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Research on electrostatic hazards associated with tank washing in very large crude carriers (supertankers) II. Study of the charging mechanism during the production of water aerosols
Journal of Electrostatics, 1 (1975) 47--60 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
R E S E A R C H ON ELECTROSTATIC H A Z A R D S ASSOCIATED WITH TANK WASHING IN VERY L A R G E CRUDE C A R R I E R S (SUPERTANKERS) II. STUDY OF THE CHARGING MECHANISM D U R I N G THE PRODUCTION OF WATER AEROSOLS*
J.D. BASSETT
Department of Electrical Engineering, University of Southampton (Great Britain) (Received July 29, 1974; in revised form September 24, 1974)
Summary The paper describes some initial results in an investigation into the charging mechanisms which operate when water droplets in the size range observed during tank cleaning are produced. A brief review of relevant previous work is given, followed by a discussion of the mechanisms which might be important. An experimental system designed to investigate the mechanisms is described, and experimental results for the droplets produced from carbon dioxide and sodium nitrate solutions are given and discussed. The atomisation process was also briefly investigated and preliminary high speed cine observations are discussed.
1. Introduction The object of the study described in this paper is to investigate the mechanisms whereby atomisation of water produces an electrically charged mist. During tank washing a charged mist accumulates in the tank as described in the paper by Van der Meet and White [1]. Because this aerosol has a size distribution in the range 0.1--50 X 10 -6 m, the study was confined to a system which conveniently produced droplets within this range. The phenomenon of charging of the aerosol formed when water is broken up into droplets has been well known for over a century. Work on trying to understand the mechanisms by which the droplets become charged started in 1890, and a considerable amount of work on the subject has been undertaken since. These previous studies of spray electrification have indicated four mechanisms by which charge may be transferred to a forming droplet. These are charging from the electrical double layer at the air--water interface, charging arising from contact potentials between the liquid and any solid surface it might encounter during atomisation, the charging caused by droplets being formed in an external electric field, and, finally, charging originating from the random distribution of ions in the bulk liquid. * Paper presented in the Special Symposium on Tanker Explosions at the 2nd International Conference on Static Electricity, Frankfurt, 6 April, 1973.
48 Investigations by Iribarne and Mason [2], Jonas and Mason [3], and Levin and H o b b s [ 4 ] , have indicated that the important process for the droplets acquiring a net charge is the double-layer effect. In a review article, Iribarne[5] has shown that an equation of the form: Q = I~(1 - e x p (--t/r))
(1.1)
will describe the charging of a droplet as a function of the charging current calculated from double-layer theory, I; the relaxation time of ions in the liquid, ~; and the formation time of the droplet, t. When the relaxation time is much greater than the formation time, it can be seen that eqn. (1.1) will reduce to an equation of the form Q = Ir
(1.2)
Iribarne [ 5] has discussed fully h o w these equations have been applied to charging of droplets from a variety of atomising processes. Levin and Hobbs [4] discussed the role of contact potentials on charging, and suggested that as these potentials are relatively small they would n o t significantly affect charging. This is borne out by the work of Vos [6] who found no significant difference between the charging produced from a jet impacting on several different metal surfaces. Immediately the charged aerosol has started to build up, the droplets subsequently forming will be atomised in an electric field, which will affect the net charge being transferred to the aerosol. Latham and Mason [ 7 ] developed a theory for the charge transferred between two conducting spheres of radii R and r, when they came into contact and then separated in an electric field. The charge transferred is given by: Q = 3.3 × lO-l°71ErZcosO
(1.3) 7 2
where 71 is a function of ~ (71 = B- for equally sized spheres), E is the applied field and 0 is the angle between this field and the line of centres of the two spheres. The work of Jennings and Latham [8] has shown that eqn.(1.3) can give the charge transferred between two droplets colliding in an electric field, and that this is n o t significantly affected by the length of filament joining the drops. It should be possible to apply a similar equation for a droplet breaking from a jet in an applied field. In any atomising process, where fragments of liquid are being separated, because the ions in a liquid are distributed at random, any one fragment may contain a net charge of either sign. The charge transferred to the aerosol by this mechanism, however, will be statistically distributed and the total charge transfer should be zero. Work by Dodd [9] has indicated that a theory of statistical charging, where the standard deviation of the charge distribution is given by: o = 2 . 9 × 10 -19 N1/2d 3/2
(1.4)
where N is the concentration of monovalent ion pairs and d is the droplet size, can be applied to the spray charging of several non-polar liquids.
49 Loeb [10] has suggested that a mechanism of this type will also occur with pure water. As the relaxation time of the charge in the liquid becomes shorter, the probability of highly charged droplets being produced by this mechanism should be reduced. There has been no investigation on the charging of water aerosols which has analysed the size and charge data of the aerosol in detail to gain an understanding of the processes involved. The mean electric field at the point of impact of a cleaning jet during washing can achieve a value of about 104 V m -1 , due to the charged aerosol. It was considered that this field would tend to produce charged droplets of opposite sign to the original by induction. Very little work has been done on water atomised in the presence of low electric fields. The experimental rig described below was designed so that a number of important parameters could be varied and their influence on the aerosol studied. In particular, electric field at the surface of the liquid and the effect of chemical additives could be investigated. 2. Experimental work In designing an experimental system, the main object was to construct a system capable of distinguishing the relative importance of the charging processes mentioned in Section 1. To achieve this, the experimental set-up differed uniquely, in several ways, from previous work by others in the field [1, 2, 3, 9]. Firstly, atomisation t o o k place in a well-defined area so that a known electric field could be applied. Secondly, only the air--water interface was involved in the atomising process, thus eliminating any effects of contact potentials. This was achieved using ultrasonic atomisation. Thirdly, the aerosol was analysed from individual droplets to give size and charge data. In this way, the influences of the double layer, ion concentration fluctuations, and the external field, could be analysed and separated. The atomising process could be investigated using high speed cine techniques.
2. 1 Aerosol analysis The experimental system was an adaptation of the technique used by Dodd [9] which was based on the Hopper and Laby [11] determination of the charge of an electron. The positions of the droplets as a function of time were recorded photographically while the aerosol was undergoing settling in crossed gravitational and electric fields. The film record thus yielded vertical and horizontal velocities. These, in turn, gave size and charge. There were two main differences between Dodd's technique and that used here. The first was that the dark field illumination used for observing droplet position was at 90 ° to the viewing axis. The advantage of this was that all droplets illuminated would be in focus. The second difference was that the aerosol was introduced from the b o t t o m of the settling duct and allowed to flow through it for a certain time. The flow was then stopped and the aerosol photographed under-
50 going sedimentation. Evaporation of droplets was considerably reduced by this procedure, because of saturation of the atmosphere in the settling region. Even the smaller droplets only reduced their diameter by a maximum of 6% during the period of measurement. Dodd was unable to observe water droplets in his apparatus because of evaporation. At equilibrium, the particle diameter is given by: 1
3
(2.1)
6uvrVvC = -6 ~d (pp -- Pm)g giving
_1
18VvnC 12 d = [ ~pp~p-pm)g u
(2.2)
C is a correction factor for particles t o o small, or too large, to o b e y Stokes Law. ~, pp, Pm and g are the viscosity of air, the density of the droplet, the density of air, and gravitational acceleration, respectively. Similarly, charge is given by:
6 ~ r V h C = ne E
(2.3)
giving 1
18 Vv~ C n - 37r~eEVh C L[(pp -- pr~)g
.1~
(2.4)
.J
E is the electric field and n the number of unit charges. For particles with 1 0 -6 ( d < 4 × 10 -s m the correction factor, C, is 1.
2.2 Atomiser The solutions to be atomised had to be carefully prepared as small amounts of impurities drastically affect charging. All the water used to make solutions was first de-ionised and then double distilled in a nitrogen atmosphere. This procedure was adopted as an ion exchange column would not remove surface active impurities such as algae from tap water. Distilling in a nitrogen atmosphere was necessary to avoid contamination by carbon dioxide from the atmosphere. A liquid spray of similar size to that observed in a tank during cleaning was produced by a 1 MHz ultrasonic focusing transducer. The focal length of the transducer was 5 X 10 -2 m and it was powered from a signal generator and a 50 W R.F. amplifier. The ring applying the electric field during atomisation was 6 X 10-2 m in diameter and was suspended 2 . 5 X 10 -2 m above the liquid surface. The atomising system is shown in Fig.1. The vessel containing the solution to be atomised could be cleaned by circulating de-ionised water. A sample of solution could be introduced as indicated in the diagram.
51
WASHING •
ADDING SOLUTION
ELECTRIC
?!i ULTRASONIC TRANSDUCER
~DRIDAIN t
Fig.l. Atomising system. Conductivity cells connected to a capacitance--conductance bridge monitored both the cleaning water and the solutions.
2. 3 Sedimentation cell The cell in which the aerosol was observed consisted of a 1-cm-square-section duct into which a glass tube of the same section fitted. On two sides of this tube were pmces of conducting glass such that a horizontal electric field could be applied (see Fig.2). At the top of the duct, a low vacuum (15 torr) was applied through two millipore sintered glass filters. The whole duct was enclosed in 1-cm-thick brass to aid temperature stability. There were two thermocouples to monitor the temperature at the top and b o t t o m of the duct. Temperature differences of 0.06°C could be measured using a digital voltmeter. 2. 4 Photographic recording The recording of the droplets is illustrated in Fig.3. The light source was a He--Ne laser. The beam was passed through a heat filter and through a pol~dser to adjust the intensity. A shutter was used to cut o f f light to the cell except when droplets were being filmed. This avoided any heating which might occur. A chopping disc was included to produce intermittent lighting of the settling area of known frequency. This also reduced heating still further. The image of the droplets formed by a × 10 microscope was focused on the photocathode of an image intensifier tube, and the image produced by this was bright enough to film. 2. 5 Control system A control system for the experiment was constructed so that it was easy to photograph whilst operating the apparatus. The amplifier supplying the transducer was switched on by a relay. There was a solenoid valve to stop the
52
orr)
MILLIPORE FILTERS
BF CAI .THERMOCOUPLE
CONDUCTING GLASS ELECTRODE GL
WINI
TERMINAL FOR FIELD Gt
THERMOCOUPLE
Fig.2. Sedimentation cell.
aerosol flow and the shutter was also electrically operated. The deflecting electrodes in the sedimentation cell were connected to earth through a relay which could be energised to apply the required voltage when the droplet trajectories were being recorded. The experiment could thus be controlled from a single rotary switch placed near the camera. To record a sample of droplets, the procedure was as follows: 1. atomise some liquid for a few seconds; 2. allow the aerosol to flow up the duct; 3. stop the flow; 4. apply the deflecting field; 5. immediately photograph the sample.
53
GLASS DUCT .
~
CONDUCTING GLASS ELECTRODES
0 MICROSCOPE ' ~ C H O P P I N G DISC c=== ~ S H U T T E R |
I~POLARISER .--,J::z~"~"HEAT FILTER
IMAGE INTENSIFIER
CINE CAMERA CONTROL SWITCH
LASER
Fig.3. Photographic recording system. The R.F. power to the atomiser was adjusted to give a sample which was of the right droplet concentration for ease of counting later. 2. 6 Data analysis The size and charge data were obtained by measuring the vertical and horizontal deflections of the particles from the film. A computer program produced the statistical distributions, means, and other quantities, from this data. 3. Results and discussion 3.1 De.ionised water The de-ionised water used for the initial experiments when these results were taken was contaminated with carbon dioxide from the atmosphere. The conductivity was 4 X 10 -4 S m-1 . The size distribution of a sample of aerosol is shown in Fig.4. The dashed curve is a log normal distribution whose parameters were estimated from the experimental data. The geometric mean particle size was 10 -s m and the range of sizes observed was within that quoted by Lindbauer [12] for photographic measurements on the mist found during tank cleaning. The distribution of particle charge is shown in Fig.5 and the dashed curve shows the normal (Gaussian) distribution whose parameters were estimated from the experimental data. The mean charge was 43 electrons (--7 X 10 -18 C) per drop and the standard deviation of the distribution was 173 electronic units (--2.8 X 10 -17 C). It can be seen that the aerosol contained particles of both signs, the majority with low values of charge. The charge contained in 10 -3 kg of aerosol of 10 -s m droplets, each containing a charge of 43 electrons (--7 X 10 -1~ C), is 10 -s C. As the estimated particle concentration in a tanker
54
Probability Density
0"20
// //
0-10
. 15
10
5
rl
1"f'~--
20 Particle
2~
Size X 106(m)
Fig.4. Particle size distribution for de-ionised water sample.
Probability Density 0.0085
O. 0 0 5 0
0-0025
t/I
\
/i
\x\
J -lOOO
-50o
0
50o
rn
I"I
lOO0
15o0
Charge [Electrons]
Fig.5. Particle charge distribution for de-ionised water sample.
m i s t is 2 X 10 -3 kg m -3 , this value o f m e a n charge c o u l d readily give t h e observed values o f 10 -s C m -3 f o r charge d e n s i t y . T h e value o f ~-- 10 -17 C p e r 10 - s m d r o p f o r a 4 X 10 -4 M c a r b o n d i o x i d e s o l u t i o n is o f t h e s a m e o r d e r as t h a t o b s e r v e d b y I r i b a m e a n d M a s o n f o r t h e charging d u r i n g b u b b l e bursting. I f t h e e s t i m a t e d value o f t h e s t a n d a r d d e v i a t i o n c a n be r e l a t e d t o a sta-
55 / .S
t
/
/
/ / t / ,~.
X"'" I 6
X i"'l 8
I 10
I 12
-101
,. ....,o-'"
I 14
I
particle size 1 6 X 106(m)
Fig.6. Size--charge relationship for de-ionised water.
tistical charging t h e o r y calculating the standard deviation from eqn.(1.4), the observed value is t o o low, pr obabl y because the t h e o r y was developed for n o n p o lar liquids with immobile ions and does n o t a c c o u n t for charge relaxation. The charge--size relationship is shown in Fig.6. The dashed curve was calculated f r o m eqn.(1.1) for a molar c o n c e n t r a t i o n of 4 × 10 -4 M. However, as a small error in c o n c e n t r a t i o n produces a considerable change in the value o f Q given by the equation due to the exponential dependence on relaxation time, only the general trend of the curves should be compared. 3.2 S o d i u m nitrate s o l u t i o n
The conductivity of the solution used was 1.7 × 10 -3 S m -1 , the molar c o n c e n t r a t i o n being 10 -3 M. The size distributions of samples atomised under different electric fields were similar e x c e p t t hat the mean size decreased slightly with increasing field. This would be e xpe c t e d as the field gives the forming droplet an extra acceleration. The mean size was 10 -s m for no applied field and 8 . 4 X 10 .6 m for a field o f 8.3 × 104 V m -1 . A typical size distribution is shown in Fig.7 and the dashed line is the log normal curve. The mist was again within the diam eter range q u o t e d for tank washing. The charge distributions of samples of aerosol atomised under different electric fields are shown in Fig.8, and the dashed curves are t he normal distributions. Again, the aerosol contained particles o f b o th signs most of whose values were close to zero. The standard deviation o f the f o u r curves were within 6 % of the mean standard deviation, which was 285 electronic units ( - - 4 . 6 × 10 -17 C). This indicates t hat if these values could be used as an indication of a statistical charging mechanism, the external field did n o t affect it; as would be expected. The value of the standard deviation was again t o o low and charge relaxation was p r o b a b l y the explanation. The effect o f the field on the charge distributions was to shift the mean value o f charge. A graph of mean charge versus applied field is shown in Fig.9. The straight line is eqn.(1.3) assuming 71 cos0 = 1. It appears t hat
56 0.3 Probability density
0.2
,
0.1 !
!
=f 5
10
15
20 Particle size
XlOS(m)
Fig.'/. Particle s i z e d i s t r i b u t i o n for s o d i u m n i t r a t e s o l u t i o n . Fig 8(b)
Fig 8(a)
0"005 ' Probabitity density
Probability 0.005 t density
0.003
/ n, -1500
-1000
Fig. 8(c)
.,
-500
[
n -2000
0.005 Probab~lity density
j in -1500
Fig.8 Fig.8 Fig.8 Fig.8
1000 500 (Particle charge e- )
(a). (b). (c). (d).
-lOaD
-
i -1500
~" -I000
-500
I
~'i.t-~ , 500 1000
, 1500
,~, 2000
~Particle charge e- ~,
0.005 Probabilit y density
"., 500
~" ' I , 1000 1500 ( Particle charge e- )
/ I ITI . ¢ / d l l -1000 -500
500
n. ~0
n, ,n 1500 2000 ( Particle charge e- )
Particle c h a r g e d i s t r i b u t i o n s for s o d i u m n i t r a t e s o l u t i o n s w i t h d i f f e r e n t a p p l i e d e l e c t r i c fields: - - 1 0 4 V m -1 , N o field, 1 0 4 V m -1 , 8 . 3 × 1 0 4 V m - 1 .
57
Q (e-)
alculated f r o m e q u a t i o n
+100
E ( V m -1 ) -10,000
i -5000
i + 5000
j./ p//t~
i + 10,000
J
Fig.9. Relationship between mean droplet charge and applied electric field for sodium nitrate solution.
the charge on the aerosol, caused by applying a field, reached a saturation value. It is known from work on electrostatic paint spraying that particles below about 10 -s m cannot readily be electrostatically atomised in air. This is possibly because the surface field on the smaller drops reaches a value where a discharge will take place. If high surface fields were present, more highly charged droplets would be expected to be formed. However, as the aerosol density was high at the instant of atomisation, sites would be screened from the field, and highly charged droplets would probably be lost by coagulation. The charge--size relationships at different values of field are shown in Fig.10. It can be seen that the gradient increased only at particle sizes above about 8 X 10 -6 m. This could, again, have been due to the surface field. The relaxation time would also affect both the charge--field relationship and the charge--size relationship. At a concentration of 10 -3 M the relaxation time is of the order of 10 -6 sec. Droplet formation time calculated from the equation of Newitt et al. [13] for a 5 X 10 -6 m droplet is of this order and for a 10 -s m droplet about 5 X 10 -6 sec.
3. 3 High speed cine investigation Three frames of each of the two sequences of film taken are shown in Fig. 11. The top set shows the whole ultrasonic fountain and the other set shows a closer view of the top of the jet. Both films were taken at 5,000 frames per second. It appeared that the aerosol was produced intermittantly from the globule-shaped part of the jet at the top. One globule seemed to burst, producing a large number of small droplets. Crawford [ 14] mentions t h a t the appearance of these globules indicates that air is being absorbed into the ul-
58
+ O ®
(e-)
/ +2500v
//
300 '
// x
/
x/,
/
+300v
,/
200
®
100
x
i 6
x
. . . .i. . 8
x._
-~" X ...... 10
--7
mr''"
x'"
. . - Ov i
12
14 Particle
size
X lOP(m)
-100
-200
x -300
-%
-300v
Fig. 10. Size--charge relationship for sodium nitrate solution with different applied electric fields.
Fig. 11. Stills from film of atomisation. Top set shows whole jet; Bottom set shows close-up of top of jet.
59 trasonic fountain due to the presence of cavitation bubbles at the base of the jet. Thus the mechanism for atomisation was probably cavitation ihduced. 4. Conclusions The experimental system which was developed enabled atomisation and charge generation processes in water to be studied under controlled conditions. The investigation was far from complete, but results up to April 1973 suggested that charge generation by disintegration of the liquid was sufficient to explain the observed charge densities in tanks. Charge exchange between the liquid and any electrode (such as a tank wall} did n o t seem to be an essential part of the electrical process. The statistical charging mechanism was found to predominate the observed charge distributions. The simple theory developed for nonpolar liquids did not describe these distributions, probably because of the change caused by charge relaxation. The development of the theory is being studied. The effect of electric field upon charge production, such that the charge value saturated at the high fields observed, was of significance in determining the time constant of charge build-up in a ship's tank. This aspect of the work is being studied in more detail. It appeared that atomisation by cavitation might predominate in the ultrasonic process and further high speed photography would provide more evidence for this.
5. Acknowledgements I would like to thank Shell International Marine Ltd., who sponsored the studentship which enabled this work to be done. Nomenclature C E I N Q R d e g n r
Cunningham correction to Stokes Law Undisturbed electric field in which a droplet is formed, (V m -~ ) Droplet charging current calculated from double-layer theory and the mode of droplet formation, (A) Number of monovalent ion pairs in the liquid, (m -3 ) Droplet charge, (C) Radius of one sphere when contacting another of radius r in an electric field, (m) Droplet diameter, (m) Charge of the electron, (C) Acceleration due to gravity, (m s-~ ) Number of elementary charges on a droplet Radius o f one sphere when contacting another of radius r in an electric field, (m)
60
t Vm Vv 71
Formation time of a droplet, (s) Horizontal drift velocity of a charged droplet in an electric field, (m s-~ ) Vertical velocity of droplet settling under gravity, (m s-~ ) Numerical factor related to ratio of radii of two spheres Viscosity of air, (Pa s) Pm Density of air, (kg m -3 ) pp Density of water (kg m -3 ) Standard deviation of charge distribution calculated from statistical theory, (C) 0 Angle between line of centres of two spheres and the electric field, (tad) r Relaxation time of ions in the liquid, (s) References 1 2 3 4
5 6
7 8
9 10 11 12 13
14
D. van der Meet and J.W. White. Electrostatic Charge Generation During Tank Washing, Project Summary and Introduction, J. Electrostatics, to be published. J.V. Iribarne and B.J. Mason, Electrification accompanying the bursting of bubbles in water and dilute aqueous solutions, Trans. Farad. Soc., 63 (1967) 2234. P.R. Jonas and B.J. Mason, Systematic charging of water droplets produced by breaking of liquid jets and filaments, Trans. Farad. Soc., 64 (1968) 1971. Z. Levin and P.V. Hobbs, Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation, Phil. Trans. Roy. Soc. (London), 269 (1971 ) 555. J.V. Iribarne, The electrical double layer and electrification associated with water disruption processes, J. Rech. Atmos., 6 (1972) 265. B. Vos, Electrostatic charge generation during washing of tanks with water sprays -IV: Mechanism studies, Proc. 3rd Conf. Static Electrification, London, May 1971, Inst. Phys. Conf. Set. No. 11, p. 184. J. Latham and B.J. Mason, Electrical ~charging of hail pellets in a polarising electric field, Proc. Roy. Soc. A, 266 (1962) 387. S.G. Jennings and J. Latham, The charging of water drops falling and colliding in an electric field, Proc. 3rd Conf. Static Electrification, London, May 1971, Inst. Phys. Conf. Ser. No. 11, p. 84. E.E. Dodd, The statistics of liquid spray and dust electrification by the Hopper and Laby method, J. Appl. Phys., 24 {1953) 73. L.B. Loeb, Static Electrification II. 1. Homogeneous or symmetrical charging of liquids and solids on dispersion, Progr. in Dielectrics, 5 (1963) 235. V.D. Hopper and T.H. Laby, The electronic charge, Proc. Roy. Soc. A, 178 (1941) 243. R.L. Lindbauer, Some properties of charged mist produced by gun cleaning, Koninklijke/Shell--Laboratorium, Amsterdam, Internal Report 6, Nov. 1971. D.M. Newitt, N. Dombrowski and F.H. Knelman, Liquid entrainment. 1. The mechanism of drop formation from gas or vapour bubbles, Trans. Inst. Chem. Engrs., 32 (1954) 244. A. Crawford, Ultrasonic Engineering, Butterworths, 1955.
R E S E A R C H ON ELECTROSTATIC H A Z A R D S ASSOCIATED WITH TANK WASHING IN VERY L A R G E CRUDE C A R R I E R S (SUPERTANKERS) II. STUDY OF THE CHARGING MECHANISM D U R I N G THE PRODUCTION OF WATER AEROSOLS*
J.D. BASSETT
Department of Electrical Engineering, University of Southampton (Great Britain) (Received July 29, 1974; in revised form September 24, 1974)
Summary The paper describes some initial results in an investigation into the charging mechanisms which operate when water droplets in the size range observed during tank cleaning are produced. A brief review of relevant previous work is given, followed by a discussion of the mechanisms which might be important. An experimental system designed to investigate the mechanisms is described, and experimental results for the droplets produced from carbon dioxide and sodium nitrate solutions are given and discussed. The atomisation process was also briefly investigated and preliminary high speed cine observations are discussed.
1. Introduction The object of the study described in this paper is to investigate the mechanisms whereby atomisation of water produces an electrically charged mist. During tank washing a charged mist accumulates in the tank as described in the paper by Van der Meet and White [1]. Because this aerosol has a size distribution in the range 0.1--50 X 10 -6 m, the study was confined to a system which conveniently produced droplets within this range. The phenomenon of charging of the aerosol formed when water is broken up into droplets has been well known for over a century. Work on trying to understand the mechanisms by which the droplets become charged started in 1890, and a considerable amount of work on the subject has been undertaken since. These previous studies of spray electrification have indicated four mechanisms by which charge may be transferred to a forming droplet. These are charging from the electrical double layer at the air--water interface, charging arising from contact potentials between the liquid and any solid surface it might encounter during atomisation, the charging caused by droplets being formed in an external electric field, and, finally, charging originating from the random distribution of ions in the bulk liquid. * Paper presented in the Special Symposium on Tanker Explosions at the 2nd International Conference on Static Electricity, Frankfurt, 6 April, 1973.
48 Investigations by Iribarne and Mason [2], Jonas and Mason [3], and Levin and H o b b s [ 4 ] , have indicated that the important process for the droplets acquiring a net charge is the double-layer effect. In a review article, Iribarne[5] has shown that an equation of the form: Q = I~(1 - e x p (--t/r))
(1.1)
will describe the charging of a droplet as a function of the charging current calculated from double-layer theory, I; the relaxation time of ions in the liquid, ~; and the formation time of the droplet, t. When the relaxation time is much greater than the formation time, it can be seen that eqn. (1.1) will reduce to an equation of the form Q = Ir
(1.2)
Iribarne [ 5] has discussed fully h o w these equations have been applied to charging of droplets from a variety of atomising processes. Levin and Hobbs [4] discussed the role of contact potentials on charging, and suggested that as these potentials are relatively small they would n o t significantly affect charging. This is borne out by the work of Vos [6] who found no significant difference between the charging produced from a jet impacting on several different metal surfaces. Immediately the charged aerosol has started to build up, the droplets subsequently forming will be atomised in an electric field, which will affect the net charge being transferred to the aerosol. Latham and Mason [ 7 ] developed a theory for the charge transferred between two conducting spheres of radii R and r, when they came into contact and then separated in an electric field. The charge transferred is given by: Q = 3.3 × lO-l°71ErZcosO
(1.3) 7 2
where 71 is a function of ~ (71 = B- for equally sized spheres), E is the applied field and 0 is the angle between this field and the line of centres of the two spheres. The work of Jennings and Latham [8] has shown that eqn.(1.3) can give the charge transferred between two droplets colliding in an electric field, and that this is n o t significantly affected by the length of filament joining the drops. It should be possible to apply a similar equation for a droplet breaking from a jet in an applied field. In any atomising process, where fragments of liquid are being separated, because the ions in a liquid are distributed at random, any one fragment may contain a net charge of either sign. The charge transferred to the aerosol by this mechanism, however, will be statistically distributed and the total charge transfer should be zero. Work by Dodd [9] has indicated that a theory of statistical charging, where the standard deviation of the charge distribution is given by: o = 2 . 9 × 10 -19 N1/2d 3/2
(1.4)
where N is the concentration of monovalent ion pairs and d is the droplet size, can be applied to the spray charging of several non-polar liquids.
49 Loeb [10] has suggested that a mechanism of this type will also occur with pure water. As the relaxation time of the charge in the liquid becomes shorter, the probability of highly charged droplets being produced by this mechanism should be reduced. There has been no investigation on the charging of water aerosols which has analysed the size and charge data of the aerosol in detail to gain an understanding of the processes involved. The mean electric field at the point of impact of a cleaning jet during washing can achieve a value of about 104 V m -1 , due to the charged aerosol. It was considered that this field would tend to produce charged droplets of opposite sign to the original by induction. Very little work has been done on water atomised in the presence of low electric fields. The experimental rig described below was designed so that a number of important parameters could be varied and their influence on the aerosol studied. In particular, electric field at the surface of the liquid and the effect of chemical additives could be investigated. 2. Experimental work In designing an experimental system, the main object was to construct a system capable of distinguishing the relative importance of the charging processes mentioned in Section 1. To achieve this, the experimental set-up differed uniquely, in several ways, from previous work by others in the field [1, 2, 3, 9]. Firstly, atomisation t o o k place in a well-defined area so that a known electric field could be applied. Secondly, only the air--water interface was involved in the atomising process, thus eliminating any effects of contact potentials. This was achieved using ultrasonic atomisation. Thirdly, the aerosol was analysed from individual droplets to give size and charge data. In this way, the influences of the double layer, ion concentration fluctuations, and the external field, could be analysed and separated. The atomising process could be investigated using high speed cine techniques.
2. 1 Aerosol analysis The experimental system was an adaptation of the technique used by Dodd [9] which was based on the Hopper and Laby [11] determination of the charge of an electron. The positions of the droplets as a function of time were recorded photographically while the aerosol was undergoing settling in crossed gravitational and electric fields. The film record thus yielded vertical and horizontal velocities. These, in turn, gave size and charge. There were two main differences between Dodd's technique and that used here. The first was that the dark field illumination used for observing droplet position was at 90 ° to the viewing axis. The advantage of this was that all droplets illuminated would be in focus. The second difference was that the aerosol was introduced from the b o t t o m of the settling duct and allowed to flow through it for a certain time. The flow was then stopped and the aerosol photographed under-
50 going sedimentation. Evaporation of droplets was considerably reduced by this procedure, because of saturation of the atmosphere in the settling region. Even the smaller droplets only reduced their diameter by a maximum of 6% during the period of measurement. Dodd was unable to observe water droplets in his apparatus because of evaporation. At equilibrium, the particle diameter is given by: 1
3
(2.1)
6uvrVvC = -6 ~d (pp -- Pm)g giving
_1
18VvnC 12 d = [ ~pp~p-pm)g u
(2.2)
C is a correction factor for particles t o o small, or too large, to o b e y Stokes Law. ~, pp, Pm and g are the viscosity of air, the density of the droplet, the density of air, and gravitational acceleration, respectively. Similarly, charge is given by:
6 ~ r V h C = ne E
(2.3)
giving 1
18 Vv~ C n - 37r~eEVh C L[(pp -- pr~)g
.1~
(2.4)
.J
E is the electric field and n the number of unit charges. For particles with 1 0 -6 ( d < 4 × 10 -s m the correction factor, C, is 1.
2.2 Atomiser The solutions to be atomised had to be carefully prepared as small amounts of impurities drastically affect charging. All the water used to make solutions was first de-ionised and then double distilled in a nitrogen atmosphere. This procedure was adopted as an ion exchange column would not remove surface active impurities such as algae from tap water. Distilling in a nitrogen atmosphere was necessary to avoid contamination by carbon dioxide from the atmosphere. A liquid spray of similar size to that observed in a tank during cleaning was produced by a 1 MHz ultrasonic focusing transducer. The focal length of the transducer was 5 X 10 -2 m and it was powered from a signal generator and a 50 W R.F. amplifier. The ring applying the electric field during atomisation was 6 X 10-2 m in diameter and was suspended 2 . 5 X 10 -2 m above the liquid surface. The atomising system is shown in Fig.1. The vessel containing the solution to be atomised could be cleaned by circulating de-ionised water. A sample of solution could be introduced as indicated in the diagram.
51
WASHING •
ADDING SOLUTION
ELECTRIC
?!i ULTRASONIC TRANSDUCER
~DRIDAIN t
Fig.l. Atomising system. Conductivity cells connected to a capacitance--conductance bridge monitored both the cleaning water and the solutions.
2. 3 Sedimentation cell The cell in which the aerosol was observed consisted of a 1-cm-square-section duct into which a glass tube of the same section fitted. On two sides of this tube were pmces of conducting glass such that a horizontal electric field could be applied (see Fig.2). At the top of the duct, a low vacuum (15 torr) was applied through two millipore sintered glass filters. The whole duct was enclosed in 1-cm-thick brass to aid temperature stability. There were two thermocouples to monitor the temperature at the top and b o t t o m of the duct. Temperature differences of 0.06°C could be measured using a digital voltmeter. 2. 4 Photographic recording The recording of the droplets is illustrated in Fig.3. The light source was a He--Ne laser. The beam was passed through a heat filter and through a pol~dser to adjust the intensity. A shutter was used to cut o f f light to the cell except when droplets were being filmed. This avoided any heating which might occur. A chopping disc was included to produce intermittent lighting of the settling area of known frequency. This also reduced heating still further. The image of the droplets formed by a × 10 microscope was focused on the photocathode of an image intensifier tube, and the image produced by this was bright enough to film. 2. 5 Control system A control system for the experiment was constructed so that it was easy to photograph whilst operating the apparatus. The amplifier supplying the transducer was switched on by a relay. There was a solenoid valve to stop the
52
orr)
MILLIPORE FILTERS
BF CAI .THERMOCOUPLE
CONDUCTING GLASS ELECTRODE GL
WINI
TERMINAL FOR FIELD Gt
THERMOCOUPLE
Fig.2. Sedimentation cell.
aerosol flow and the shutter was also electrically operated. The deflecting electrodes in the sedimentation cell were connected to earth through a relay which could be energised to apply the required voltage when the droplet trajectories were being recorded. The experiment could thus be controlled from a single rotary switch placed near the camera. To record a sample of droplets, the procedure was as follows: 1. atomise some liquid for a few seconds; 2. allow the aerosol to flow up the duct; 3. stop the flow; 4. apply the deflecting field; 5. immediately photograph the sample.
53
GLASS DUCT .
~
CONDUCTING GLASS ELECTRODES
0 MICROSCOPE ' ~ C H O P P I N G DISC c=== ~ S H U T T E R |
I~POLARISER .--,J::z~"~"HEAT FILTER
IMAGE INTENSIFIER
CINE CAMERA CONTROL SWITCH
LASER
Fig.3. Photographic recording system. The R.F. power to the atomiser was adjusted to give a sample which was of the right droplet concentration for ease of counting later. 2. 6 Data analysis The size and charge data were obtained by measuring the vertical and horizontal deflections of the particles from the film. A computer program produced the statistical distributions, means, and other quantities, from this data. 3. Results and discussion 3.1 De.ionised water The de-ionised water used for the initial experiments when these results were taken was contaminated with carbon dioxide from the atmosphere. The conductivity was 4 X 10 -4 S m-1 . The size distribution of a sample of aerosol is shown in Fig.4. The dashed curve is a log normal distribution whose parameters were estimated from the experimental data. The geometric mean particle size was 10 -s m and the range of sizes observed was within that quoted by Lindbauer [12] for photographic measurements on the mist found during tank cleaning. The distribution of particle charge is shown in Fig.5 and the dashed curve shows the normal (Gaussian) distribution whose parameters were estimated from the experimental data. The mean charge was 43 electrons (--7 X 10 -18 C) per drop and the standard deviation of the distribution was 173 electronic units (--2.8 X 10 -17 C). It can be seen that the aerosol contained particles of both signs, the majority with low values of charge. The charge contained in 10 -3 kg of aerosol of 10 -s m droplets, each containing a charge of 43 electrons (--7 X 10 -1~ C), is 10 -s C. As the estimated particle concentration in a tanker
54
Probability Density
0"20
// //
0-10
. 15
10
5
rl
1"f'~--
20 Particle
2~
Size X 106(m)
Fig.4. Particle size distribution for de-ionised water sample.
Probability Density 0.0085
O. 0 0 5 0
0-0025
t/I
\
/i
\x\
J -lOOO
-50o
0
50o
rn
I"I
lOO0
15o0
Charge [Electrons]
Fig.5. Particle charge distribution for de-ionised water sample.
m i s t is 2 X 10 -3 kg m -3 , this value o f m e a n charge c o u l d readily give t h e observed values o f 10 -s C m -3 f o r charge d e n s i t y . T h e value o f ~-- 10 -17 C p e r 10 - s m d r o p f o r a 4 X 10 -4 M c a r b o n d i o x i d e s o l u t i o n is o f t h e s a m e o r d e r as t h a t o b s e r v e d b y I r i b a m e a n d M a s o n f o r t h e charging d u r i n g b u b b l e bursting. I f t h e e s t i m a t e d value o f t h e s t a n d a r d d e v i a t i o n c a n be r e l a t e d t o a sta-
55 / .S
t
/
/
/ / t / ,~.
X"'" I 6
X i"'l 8
I 10
I 12
-101
,. ....,o-'"
I 14
I
particle size 1 6 X 106(m)
Fig.6. Size--charge relationship for de-ionised water.
tistical charging t h e o r y calculating the standard deviation from eqn.(1.4), the observed value is t o o low, pr obabl y because the t h e o r y was developed for n o n p o lar liquids with immobile ions and does n o t a c c o u n t for charge relaxation. The charge--size relationship is shown in Fig.6. The dashed curve was calculated f r o m eqn.(1.1) for a molar c o n c e n t r a t i o n of 4 × 10 -4 M. However, as a small error in c o n c e n t r a t i o n produces a considerable change in the value o f Q given by the equation due to the exponential dependence on relaxation time, only the general trend of the curves should be compared. 3.2 S o d i u m nitrate s o l u t i o n
The conductivity of the solution used was 1.7 × 10 -3 S m -1 , the molar c o n c e n t r a t i o n being 10 -3 M. The size distributions of samples atomised under different electric fields were similar e x c e p t t hat the mean size decreased slightly with increasing field. This would be e xpe c t e d as the field gives the forming droplet an extra acceleration. The mean size was 10 -s m for no applied field and 8 . 4 X 10 .6 m for a field o f 8.3 × 104 V m -1 . A typical size distribution is shown in Fig.7 and the dashed line is the log normal curve. The mist was again within the diam eter range q u o t e d for tank washing. The charge distributions of samples of aerosol atomised under different electric fields are shown in Fig.8, and the dashed curves are t he normal distributions. Again, the aerosol contained particles o f b o th signs most of whose values were close to zero. The standard deviation o f the f o u r curves were within 6 % of the mean standard deviation, which was 285 electronic units ( - - 4 . 6 × 10 -17 C). This indicates t hat if these values could be used as an indication of a statistical charging mechanism, the external field did n o t affect it; as would be expected. The value of the standard deviation was again t o o low and charge relaxation was p r o b a b l y the explanation. The effect o f the field on the charge distributions was to shift the mean value o f charge. A graph of mean charge versus applied field is shown in Fig.9. The straight line is eqn.(1.3) assuming 71 cos0 = 1. It appears t hat
56 0.3 Probability density
0.2
,
0.1 !
!
=f 5
10
15
20 Particle size
XlOS(m)
Fig.'/. Particle s i z e d i s t r i b u t i o n for s o d i u m n i t r a t e s o l u t i o n . Fig 8(b)
Fig 8(a)
0"005 ' Probabitity density
Probability 0.005 t density
0.003
/ n, -1500
-1000
Fig. 8(c)
.,
-500
[
n -2000
0.005 Probab~lity density
j in -1500
Fig.8 Fig.8 Fig.8 Fig.8
1000 500 (Particle charge e- )
(a). (b). (c). (d).
-lOaD
-
i -1500
~" -I000
-500
I
~'i.t-~ , 500 1000
, 1500
,~, 2000
~Particle charge e- ~,
0.005 Probabilit y density
"., 500
~" ' I , 1000 1500 ( Particle charge e- )
/ I ITI . ¢ / d l l -1000 -500
500
n. ~0
n, ,n 1500 2000 ( Particle charge e- )
Particle c h a r g e d i s t r i b u t i o n s for s o d i u m n i t r a t e s o l u t i o n s w i t h d i f f e r e n t a p p l i e d e l e c t r i c fields: - - 1 0 4 V m -1 , N o field, 1 0 4 V m -1 , 8 . 3 × 1 0 4 V m - 1 .
57
Q (e-)
alculated f r o m e q u a t i o n
+100
E ( V m -1 ) -10,000
i -5000
i + 5000
j./ p//t~
i + 10,000
J
Fig.9. Relationship between mean droplet charge and applied electric field for sodium nitrate solution.
the charge on the aerosol, caused by applying a field, reached a saturation value. It is known from work on electrostatic paint spraying that particles below about 10 -s m cannot readily be electrostatically atomised in air. This is possibly because the surface field on the smaller drops reaches a value where a discharge will take place. If high surface fields were present, more highly charged droplets would be expected to be formed. However, as the aerosol density was high at the instant of atomisation, sites would be screened from the field, and highly charged droplets would probably be lost by coagulation. The charge--size relationships at different values of field are shown in Fig.10. It can be seen that the gradient increased only at particle sizes above about 8 X 10 -6 m. This could, again, have been due to the surface field. The relaxation time would also affect both the charge--field relationship and the charge--size relationship. At a concentration of 10 -3 M the relaxation time is of the order of 10 -6 sec. Droplet formation time calculated from the equation of Newitt et al. [13] for a 5 X 10 -6 m droplet is of this order and for a 10 -s m droplet about 5 X 10 -6 sec.
3. 3 High speed cine investigation Three frames of each of the two sequences of film taken are shown in Fig. 11. The top set shows the whole ultrasonic fountain and the other set shows a closer view of the top of the jet. Both films were taken at 5,000 frames per second. It appeared that the aerosol was produced intermittantly from the globule-shaped part of the jet at the top. One globule seemed to burst, producing a large number of small droplets. Crawford [ 14] mentions t h a t the appearance of these globules indicates that air is being absorbed into the ul-
58
+ O ®
(e-)
/ +2500v
//
300 '
// x
/
x/,
/
+300v
,/
200
®
100
x
i 6
x
. . . .i. . 8
x._
-~" X ...... 10
--7
mr''"
x'"
. . - Ov i
12
14 Particle
size
X lOP(m)
-100
-200
x -300
-%
-300v
Fig. 10. Size--charge relationship for sodium nitrate solution with different applied electric fields.
Fig. 11. Stills from film of atomisation. Top set shows whole jet; Bottom set shows close-up of top of jet.
59 trasonic fountain due to the presence of cavitation bubbles at the base of the jet. Thus the mechanism for atomisation was probably cavitation ihduced. 4. Conclusions The experimental system which was developed enabled atomisation and charge generation processes in water to be studied under controlled conditions. The investigation was far from complete, but results up to April 1973 suggested that charge generation by disintegration of the liquid was sufficient to explain the observed charge densities in tanks. Charge exchange between the liquid and any electrode (such as a tank wall} did n o t seem to be an essential part of the electrical process. The statistical charging mechanism was found to predominate the observed charge distributions. The simple theory developed for nonpolar liquids did not describe these distributions, probably because of the change caused by charge relaxation. The development of the theory is being studied. The effect of electric field upon charge production, such that the charge value saturated at the high fields observed, was of significance in determining the time constant of charge build-up in a ship's tank. This aspect of the work is being studied in more detail. It appeared that atomisation by cavitation might predominate in the ultrasonic process and further high speed photography would provide more evidence for this.
5. Acknowledgements I would like to thank Shell International Marine Ltd., who sponsored the studentship which enabled this work to be done. Nomenclature C E I N Q R d e g n r
Cunningham correction to Stokes Law Undisturbed electric field in which a droplet is formed, (V m -~ ) Droplet charging current calculated from double-layer theory and the mode of droplet formation, (A) Number of monovalent ion pairs in the liquid, (m -3 ) Droplet charge, (C) Radius of one sphere when contacting another of radius r in an electric field, (m) Droplet diameter, (m) Charge of the electron, (C) Acceleration due to gravity, (m s-~ ) Number of elementary charges on a droplet Radius o f one sphere when contacting another of radius r in an electric field, (m)
60
t Vm Vv 71
Formation time of a droplet, (s) Horizontal drift velocity of a charged droplet in an electric field, (m s-~ ) Vertical velocity of droplet settling under gravity, (m s-~ ) Numerical factor related to ratio of radii of two spheres Viscosity of air, (Pa s) Pm Density of air, (kg m -3 ) pp Density of water (kg m -3 ) Standard deviation of charge distribution calculated from statistical theory, (C) 0 Angle between line of centres of two spheres and the electric field, (tad) r Relaxation time of ions in the liquid, (s) References 1 2 3 4
5 6
7 8
9 10 11 12 13
14
D. van der Meet and J.W. White. Electrostatic Charge Generation During Tank Washing, Project Summary and Introduction, J. Electrostatics, to be published. J.V. Iribarne and B.J. Mason, Electrification accompanying the bursting of bubbles in water and dilute aqueous solutions, Trans. Farad. Soc., 63 (1967) 2234. P.R. Jonas and B.J. Mason, Systematic charging of water droplets produced by breaking of liquid jets and filaments, Trans. Farad. Soc., 64 (1968) 1971. Z. Levin and P.V. Hobbs, Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation, Phil. Trans. Roy. Soc. (London), 269 (1971 ) 555. J.V. Iribarne, The electrical double layer and electrification associated with water disruption processes, J. Rech. Atmos., 6 (1972) 265. B. Vos, Electrostatic charge generation during washing of tanks with water sprays -IV: Mechanism studies, Proc. 3rd Conf. Static Electrification, London, May 1971, Inst. Phys. Conf. Set. No. 11, p. 184. J. Latham and B.J. Mason, Electrical ~charging of hail pellets in a polarising electric field, Proc. Roy. Soc. A, 266 (1962) 387. S.G. Jennings and J. Latham, The charging of water drops falling and colliding in an electric field, Proc. 3rd Conf. Static Electrification, London, May 1971, Inst. Phys. Conf. Ser. No. 11, p. 84. E.E. Dodd, The statistics of liquid spray and dust electrification by the Hopper and Laby method, J. Appl. Phys., 24 {1953) 73. L.B. Loeb, Static Electrification II. 1. Homogeneous or symmetrical charging of liquids and solids on dispersion, Progr. in Dielectrics, 5 (1963) 235. V.D. Hopper and T.H. Laby, The electronic charge, Proc. Roy. Soc. A, 178 (1941) 243. R.L. Lindbauer, Some properties of charged mist produced by gun cleaning, Koninklijke/Shell--Laboratorium, Amsterdam, Internal Report 6, Nov. 1971. D.M. Newitt, N. Dombrowski and F.H. Knelman, Liquid entrainment. 1. The mechanism of drop formation from gas or vapour bubbles, Trans. Inst. Chem. Engrs., 32 (1954) 244. A. Crawford, Ultrasonic Engineering, Butterworths, 1955.