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The production of essentially uniform-sized liquid droplets in gaseous or immiscible liquid media under applied a.c. potential
Journal of Electrostatics, 15 (1984) 237--247
237
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
THE PRODUCTION OF ESSENTIALLY UNIFORM-SIZED LIQUID DROPLETS IN GASEOUS OR IMMISCIBLE LIQUID MEDIA UNDER APPLIED A.C. POTENTIAL
MASAYUKI
SATO
Department of Chemical Engineering, Faculty of Engineering, Gunma University, Kiryu, Gunma 3 76 (Japan) (Received April 15, 1983; accepted in revised form January 31, 1984)
Summary Recently, uniform-sized droplets have become desirable in highly advanced industrial processes in which liquid atomization systems are comprised. Uniform droplets have been difficult to produce by prevalent methods. The present study makes the production of essentially-uniform liquid droplets possible in a gaseous or immiscible liquid m e d i u m by applying a non-uniform a.c. electric field. Each droplet was formed synchronously with each cycle change of applied a.c. potential. The diameter of the uniform droplets was controllable from 2.4 m m to 28 # m in gaseous media, and was determined only by the factors of liquid flow rate and applied a.c. frequency.
1. Introduction A good deal of research work has been carried out on the dispersion of liquids in gaseous or immiscible liquid media and it has been applied practically in industry and laboratories. The size of the droplets produced by prevalent methods usually have a widely spread frequency distribution. Similarly, gas bubbles in a liquid medium, which are produced by a high speed air stream issuing from a nozzle, have a wide range of size distribution. It has been somewhat difficult to predict operative conditions of heat and mass transfer or chemical reactions for many gas--liquid or liquid--liquid dispersion systems. Recently, several atomization methods which produce uniform-sized droplets have been studied and reported [1--3]. One of these is the oscillating-nozzle method, which makes use of mechanical vibration on the smooth liquid jet issuing from a nozzle. Uniform droplets are formed at the end of the laminar smooth jet with the same frequency as the applied vibrations. Although it is possible to produce uniform-sized droplets, the operative conditions are limited to within a narrow frequency range. The diameter range of the uniform droplets produced is also narrow, because the mechanical oscillation frequency only exists around the spontaneous self-induced oscillating frequency of the laminar smooth jet. 0304-3886/84/$03.00
© 1984 Elsevier Science Publishers B.V.
238 It is possible to decrease the diameter of the droplets and to reduce their distribution range, by the application of electrostatics to the liquid dispersion system; typically an electrostatic atomization [4--6]. It is applied industrially for painting processes, in which the electric charges o f each drop work effectively to stain the object materials. The effective decrease in diameter of gas bubbles formed at the tip of the nozzle in a liquid m e d i u m was accomplished under an applied non-uniform electric field [7, 8]. The bubble diameters varied widely with decreasing or increasing applied potential, and t h e y had a rather narrow range of size distribution. Furthermore, when an a.c. electric potential was applied to the tip o f the gas-bubbling nozzle, the number of bubbles formed per second agreed with the applied a.c. frequency, and their diameters were extremely uniform [9, 10]. In this paper, the author proposes a new m e t h o d for producing uniform droplets successively in a wide range of sizes by the application of an electrical a.c. potential. When a liquid issuing from a single nozzle was exposed to a non-uniform a.c. electrical field at the tip of the nozzle, it disintegrated into droplets having an exactly uniform diameter. A wide range o f droplet diameters was obtainable when the a.c. frequency and the liquid flow rate were changed, since uniform droplets were produced synchronously with each cycle change of the a.c. frequency. The diameter o f the uniform droplets could be controlled and were determined only by the applied frequency and the liquid flow rate. 2. Experiment The experimental apparatus is shown schematically in Fig. 1. Distilled water was introduced into the nozzle (N) by a microfeeder p u m p (MF) through a m a n o m e t e r (M). The nozzle o f a stainless steel hypodermic needle was attached to a syringe-like adapter. An a.c. voltage f r o m a high voltage a.c. source (HV) was applied between the nozzle and the earth electrode (E). The earch electrode used consisted o f an aluminium plate with a diameter o f 60 mm, in which a hole o f diameter 6 m m was drilled for the formed droplets to pass through. In order to detect the droplets issuing from the nozzle, a light beam from a gas laser (L) crossed the point of droplet formation at the nozzle tip. The light beam was interrupted by the passage o f a d r o p l e t across its path, and this was detected b y a silicon photoelectric cell (D). The signal was input into an electronic counter (C) (where the number of droplets was counted) and the first input channel of a dual-beam oscilloscope ( 0 ) , where a correlation between the wave form of the a.c. voltage recorded on the second channel and the liquid disintegration pattern recorded on the first channel was observed simultaneously. The e f f e c t o f t h e w a v e f o r m o f t h e applied electrical potential was tested w i t h t h r e e k i n d s o f w a v e patterns, in a d d i t i o n t o an a.c. sine w a v e . T h e s e are
239
shown schematically in Fig. 2 (a)--(d). In the figure, the patterns of (a) and (b) were generated by means of a high voltage transformer with 50 Hz only. The pattern of (b) was shown the negative half-wave of (a), which was rectified by a silicon semiconductor diode. Wave patterns (c) and (d) were generated by a variable frequency high voltage source, in which the input signal from a pulse generator was amplified into a high-voltage wave form by means of a triode-transmitter tube. The voltages used in this work are not the average or RMS value but the peak value of applied potentials.
(a)
+U 0 -U
(b)
0 -U
-~
*U
(c)
0
+U
(d)
0
Fig. 1. Schematic diagram of experimental apparatus: A: d.c. amplifier, B: reservoir, C: electronic counter, CL: condenser lens, D: light detector, E: earth electrode, HV: highvoltage source, L: laser light source, M: manometer, MF: micro feeder, N: nozzle, O: dualbeam oscilloscope. Fig. 2. Wave patterns used in this experiment, in which (a), (b), (c) and (d) are a.c. sine wave, rectified negative a.c., positive sine and positive square pulse wave, respectively.
3. Results and discussion Figure 3 shows the variations of droplet diameter as the applied voltage, as shown in Fig. 2 (b), was varied. As the applied voltage was gradually increased from 0 to 3000 V, the droplet diameter decreased. At a potential of 3200 V, the formation rate was 50 per second. It continued up to 4500 V and the droplet diameter kept constant over this range. The droplets were formed one by one synchronously with each cycle change of applied potential. Hereafter, this region is referred to as the "synchronous region". At higher voltages, droplets were formed in a dispersed state, and numerous finer droplets of irregular sizes were produced. Within the synchronous region, droplets were formed at the moment when the applied voltage entered the peak value of each cycle, and their diameters kept exactly uniform in size.
240
When an a.c. sine wave, as shown in Fig. 2 (a), was applied to the nozzle, synchronized droplet formation was also observed within a similar range of voltage indicated in Fig. 3. However, the droplets were formed at the rate of 100 per second, although the applied frequency was 50 Hz. F r o m the pictures observed on an oscilloscope, the droplets were formed when the applied potential entered the peak value of each positive and negative voltage in the a.c. sine wave. The synchronous region was rather narrow as compared with that o f the wave form shown in Fig. 2 (b).
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-U [V] Fig. 3. Variations of droplet diameter with applied rectified negative 50 Hz a.c. potential.
Figure 4 shows examples of instantaneous photographs of droplet formation. A nozzle, which was set up perpendicular t o the earth plate was directed downwards. The liquid flow rate Ql was k e p t at 5.9 X 10 -3 ml/s and the distance L b e t w e e n the nozzle tip and the earth plate was 15 ram. Large drops having a diameter of 2.4 mm dripped from the nozzle tip at the rate o f 0.8 drop per second, when voltage was n o t applied, as shown in Fig. 4 (a). Figures 4(b)--4(e) give examples of the disintegration pattern within the synchronous region. Where the applied voltage was 4000 V at 50 Hz, the applied wave form was shown in Fig. 2 (b), and the resulting droplet diameter was 0.61 ram. At first, as shown in (b), the liquid was elongated downward, having a " n e c k " just below the nozzle tip. Then, after the neck had become a thinner ligament, the drop split from the neck as shown in (c). If the applied voltage was excessively higher than that needed for synchronization, the ligament disintegrated into small droplets. After the droplet split from the neck, the ligament contracted back to the nozzle tip, as shown in (d). At the same time, a few damped oscillations of the liquid surface left at the nozzle tip were observed. Within the synchronous region, the above-mentioned droplet formation was repeated from the state
241
(b) to (e) at the rate of 50 Hz. In the case where a square pulse wave, as shown in Fig. 2 (d), was applied, the ligament became shorter or thinner, and the droplets split more clearly, as compared with the case of Fig. 4, where the wave form of Fig. 2 (b) was used. The distance L affected the voltage of the synchronous region. When L was increased, the voltage which was required to synchronize also increased, and vice versa. However, if the voltage was too high when L was large, undesired small droplets were readily produced. It was suggested that the distance L should be shortened as much as possible, because the range of voltages for synchronous formation would then be widened and consequently it would be preferable to operate within the synchronous region. •-
::
l m m
! O (a)
(b)
(c)
(d)
(e)
Fig. 4. Examples of instantaneous photographs of disintegration patterns of a droplet, in which (a) indicates natural dropping and (b) to (e) are states of synchronizing with an applied rectified negative a.c. potential of 50 Hz.
Figure 5 shows the synchronous region in relation to liquid flow rate QI and applied voltage U, where the applied wave form was a positive sine wave from a variable frequency high-voltage source, as shown in Fig. 2 (c). When the liquid flow rate Q1 was kept constant and the applied voltage was increased, synchronous formation began at a lower limit of voltage, Umin. When the voltage was increased above the upper limit voltage, Umax, a number of non-uniform sized droplets were produced. When the flow rate Q1 was varied, the lower limit Ql,min and the upper limit Ql,max for the synchronous region were observed. When the frequency of the applied voltage was increased, ~mJn, Umax, ~ l , m i n and Ql,max increased. The synchronous region seemed to resemble a parallelogram with Umin and Umax as the oblique sides, and ~ l , m i n and Ql,max as the perpendicular sides. Smaller and more uniformly-sized droplets could be produced in the following manner: (i) the outer diameter of the nozzle dn,o should be made smaller for the purpose of obtaining a thinner ligament at the tip of the nozzle; (ii) the frequency of the applied potential should be higher for in-
242
creasing the number of droplets produced per second; (iii) the liquid flow rate should be smaller for decreasing the volume of each droplet. Under the experimental conditions of the present study, uniform-sized droplets having a minimum diameter of 28 ttm were obtained, in which dn,o, v, Q1, L and U were 27 t~m, 2700 Hz, 3.25 × 10 -s ml/s, 3 mm and 3120 V, respectively. On the other hand, large droplets having a uniform diameter of 2.4 mm were obtained, when the pulse voltage, as shown in Fig. 2 (d), was applied. They were formed if the applied frequency was around 0.8 Hz, when the natural dripping frequency without applied potential was 0.8 Hz, as shown in Fig. 4 (a). Therefore, the proposed method in this study was practicable for the production of uniform-sized droplets of diameter range 2.4 mm to 28 ttm. However, operating conditions are limited to an extremely low Q1 in this method, as mentioned above, because the droplets split from the tip of nozzle by dripping. 4 dn,0:0 13x10-3m L
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=20 xl0-3m
~_:-<> . . . . . . . . .
;
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I
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2
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3
QI [m3/s] Fig. 5. Synchronous regions with varying liquid flow rate under applied positive sine wave.
A considerable increase in the number of droplets produced per second was attained using a laminar smooth jet having a diameter corresponding to the inner diameter of a nozzle dn,i. The smooth jet issuing from the nozzle, breaks up sontaneously with a high frequency in self-induced oscillations without any applied voltage. When the proper frequency of an appropriate voltage was applied to the jet, a great many uniform droplets could be produced successively at the rate of more than 20 000 drops per second. Figure 6 shows instantaneous photographs of the breakup pattern of a laminar smooth jet within the synchronous region. The wave form of the applied voltage was shown in Fig. 2 (c). In the figure, the smooth liquid jet issuing downwards from the nozzle is positioned in upper part of the picture, and the black portion is a shadow of the earth electrode plate. Microphotographs of droplets, which were immersed in kerosene containing a small amount of Span-80, are shown in Fig. 7. The photographs show that the droplets are fairly uniform in size like a number of beads of equal size. Figure 8 supports the uniformity of the particles shown in Fig. 7, in which the operating conditions are the same as
243
.~_j
Imm
"i
e m
i
(a)
, i
(b)
(c)
F i g . 6. I n s t a n t a n e o u s p h o t o g r a p h s o f d r o p l e t f o r m a t i o n f r o m t h e e n d o f s m o o t h l i q u i d j e t w i t h v a r y i n g f r e q u e n c y o f a p p l i e d p o s i t i v e s i n e w a v e , w h e r e Q1 = 9 . 5 5 x 1 0 -9 m 3 / s a n d dn, i f 5 3 . 3 X 1 0 -4 m. (a) ~ = 2 7 k H z , d d , o b s = 7 6 X 1 0 "6 m , dd,cal© = 8 8 X 1 0 -6 m ; ( b ) ~ = 17 k H z , dd,ob s ffi I 0 0 X I 0 -6 m , dd,calc ffi 1 0 2 X I 0 - ' m ; ( c ) ~ = 1 0 k H z , dd,ob s = 1 2 1 X 1 0 -6 m , dd,calc = 1 2 2 X 1 0 -6 m.
:
(a)
.:
Imm
(b)
(c)
Fig. 7. U n i f o ~ - s i z e d droplets of distilled water which were obtained by means of the immez~ion sampling method in a Span-80--kere~ene solution, where the conditions are the sarne as in Fig. 6.
244
that o f Figs. 6 and 7. In the figure, the smaller portions of the histograms indicate the disintegrated or coagulated drops when t h e y were moved to the surface o f a glass plate for the purpose of photographing. There was good agreement between the average diameters which were measured directly from photographs, and these calculated from Q1 and v using the correlation d d = (6Q1/~v) ~/3. 100
I
--
(a)
U c"
100
(b) CI
E z
100
0 (c)
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I
-
x10 -~-
2
dd [ m ] Fig. 8. Histograms of the size distribution of droplets which appeared in Fig. 7.
The disintegration mechanisms of liquid at the nozzle tip under an applied a.c. potential are thought to rely on m a n y complicated factors, since the electric field is concentrated at the liquid surface. The following might be some o f the explanations for droplet formation: (i) the liquid at the nozzle tip which is exposed to the non-uniform electric field would be d r s ~ e d downwards to the opposite earth electrode because o f its electric charge. The liquid would detach from the nozzle as a droplet, when the balance is lost between the upward force due to surface tension and the downward force due to gravity and the electric field; (ii) the surface tension o f the liquid would decrease as an effect o f the surface charge on the liquid surface which is proportional to the square of the applied electric field strength [11] ; the droplet would detach from the nozzle at the m o m e n t when the applied potential has reached its peak voltage. This synchronized formation was also applicable to a dispersion of uniform liquid droplets in an immiscible liquid. A non-uniform a.c. electric field was applied to the liquid issuing from the tip of the nozzle which was
245 placed in an immiscible liquid. For example, the synchronized formation of kerosene droplets in distilled water was observed over a wide range of applied a.c. frequency. The applied potential needed to synchronize in distilled water was much lower than that of the dispersion in a gaseous medium; it was about 200 to 1000 V peak value of a.c. sine wave. The range of a.c. frequency for the synchronous formation was 0.7 Hz to 5800 Hz, and the diameter range was 3 mm to 140 ~m, for which the inner diameter of the nozzle was 0.23 ram. Similar synchronous phenomena were observed in other liquid systems, for example, carbon tetra-chloride, benzene and n-hexane in distilled water. However, synchronous formation was impossible in the opposite systems; that is to say the dispersion of distilled water in organic liquids which had low electrical conductivity and dielectric constant, although the diameter of the droplets decreased with increasing applied potential. If a small amount of Span-80 was added to the organic solvent, for the purpose of increasing electrical conductivity, synchronous formation could be observed within the voltage of 1000 V. The formation of uniform liquid droplets in immiscible liquids could be useful for the operation of liquid--liquid extraction, and for the collapse and collection of used emulsions, where the size distribution of the emulsion had been the main problem in deciding its operative conditions and the design of its processes. The proposed methods make the production of uniform droplets of a desired size and the control of their size possible. Many applications of the uniform droplets are foreseen, for example, the production of uniform emulsions and micro-capcels, drying processes for producing fine uniform solid particles, ink jet systems or other mass transport processes. 4. Conclusion A new method of producing uniform~ized liquid droplets in gaseous or immiscible liquid media was investigated by applying a non-uniform a.c. electric field to the surface of liquid which was issuing from the tip of a capillary nozzle. The number of the droplets formed per second was the same as, or was double the applied frequency of the a.c. potential. The synchronous formation occurred within a region which was bounded by the applied voltage, frequency, flow rate and the other parameters of the equipment. The diameter of the droplets was extremely uniform, when the liquid flow rate and the applied frequency were kept constant. The droplet diameter, therefore was essentially dependent only on the flow rate and the frequency, within the synchronous region. With the present experimental apparatus and conditions, the upper limit of frequency for the synchronous formation was 30 kHz in the case of a laminar smooth jet, and the lower limit was 0.8 Hz in dripping mode, so the droplet
246
diameter was controllable within a range of 28 ~m to 2.4 mm. It was shown that similar synchronous formation was also possible in other immiscible liquids within a wide range of frequency; i.e. droplets of organic solvents in distilled water or water droplets in organic solvents. The applied potential for synchronous formation was varied with changing electrical properties of the liquid medium. For industrial or laboratory use, many problems based upon the size distribution of droplets in gaseous or liquid media could be lessened by the use of uniform-sized droplets produced by the present method. Acknowledgements The author wishes to thank Prof. S. Masuda, Tokyo University, for his valuable discussions, and also to acknowledge Prof. T. Sakai, Dr. M. Sadakata and Prof. M. Kuroda, Gunma University, and Mr. Y. Ito, Mr. M. Sato and Mr. N. Ohta, for their valuable suggestions and help with the experiments. Notation
d L
Q U
diameter (m) distance between nozzle tip and earth electrode (m) flow rate (mS/s) applied voltage (V) frequency (Hz)
Subscripts d i 1 max
rain n o
0
drop inner liquid maximum minimum nozzle outer at zero potential
References 1 T. Sakai and N. Hoshino, Production of uniform droplets by longitudinal vibration of audio frequency, J. Chem. Eng., Japan, 13 (1980) 263. 2 P. Schummer and K.H. Tebel, Production of monodmpemed drolm by forced longitudinal vibration of a liquid jet, International Conference on Liquid Atomization and Spray Systems, (1982) 47. 3 T. Miura, S. Kano, S. Tanno and S. Oh'tani, Formation of uniformly-sized drops in another immiscible liquid, Kagaku Kogaku Ronbunahu, 8 (1982) 366. 4 B. Vonnegut and R.L. Neubauer, Production of monodkpet~e liquid particles by electrical atomization, J. Colloid Sci., 7 (1952) 616.
247
5 V.G. Drozin, The electricaldispersion of liquids as aerosols,J. Colloid Sci., 10 (1955) 158.
6 A. Watanabe, Charge of liquid drop shapes electrification,Oyo Butsuri, 37 (1968) 314. 7 M. Sato, Cloudy bubble formation in a strong non-uniform electricfield,J. Electrostatics,8 (1980) 285. 8 M. Sato, M. Kuroda and T. Sakai, Effect of electrostaticson bubble formation, Kagaku Kogaku Ronbunshu, 5 (1979) 380. 9 M. Sato, The formation of gas bubbles synchronized with a.c. potential, J. Phys. D: Apph Phys., 13 (1980) L1. 10 M. Sato, S. Miyazaki, M. Kuroda and T. Sakai, The synchronized formation of uniformsized bubbles under applied a.c.potential, Kagaku Kogaku Ronbunshu, 7 (1981) 115. 11 M. Sato, M. Kito and T. Sakai, Surface tension reduction under high potential by vibrating jet method, Kagaku Kogaku Ronbunshu, 3 (1977) 504.
237
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
THE PRODUCTION OF ESSENTIALLY UNIFORM-SIZED LIQUID DROPLETS IN GASEOUS OR IMMISCIBLE LIQUID MEDIA UNDER APPLIED A.C. POTENTIAL
MASAYUKI
SATO
Department of Chemical Engineering, Faculty of Engineering, Gunma University, Kiryu, Gunma 3 76 (Japan) (Received April 15, 1983; accepted in revised form January 31, 1984)
Summary Recently, uniform-sized droplets have become desirable in highly advanced industrial processes in which liquid atomization systems are comprised. Uniform droplets have been difficult to produce by prevalent methods. The present study makes the production of essentially-uniform liquid droplets possible in a gaseous or immiscible liquid m e d i u m by applying a non-uniform a.c. electric field. Each droplet was formed synchronously with each cycle change of applied a.c. potential. The diameter of the uniform droplets was controllable from 2.4 m m to 28 # m in gaseous media, and was determined only by the factors of liquid flow rate and applied a.c. frequency.
1. Introduction A good deal of research work has been carried out on the dispersion of liquids in gaseous or immiscible liquid media and it has been applied practically in industry and laboratories. The size of the droplets produced by prevalent methods usually have a widely spread frequency distribution. Similarly, gas bubbles in a liquid medium, which are produced by a high speed air stream issuing from a nozzle, have a wide range of size distribution. It has been somewhat difficult to predict operative conditions of heat and mass transfer or chemical reactions for many gas--liquid or liquid--liquid dispersion systems. Recently, several atomization methods which produce uniform-sized droplets have been studied and reported [1--3]. One of these is the oscillating-nozzle method, which makes use of mechanical vibration on the smooth liquid jet issuing from a nozzle. Uniform droplets are formed at the end of the laminar smooth jet with the same frequency as the applied vibrations. Although it is possible to produce uniform-sized droplets, the operative conditions are limited to within a narrow frequency range. The diameter range of the uniform droplets produced is also narrow, because the mechanical oscillation frequency only exists around the spontaneous self-induced oscillating frequency of the laminar smooth jet. 0304-3886/84/$03.00
© 1984 Elsevier Science Publishers B.V.
238 It is possible to decrease the diameter of the droplets and to reduce their distribution range, by the application of electrostatics to the liquid dispersion system; typically an electrostatic atomization [4--6]. It is applied industrially for painting processes, in which the electric charges o f each drop work effectively to stain the object materials. The effective decrease in diameter of gas bubbles formed at the tip of the nozzle in a liquid m e d i u m was accomplished under an applied non-uniform electric field [7, 8]. The bubble diameters varied widely with decreasing or increasing applied potential, and t h e y had a rather narrow range of size distribution. Furthermore, when an a.c. electric potential was applied to the tip o f the gas-bubbling nozzle, the number of bubbles formed per second agreed with the applied a.c. frequency, and their diameters were extremely uniform [9, 10]. In this paper, the author proposes a new m e t h o d for producing uniform droplets successively in a wide range of sizes by the application of an electrical a.c. potential. When a liquid issuing from a single nozzle was exposed to a non-uniform a.c. electrical field at the tip of the nozzle, it disintegrated into droplets having an exactly uniform diameter. A wide range o f droplet diameters was obtainable when the a.c. frequency and the liquid flow rate were changed, since uniform droplets were produced synchronously with each cycle change of the a.c. frequency. The diameter o f the uniform droplets could be controlled and were determined only by the applied frequency and the liquid flow rate. 2. Experiment The experimental apparatus is shown schematically in Fig. 1. Distilled water was introduced into the nozzle (N) by a microfeeder p u m p (MF) through a m a n o m e t e r (M). The nozzle o f a stainless steel hypodermic needle was attached to a syringe-like adapter. An a.c. voltage f r o m a high voltage a.c. source (HV) was applied between the nozzle and the earth electrode (E). The earch electrode used consisted o f an aluminium plate with a diameter o f 60 mm, in which a hole o f diameter 6 m m was drilled for the formed droplets to pass through. In order to detect the droplets issuing from the nozzle, a light beam from a gas laser (L) crossed the point of droplet formation at the nozzle tip. The light beam was interrupted by the passage o f a d r o p l e t across its path, and this was detected b y a silicon photoelectric cell (D). The signal was input into an electronic counter (C) (where the number of droplets was counted) and the first input channel of a dual-beam oscilloscope ( 0 ) , where a correlation between the wave form of the a.c. voltage recorded on the second channel and the liquid disintegration pattern recorded on the first channel was observed simultaneously. The e f f e c t o f t h e w a v e f o r m o f t h e applied electrical potential was tested w i t h t h r e e k i n d s o f w a v e patterns, in a d d i t i o n t o an a.c. sine w a v e . T h e s e are
239
shown schematically in Fig. 2 (a)--(d). In the figure, the patterns of (a) and (b) were generated by means of a high voltage transformer with 50 Hz only. The pattern of (b) was shown the negative half-wave of (a), which was rectified by a silicon semiconductor diode. Wave patterns (c) and (d) were generated by a variable frequency high voltage source, in which the input signal from a pulse generator was amplified into a high-voltage wave form by means of a triode-transmitter tube. The voltages used in this work are not the average or RMS value but the peak value of applied potentials.
(a)
+U 0 -U
(b)
0 -U
-~
*U
(c)
0
+U
(d)
0
Fig. 1. Schematic diagram of experimental apparatus: A: d.c. amplifier, B: reservoir, C: electronic counter, CL: condenser lens, D: light detector, E: earth electrode, HV: highvoltage source, L: laser light source, M: manometer, MF: micro feeder, N: nozzle, O: dualbeam oscilloscope. Fig. 2. Wave patterns used in this experiment, in which (a), (b), (c) and (d) are a.c. sine wave, rectified negative a.c., positive sine and positive square pulse wave, respectively.
3. Results and discussion Figure 3 shows the variations of droplet diameter as the applied voltage, as shown in Fig. 2 (b), was varied. As the applied voltage was gradually increased from 0 to 3000 V, the droplet diameter decreased. At a potential of 3200 V, the formation rate was 50 per second. It continued up to 4500 V and the droplet diameter kept constant over this range. The droplets were formed one by one synchronously with each cycle change of applied potential. Hereafter, this region is referred to as the "synchronous region". At higher voltages, droplets were formed in a dispersed state, and numerous finer droplets of irregular sizes were produced. Within the synchronous region, droplets were formed at the moment when the applied voltage entered the peak value of each cycle, and their diameters kept exactly uniform in size.
240
When an a.c. sine wave, as shown in Fig. 2 (a), was applied to the nozzle, synchronized droplet formation was also observed within a similar range of voltage indicated in Fig. 3. However, the droplets were formed at the rate of 100 per second, although the applied frequency was 50 Hz. F r o m the pictures observed on an oscilloscope, the droplets were formed when the applied potential entered the peak value of each positive and negative voltage in the a.c. sine wave. The synchronous region was rather narrow as compared with that o f the wave form shown in Fig. 2 (b).
I
I
I
I
I
Q~ [m3/s] © 5 92x10 -9 _
[]
"~
~
O0
,
l
o
_
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i
I
i
i
1
2
3
4
1
-5xlO 3
-U [V] Fig. 3. Variations of droplet diameter with applied rectified negative 50 Hz a.c. potential.
Figure 4 shows examples of instantaneous photographs of droplet formation. A nozzle, which was set up perpendicular t o the earth plate was directed downwards. The liquid flow rate Ql was k e p t at 5.9 X 10 -3 ml/s and the distance L b e t w e e n the nozzle tip and the earth plate was 15 ram. Large drops having a diameter of 2.4 mm dripped from the nozzle tip at the rate o f 0.8 drop per second, when voltage was n o t applied, as shown in Fig. 4 (a). Figures 4(b)--4(e) give examples of the disintegration pattern within the synchronous region. Where the applied voltage was 4000 V at 50 Hz, the applied wave form was shown in Fig. 2 (b), and the resulting droplet diameter was 0.61 ram. At first, as shown in (b), the liquid was elongated downward, having a " n e c k " just below the nozzle tip. Then, after the neck had become a thinner ligament, the drop split from the neck as shown in (c). If the applied voltage was excessively higher than that needed for synchronization, the ligament disintegrated into small droplets. After the droplet split from the neck, the ligament contracted back to the nozzle tip, as shown in (d). At the same time, a few damped oscillations of the liquid surface left at the nozzle tip were observed. Within the synchronous region, the above-mentioned droplet formation was repeated from the state
241
(b) to (e) at the rate of 50 Hz. In the case where a square pulse wave, as shown in Fig. 2 (d), was applied, the ligament became shorter or thinner, and the droplets split more clearly, as compared with the case of Fig. 4, where the wave form of Fig. 2 (b) was used. The distance L affected the voltage of the synchronous region. When L was increased, the voltage which was required to synchronize also increased, and vice versa. However, if the voltage was too high when L was large, undesired small droplets were readily produced. It was suggested that the distance L should be shortened as much as possible, because the range of voltages for synchronous formation would then be widened and consequently it would be preferable to operate within the synchronous region. •-
::
l m m
! O (a)
(b)
(c)
(d)
(e)
Fig. 4. Examples of instantaneous photographs of disintegration patterns of a droplet, in which (a) indicates natural dropping and (b) to (e) are states of synchronizing with an applied rectified negative a.c. potential of 50 Hz.
Figure 5 shows the synchronous region in relation to liquid flow rate QI and applied voltage U, where the applied wave form was a positive sine wave from a variable frequency high-voltage source, as shown in Fig. 2 (c). When the liquid flow rate Q1 was kept constant and the applied voltage was increased, synchronous formation began at a lower limit of voltage, Umin. When the voltage was increased above the upper limit voltage, Umax, a number of non-uniform sized droplets were produced. When the flow rate Q1 was varied, the lower limit Ql,min and the upper limit Ql,max for the synchronous region were observed. When the frequency of the applied voltage was increased, ~mJn, Umax, ~ l , m i n and Ql,max increased. The synchronous region seemed to resemble a parallelogram with Umin and Umax as the oblique sides, and ~ l , m i n and Ql,max as the perpendicular sides. Smaller and more uniformly-sized droplets could be produced in the following manner: (i) the outer diameter of the nozzle dn,o should be made smaller for the purpose of obtaining a thinner ligament at the tip of the nozzle; (ii) the frequency of the applied potential should be higher for in-
242
creasing the number of droplets produced per second; (iii) the liquid flow rate should be smaller for decreasing the volume of each droplet. Under the experimental conditions of the present study, uniform-sized droplets having a minimum diameter of 28 ttm were obtained, in which dn,o, v, Q1, L and U were 27 t~m, 2700 Hz, 3.25 × 10 -s ml/s, 3 mm and 3120 V, respectively. On the other hand, large droplets having a uniform diameter of 2.4 mm were obtained, when the pulse voltage, as shown in Fig. 2 (d), was applied. They were formed if the applied frequency was around 0.8 Hz, when the natural dripping frequency without applied potential was 0.8 Hz, as shown in Fig. 4 (a). Therefore, the proposed method in this study was practicable for the production of uniform-sized droplets of diameter range 2.4 mm to 28 ttm. However, operating conditions are limited to an extremely low Q1 in this method, as mentioned above, because the droplets split from the tip of nozzle by dripping. 4 dn,0:0 13x10-3m L
C>--O v : 1 0 0 Hz ~ 50
=20 xl0-3m
~_:-<> . . . . . . . . .
;
o
o
3 & T
I
0
1
I
2
x l 0 -g
3
QI [m3/s] Fig. 5. Synchronous regions with varying liquid flow rate under applied positive sine wave.
A considerable increase in the number of droplets produced per second was attained using a laminar smooth jet having a diameter corresponding to the inner diameter of a nozzle dn,i. The smooth jet issuing from the nozzle, breaks up sontaneously with a high frequency in self-induced oscillations without any applied voltage. When the proper frequency of an appropriate voltage was applied to the jet, a great many uniform droplets could be produced successively at the rate of more than 20 000 drops per second. Figure 6 shows instantaneous photographs of the breakup pattern of a laminar smooth jet within the synchronous region. The wave form of the applied voltage was shown in Fig. 2 (c). In the figure, the smooth liquid jet issuing downwards from the nozzle is positioned in upper part of the picture, and the black portion is a shadow of the earth electrode plate. Microphotographs of droplets, which were immersed in kerosene containing a small amount of Span-80, are shown in Fig. 7. The photographs show that the droplets are fairly uniform in size like a number of beads of equal size. Figure 8 supports the uniformity of the particles shown in Fig. 7, in which the operating conditions are the same as
243
.~_j
Imm
"i
e m
i
(a)
, i
(b)
(c)
F i g . 6. I n s t a n t a n e o u s p h o t o g r a p h s o f d r o p l e t f o r m a t i o n f r o m t h e e n d o f s m o o t h l i q u i d j e t w i t h v a r y i n g f r e q u e n c y o f a p p l i e d p o s i t i v e s i n e w a v e , w h e r e Q1 = 9 . 5 5 x 1 0 -9 m 3 / s a n d dn, i f 5 3 . 3 X 1 0 -4 m. (a) ~ = 2 7 k H z , d d , o b s = 7 6 X 1 0 "6 m , dd,cal© = 8 8 X 1 0 -6 m ; ( b ) ~ = 17 k H z , dd,ob s ffi I 0 0 X I 0 -6 m , dd,calc ffi 1 0 2 X I 0 - ' m ; ( c ) ~ = 1 0 k H z , dd,ob s = 1 2 1 X 1 0 -6 m , dd,calc = 1 2 2 X 1 0 -6 m.
:
(a)
.:
Imm
(b)
(c)
Fig. 7. U n i f o ~ - s i z e d droplets of distilled water which were obtained by means of the immez~ion sampling method in a Span-80--kere~ene solution, where the conditions are the sarne as in Fig. 6.
244
that o f Figs. 6 and 7. In the figure, the smaller portions of the histograms indicate the disintegrated or coagulated drops when t h e y were moved to the surface o f a glass plate for the purpose of photographing. There was good agreement between the average diameters which were measured directly from photographs, and these calculated from Q1 and v using the correlation d d = (6Q1/~v) ~/3. 100
I
--
(a)
U c"
100
(b) CI
E z
100
0 (c)
I
O0-
I
-
x10 -~-
2
dd [ m ] Fig. 8. Histograms of the size distribution of droplets which appeared in Fig. 7.
The disintegration mechanisms of liquid at the nozzle tip under an applied a.c. potential are thought to rely on m a n y complicated factors, since the electric field is concentrated at the liquid surface. The following might be some o f the explanations for droplet formation: (i) the liquid at the nozzle tip which is exposed to the non-uniform electric field would be d r s ~ e d downwards to the opposite earth electrode because o f its electric charge. The liquid would detach from the nozzle as a droplet, when the balance is lost between the upward force due to surface tension and the downward force due to gravity and the electric field; (ii) the surface tension o f the liquid would decrease as an effect o f the surface charge on the liquid surface which is proportional to the square of the applied electric field strength [11] ; the droplet would detach from the nozzle at the m o m e n t when the applied potential has reached its peak voltage. This synchronized formation was also applicable to a dispersion of uniform liquid droplets in an immiscible liquid. A non-uniform a.c. electric field was applied to the liquid issuing from the tip of the nozzle which was
245 placed in an immiscible liquid. For example, the synchronized formation of kerosene droplets in distilled water was observed over a wide range of applied a.c. frequency. The applied potential needed to synchronize in distilled water was much lower than that of the dispersion in a gaseous medium; it was about 200 to 1000 V peak value of a.c. sine wave. The range of a.c. frequency for the synchronous formation was 0.7 Hz to 5800 Hz, and the diameter range was 3 mm to 140 ~m, for which the inner diameter of the nozzle was 0.23 ram. Similar synchronous phenomena were observed in other liquid systems, for example, carbon tetra-chloride, benzene and n-hexane in distilled water. However, synchronous formation was impossible in the opposite systems; that is to say the dispersion of distilled water in organic liquids which had low electrical conductivity and dielectric constant, although the diameter of the droplets decreased with increasing applied potential. If a small amount of Span-80 was added to the organic solvent, for the purpose of increasing electrical conductivity, synchronous formation could be observed within the voltage of 1000 V. The formation of uniform liquid droplets in immiscible liquids could be useful for the operation of liquid--liquid extraction, and for the collapse and collection of used emulsions, where the size distribution of the emulsion had been the main problem in deciding its operative conditions and the design of its processes. The proposed methods make the production of uniform droplets of a desired size and the control of their size possible. Many applications of the uniform droplets are foreseen, for example, the production of uniform emulsions and micro-capcels, drying processes for producing fine uniform solid particles, ink jet systems or other mass transport processes. 4. Conclusion A new method of producing uniform~ized liquid droplets in gaseous or immiscible liquid media was investigated by applying a non-uniform a.c. electric field to the surface of liquid which was issuing from the tip of a capillary nozzle. The number of the droplets formed per second was the same as, or was double the applied frequency of the a.c. potential. The synchronous formation occurred within a region which was bounded by the applied voltage, frequency, flow rate and the other parameters of the equipment. The diameter of the droplets was extremely uniform, when the liquid flow rate and the applied frequency were kept constant. The droplet diameter, therefore was essentially dependent only on the flow rate and the frequency, within the synchronous region. With the present experimental apparatus and conditions, the upper limit of frequency for the synchronous formation was 30 kHz in the case of a laminar smooth jet, and the lower limit was 0.8 Hz in dripping mode, so the droplet
246
diameter was controllable within a range of 28 ~m to 2.4 mm. It was shown that similar synchronous formation was also possible in other immiscible liquids within a wide range of frequency; i.e. droplets of organic solvents in distilled water or water droplets in organic solvents. The applied potential for synchronous formation was varied with changing electrical properties of the liquid medium. For industrial or laboratory use, many problems based upon the size distribution of droplets in gaseous or liquid media could be lessened by the use of uniform-sized droplets produced by the present method. Acknowledgements The author wishes to thank Prof. S. Masuda, Tokyo University, for his valuable discussions, and also to acknowledge Prof. T. Sakai, Dr. M. Sadakata and Prof. M. Kuroda, Gunma University, and Mr. Y. Ito, Mr. M. Sato and Mr. N. Ohta, for their valuable suggestions and help with the experiments. Notation
d L
Q U
diameter (m) distance between nozzle tip and earth electrode (m) flow rate (mS/s) applied voltage (V) frequency (Hz)
Subscripts d i 1 max
rain n o
0
drop inner liquid maximum minimum nozzle outer at zero potential
References 1 T. Sakai and N. Hoshino, Production of uniform droplets by longitudinal vibration of audio frequency, J. Chem. Eng., Japan, 13 (1980) 263. 2 P. Schummer and K.H. Tebel, Production of monodmpemed drolm by forced longitudinal vibration of a liquid jet, International Conference on Liquid Atomization and Spray Systems, (1982) 47. 3 T. Miura, S. Kano, S. Tanno and S. Oh'tani, Formation of uniformly-sized drops in another immiscible liquid, Kagaku Kogaku Ronbunahu, 8 (1982) 366. 4 B. Vonnegut and R.L. Neubauer, Production of monodkpet~e liquid particles by electrical atomization, J. Colloid Sci., 7 (1952) 616.
247
5 V.G. Drozin, The electricaldispersion of liquids as aerosols,J. Colloid Sci., 10 (1955) 158.
6 A. Watanabe, Charge of liquid drop shapes electrification,Oyo Butsuri, 37 (1968) 314. 7 M. Sato, Cloudy bubble formation in a strong non-uniform electricfield,J. Electrostatics,8 (1980) 285. 8 M. Sato, M. Kuroda and T. Sakai, Effect of electrostaticson bubble formation, Kagaku Kogaku Ronbunshu, 5 (1979) 380. 9 M. Sato, The formation of gas bubbles synchronized with a.c. potential, J. Phys. D: Apph Phys., 13 (1980) L1. 10 M. Sato, S. Miyazaki, M. Kuroda and T. Sakai, The synchronized formation of uniformsized bubbles under applied a.c.potential, Kagaku Kogaku Ronbunshu, 7 (1981) 115. 11 M. Sato, M. Kito and T. Sakai, Surface tension reduction under high potential by vibrating jet method, Kagaku Kogaku Ronbunshu, 3 (1977) 504.