental results of the collected number of siblings at each range of the sibling mass ratio show good agreement with the analytical model and support the validity of the concept of the tree-like secondary breakups. For sibling mass ratios covering the range between 5 and 50 percent, the percentage agreement with the theory is more than 80 percent. This agreement drops to about 60 percent for sibling mass ratios between 1 and 50 percent. The experimental results also clarify the demarcation between the modes of single-sibling and multisibling breakup at the sibling mass ratio of 11.1 percent.

REFERENCES

Lord Rayleigh, “On the equilibrium of liquid conducting masses charged with electricity,” Philosoph. Mag., vol. 14, pp. 184-186, 1882. J. W. Schweizer and D. N. Hanson, “Stability limit of charged drops,” J. Colloid Interface Sci., vol. 35, pp. 417-423, 1971. M. A. Abbas and J. Latham, “The instability of evaporating charged drops,” J. Fluid Mech., vol. 30, pp. 663-670, 1967. A. Doyle, D. R. Moffett, and B. Vonnegut, “Behaviour of evaporating electrically charged droplets,” J. CoNoid Sci., vol. 19, pp. 136-143, 1964. M. A. Abbas, A. K. Azad, and J. Latham, “The disintegration and electrification of liquid drops subjected to electrical forces,” in Proc. Second Conf. Static Electrification, 1967, pp. 69-77. S. A. Ryce and R. R. Wyman, “Asymmetry in the electrostatic dispersion of liquids,” Can. J. Physics, vol. 42, pp. 2185-2194, 1964.

D. G. Roth and A. J. Kelly, “Analysis of the disruption of evaporating charged droplets,” IEEE Trans. Ind. Appl., vol. IA-19, pp. 771-775, 1983. B. Vonnegut and R. L. Neubauer, “Production of monodisperse aerosol particles by electrical atomization,” J. Colloid Sei., vol. 7, pp.

S. A. Ryce and D. A. Patriarche, “Energy consideration in the electrostatic dispersion of liquids,” Can. J. Physics, vol. 43, pp.

H. A. Elghazaly and G. S. P. Castle, “Analysis of the instability of charged liquid drops,” IEEE Trans. Ind. Appl., vol. IA-22, pp. 892- 895, Sept./Oct. 1986. H. A. Elghazaly and G. S. P. Castle, “Analysis of the Multisibling instability of charged liquid drops,” IEEE Trans. Ind. Appl., vol. IA- 23, pp. 108-113, Jan./Feb. 1987.

515-522, 1952.

2 192-2 199, 1965.

Hany M. A. Elghazaly (S’84-M’86) was born in Cairo, Egypt. He received the B.Sc. and M.Sc. degrees in electrical engineering from Cairo Uni- versity, Cairo, Egypt, in 1978 and 1982, respec- tively, and the Ph.D. from the University of Western Ontario, London, ON, Canada, in 1987.

He is presently an Assistant Professor of Electri- cal Engineering at Cairo University, Cairo, Egypt.

G . S. Peter Castle (S’66-M’68-SM’77) was born in Belfast, Northern Ireland, in 1939. He received the B.E.Sc. degree in electrical engineering from the University of Western Ontario, London, ON, Canada, in 1961, the M.Sc. Eng. and D.I.C. degrees from the Imperial College of Science and Technology, London, England, in 1963, and the Ph.D. degree in 1969.

From 1963 to 1966 he was employed in the Research and Development Laboratories of the Northern Electric Company, Ottawa, ON, Canada,

where he worked on the development of microwave stripline circuitry. In 1966 he returned to the University of Western Ontario as a Research Assistant in the Applied Electrostatics Laboratory. He has worked on a wide range of projects in the field of applied electrostatics, including preciptation, corona discharges, ozone generation, electrostatic coating, and electrophotography. He has published over 65 journal papers and has been granted four patents. He is presently Professor and Chairman of Electrical Engineering at the University of Western Ontario.