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Electrostatic charge on uranium ore dust
d. Aerosol Sci., Vol. 21. No. 2, pp. 289 297, 1990. Printed in Great Britain.
0021-8502/90 $3.00+0.00 © 1990 Pergamon Press plc.
ELECTROSTATIC CHARGE ON U R A N I U M ORE DUST JIRI KVASNICKA* a n d GEOFF RILEY'~ *Department of Mines and Energy, PO Box 2901, Darwin NT 0801, Australia tSIROMATH Pty Ltd, 8/154 Hampden Road, Nedlands, WA 6009, Australia
(Received 21 April 1989; and in final form 4 August 1989) Al~tract--A system of four electrostatic elutriators was constructed in order to estimate the median charge on airborne uranium ore (U-ore) dust particles generated during the drilling in the open pit of the Ranger Uranium Mines in the Northern Territory of Australia. The surface alpha activity of the electrodes was measured as a function of distance from the elutriator's inlet. By analysing this data along with the measured activity mean aerodynamic diameter of airborne U-ore dust, a median electrostatic charge of about 33 electrons was calculated for a 1 #m particle. The above charge has a negligible effect on the lung deposition of U-ore dust generated by drilling of the U-ore body.
NOMENCLATURE Am
As A, a,(O,) a(O) At
B
C D D* Do, I
03. s Da3. s e
E
~qd) F l lmax m
M N k K Kr He
P q qm
O t t~
V u Y Z
Specific alpha activity (Bq kg-1) Surface alpha activity (Bq m-2) Air volume alpha activity (Bq m-3) Density distribution of air-borne alpha activity with respect to particle equivalent aerodynamic diameter Particle's alpha activity (Bq) Total alpha activity (Bq) Particle mechanical mobility (B = C/3mID) Slip correction factor Particle diameter (/~m) Particle equivalent aerodynamic diameter (/~m) Particle geometric mean diameter (/am) Activity mean diameter (/~m) Activity mean aerodynamic diameter (AMAD) (/~m) Elementary charge (e = 1.602 x 10-19C) Electric field strength (V m-~) Probability density function of the distribution of particle diameters Charge normalization factor (F + + F - + F ° = 1) Distance of particle deposition in the elutriator (m) Maximum distance of particle deposition from the entrance of the elutriator (m) Particle mass (kg) Electrical mobility (M = qC/3n~lD) Particle number concentration Ratio Da/D Proportionality constant (K = q/eD2n) Resistance shape factor Number of elementary charges on a particle (no = Iq/el) Penetration probability of particles through the elutriator Charge on particle (C) Median charge (C) Volumetric flow rate (m 3 s- ~) time (s) Electric drift velocity (v = CqE/3n~ID) Potential difference (V) Flow velocity (m s- 1) Width of the elutriator (m) Distance between the electrodes (m)
Greek letters r/ p po ~t
Viscosity of air (m 2 s- 1) Specific density of a particle (kg m- 3) Unit density (kg m- 3) Shape factor Surface density of particles (m- 2) # Mean of the log-normal distribution (#o=ln Do,s or ~ur.s=ln D,,8) tr8 Geometric S.D. of the log-normal distribution tr S.D. (o=lnor) 289
290
J. KVASNICKAand O. RH.EV INTRODUCTION
Surface charge density on airborne dust particles causes enhanced lung deposition of inhaled aerosols. A theoretical basis for calculation of electrostatic enhancement of deposition in the lung of inhaled aerosols was given by Yu (1985). Theoretical conclusions were supported by experimental results on humans (Melandri et al., 1983) and animals (Vincent et al., 1981). These studies have shown an increase of charged aerosol deposition in the lung. For fine particles this increase is mainly related to an enhanced deposition in the alveolar region of the lung. However, for each particle size, there exists a threshold charge level, qc(e), below which lung deposition increase is negligible (Melandri et al., 1983; John and Vincent, 1985; Yu, 1985). Assuming the unit specific density of inhaled aerosols Yu (1985) derived that Gle) is equal to 12, 30 and 54 unit charges, respectively, for 0.3, 0.6 and 1 pm particles in diameter, respectively. Calculated increase of total lung deposition vs charge, q, for unit density particles increases approximately linearly with charge (Melandri et al., 1983; Prodi and Mularoni, 1985; Yu, 1985).
Dust charging The general mechanism of electrostatic charging of aerosols is the breaking of contacts between materials or triboelectric effects. This for instance happens when powder is blown from a surface made out of different material than powder. Aerosols may be also charged in an electrostatic field, by u.v. and ionizing radiation, by corona discharge, etc. In the mining industry the charging of Uranium-ore (U-ore) dust will be mostly associated with drilling, crushing and conveying of U-ore. The situation in the uranium mining industry is different from most of the other industries because of handling of radioactive materials. Uranium-ore has very high equilibrium concentrations of electrons and holes trapped by structural defects presented in the minerals forming the U-ore. This is proportional to the dose rate inside the U-ore body or concentration of U. These localized high concentrations of electrons and holes within the microstructure of U-ore minerals are a new parameter which might have an effect on the magnitude of electrostatic charge on U-ore dust particles generated in the course of drilling of U-ore. The main goal of this study was to assess the median magnitude of the charge carried by a 1 #m diameter U-ore dust particle generated by drilling in open pit of Ranger Uranium Mines (in the Northern Territory of Australia).
EXPERIMENTAL In order to estimate the amount of electrostatic charge on the U-ore dust particles, a set of electrostatic elutriators was constructed (Vincent et al., 1981; Hochrainer, 1985). The system had been designed in such a way that U-ore dust could be sampled in parallel by up to four such elutriators operating at different d.c. voltages (Fig. 1). Each elutriator consisted of a pair of flat electrodes made of 4 era-thick perspex glass sheet. One side of the sheet was covered by mylar foil having one conductive surface. A wooden spacer was used to maintain the chosen distance Z ( Z = 6.5 ram) between the positive and negative electrodes. The width of the elutriator channel, Y, was 106 ram. The elutriator was vertical during the sampling to eliminate the gravitation effect. The vertical air stream through the channel of the elutriator had a flow rate, Q, of 5 1rain- 1. A fibre glass filter placed under the elutriator was used to collect the U-ore dust not attached to either of the two electrodes by the electric field force. After sampling, 3 x 3 cm 2 pieces of foil were cut and carefully stripped from the centre of each electrode. The total long lived alpha activity of the radioactive dust on each piece was assessed by a low-background alpha counter (DAYBREAK, by Nuclear and Medical Systems, Inc., CT, U.S.A.). With this experimental configuration, the dependence of surface alpha activity, As, on the distance, 1, from the top of the electrode, could be measured for elutriators with different d.c. potentials.
Electrostatic charge on uranium ore dust
291
I
Fig: 1. Electrostaticelutriator. The elutriator with both electrodes at zero potential was used to evaluate the total amount of the U-ore dust entering the flat channel when the trajectories of the charged dust particles were not affected by an electric field. The total alpha activity of the U-ore dust entering the elutriator is the sum of any alpha activity of U-ore particles deposited on the zero potential electrodes and the alpha activity on the collecting filter at the bottom of the flat channel. Airborne dust particles are usually log-normally distributed in size. Provided that the total alpha activity of the particle, A(D), is purely a function of the diameter of the particle (A(D) = 1/6nD3pAm), the alpha activity will also be log-normally distributed, with geometric S.D. equal to the cube of that applying to the particle diameters. The parameters (activity mean aerodynamic diameter, D~.g, and geometric standard deviation, as), of the log-normal distribution of the alpha activity of airborne U-ore particles with respect to particle diameters were assessed by Sierra Series 230 High Volume Cascade Impactors Sampler which was running parallel with the elutriator sampling. THEORY The median charge, qm, of the airborne U-ore dust may be assessed by the electrostatic elutriator and the activity mean aerodynamic diameter is usually measured by the cascade impactor. These are the main inputs for the estimation of enhanced deposition in the lung of inhaled charged U-ore dust. The theory of charged U-ore dust particle deposition inside the elutriator and formalism for evaluation of the electric charge on U-ore dust will be described in detail as there was a need to derive such theory for radioactive dust and the type of elutriator used.
Deposition of charged particles inside the elutriator When the air stream with charged U-ore dust particles passes through the flat channel of the electrostatic elutriator the electric drift velocity, v, is the product of the charge of the
292
J. KVASNICKAand G. RILEY
particle, q, the particle mechanical mobility, B, and the electric field strength, E, i.e. (1)
v=qEB,
where q B = M is the electrical mobility of the particle. The dependence of the particle charge or the particle diameter, D, can be written in the general form q = AD", where A and n are constant coefficients, and n usually lies between 1 and 2 (Johnston et al., 1985). Assuming that the U-ore dust particles have predominantly a spherical shape and the electrostatic charge on those particles is proportional to the particle surface, the following equation may give the link between the surface charges and diameter of a particle q=rcKeD 2. (2) The proportionality constant, K, is an unknown value which has to be assessed in order to quantify the electrostatic charge of U-ore airborne dust of known distribution. It is the median magnitude of charge (in equivalent electrons) carried by a surface area of 1 #m 2 of a particle. The deposition distance of a charged spherical particle with its initial trajectory parallel with the electrode surface can be calculated according to the formula z 3urlz l(D)=u - = v CEDKe
(3)
where z is the distance of the particle from the electrode in consideration on entry to the elutriator channel. By substituting Q~ YZ for u and the ratio V/Z for E, in equation (3), one may write 3Qqz l(O)= Y C V O K e"
(4)
Let us now consider the deposition of positive particles inside the elutriator. The positive particles in a stream of particles of a given diameter, D, move due to the electric force towards that negative electrode and are theoretically deposited onto the negative electrode with a constant surface density, ~b, which is given by Nf(D)F + q~(D)= Y lmax(D)"
(5)
The top part of the fraction is the total concentration of positively charged particles of diameter, D, which entered the elutriator (N is the particle number concentration entering the elutriator, f(D) is the fraction of particles with the diameter D, and F + is the fraction of positively charged particles). The bottom part is the area of particle deposition, the product of the width, Y, of the elutriator and the maximum distance, Imu, of particle deposition in the elutriator. By substituting the right hand side of equation (4) for lm~x(D) (the maximum distance of deposition) in equation (5), we can write 49(D) = Nf(D) D F +C V K e
3(2,7z
(6)
where Z is the distance between the electrodes. The link between particle density and activity
As the air volume alpha activity and the surface alpha activity of U-ore dust particles on the negative electrode are to be found, and not the surface density of particles, equation (6) has to be modified to satisfy the experiment's aims. This can be achieved by multiplication of both sides of equation (6) by the particle's alpha activity, A(D)= 1/6r~D3pA,,, of a nominallyspherical particle of diameter, D. Thus As(D)=6AmPf(D)D4 F + C V K e 3QrlZ
(7)
Electrostatic charge on uranium ore dust
293
By integrating equation (7), the extrapolated surface alpha activity A,(I--,O) at the entry to the elutriator on the negative electrode can be calculated for the log-normal particle size distribution of airborne U-ore dust +oo
As(I__.0)=NAm~Z p f f(lnD)D4d(lnD)F+ C VK e
3QZtl
(8)
After integration, equation (8) can be written in the form As(/__.0) =
AtDo gexp (3.51n2as)F + CV_~K e
(9)
where At(At= 1/6 NAmnpD],s) is the total alpha activity detected on the collecting filter at the bottom of the elutriator with both electrodes at zero potential, corrected for activity attached to both electrodes (IAEA, 1978). Because the activity mean diameter, D3,g (respective activity mean aerodynamic diameter D~, g) is measured, and Do, g is not, the Do, g in equation (9) must be replaced by an expression in D3, 8" D3, 8 can be expressed as a function of Do, s (IAEA, 1978), thus 1 •
D3. 8 = ~D3.8=Do.8 exp
(31n2o8).
(10)
The constant k is the ratio D'/D which in practice may be regarded as a separate particle shape factor: k =~-
=
Po Ka
.
(11)
If the density of U-ore dust (p = 2.6 g cm-3) and ~/Ka = 0.52 for a spherical particle (IAEA, 1978) are substituted in equation (11), k= 1.61 can be calculated. (Note: K R is a resistance shape factor related to the diameter, D.) If Do, 8 from equation (10) is then substituted in equation (9), the constant K is obtained:
K= A~(I--*O) 3Q Z~l kexp(-O.51n2as) At
F+C Ve
D ~3,g
(12)
The above formula may give an approximate value for K if an extrapolated A,(l~O) figure is used. A more accurate solution can be derived from the mathematical form of A,(/) as described in the Appendix. RESULTS The activity mean aerodynamic diameter of the U-ore airborne dust was found to be 3.69 #m and the geometric S.D. was % = 5.42. The surface alpha activities of the elutriators' collecting electrodes are presented in Table 1 for both negative and positive electrodes at 605 and 918 V. The surface alpha activity of electrodes on zero potential is also presented in Table 1. The total alpha activity which entered the elutriator was 14.7 Bq. The ratio of positive and negative U-ore dust particle activity was calculated to be F +IF- = 0.84. This ratio is equal to the ratio of the total alpha activity on the negative and the positive electrode of the elutriator at 605 V (Table 1). The surface alpha activity at the elutriator inlet A,(l~O) ,-, 2000 B q m -2 was found by extrapolating experimental results in Table 1 for the elutriator at 605 V potential. This figure was used to calculate the constant K according to equation (12) (K--- 8.3 x 1012e m - 2 or 8.3 e #m - 2). Numerical values substituted for parameters in equation (12) are summarized in Table 2. As the calculation of the constant K according to equation (12) is regarded as a very approximate one, due to the uncertainty in finding the exact value A,(l--,O), the more appropriate procedure described in the Appendix was followed. A non-linear least-squares
0.513 Bq
32 22 18 18 12 10 9.1 7.8 10 7.2 6.6 8.1
A~(0V) (Bq m 2)
5.08 Bq
572 374 191 119 91.0 71.2 52.6 41.4 27.7 24.0 20.8 13.0
- Electrode A~(605 V) - A~(0 V) (Bq m 2)
6.06 Bq
562 436 284 185 129 88.7 67.6 39.4 36.1 33.7 25.3 18.1
+ Electrode A~(605 V ) - A~(O V) (Bq m -2)
5.44 Bq
695 530 149 87.0 68.5 44.0 36.8 28.6 34.0 17.0 14.8 9.4
- Electrode A~(918V)-As(0V) (Bq m -2)
5.99 Bq
721 606 206 113 78.7 43.8 40.9 21.0 20.7 14.2 10.7 7.1
+ Electrode A~(918V)--A~(0V) (Bq m -2)
* Total alpha activity attached to the electrode is calculated by multiplying the sum in a column by a factor (0.03 x 0.106) which is the product of the width of the mylar foil strip and the width of the elutriator channel.
At* attached to the electrode
2 5 8 11 14 17 20 23 26 29 32 35
Ixl0 2 (m)
Table 1. Surface alpha activity of the elutriator electrodes as a function of distance from the air inlet
F-
295
Electrostatic charge on uranium ore dust Table 2. Input data for calculation of the constant K A t
F+/F C e
= 14.7 Bq = 0.84
Z Y
= 6 . 5 x 10 -3 m
=1
(2
= 8 . 3 3 x 1 0 - S m a s -1 = 3.69/~m = 5.42/~m = 1.61
=
=
1.6x I 0 - 1 9 C 1.88 x 1 0 - s k g m - 1 s - 1 (at 35°C)
]ll)O I
i
I
$
I0
I
=0.106 m
D~, 8 a= k
I
I
I
~3
I|
|0
3000
~E
2400
I~
llOO
100
0
, 0
n I|
n
410
I ( m ) xlO =
3100
30QO~J
'E
~400 -
0"
llO0 -
1200-
I00
0
,
I(m)xlO z Fig. 2. Graphical presentation of the surface alpha activities on the negative electrode vs distance from the air inlet of the elutriator at (a) 605 V potential and (b) 908 V potential.
procedure was used to choose K to minimize the sum of squared deviations between observed and fitted activities. Results of the least-squares procedure can be seen from Figs 2a, b, 3a and b, where the solid curves present the model calculation results and the points are the measured alpha activities of positively charged particles attached to the negative electrodes. The average constant K calculated from experimental results was 10.6 x 1012 e m-2. This average surface charge density may be used to calculate the number of elementary charges carried by a 1/+m particle: this was 33 electrons. Considering the error of experimental results and assumptions used in the theory, the accuracy of the final results is about +50%.
296
J, KVASNICKAand G. RILEY 3500
i
t
i
n
t L E
$000
E an v
~400
II00
i
I~O0
800
] i
o
1 -(0
-~!s
-~!0
*~'$
-Z'O
-I'll
-Iro
-'a'~
I
i
r
-I0
-0!
log I(m)
3100
i
,
j
I
JO00 -
)[:::
2100 -
g I100-
1200 -
IO0
• ¢0
-] 5
-50
-~.5
-LO
-I 5
-0.0
log I(m) Fig. 3. Dependence of the surface alpha activity on the negative electrode vs distance from the air inlet of the elutriator at (a) 605 V potential (b) 908 V potential. The graph is the result of a non-linear least-squares procedure to choose K.
CONCLUSIONS It has been assessed that the surface charge on a 1 # m U - o r e a i r b o r n e d u s t particle g e n e r a t e d in the course of drilling in U - o r e b o d y in the o p e n pit is u n d e r the t h r e s h o l d of 50 electrons a b o v e which electrostatic charge affects lung deposition. F u r t h e r s t u d y is p l a n n e d to estimate the charge on U - o r e dust in a crushing p l a n t a n d o n U - p r o d u c t dust in a p a c k a g i n g plant. Acknowledgements--The authors wish to thank Ranger Uranium Mines Pty Ltd for the help with assessing AMAD
of uranium ore dust and Mr K. L Mu for his assistance with the alpha counting of samples.
REFERENCES Alvey et al. (1985) GENSTAT, a General Statistical Program, Version 4:04b. Numerical Algorithms Group, Oxford, U.K. Hochrainer, D. (1985) Moasurement mothods for electric charges on aerosols. Ann. occup. Hyg, 29, 241-249. IAEA Technical Report Series No. 179 (1978) Particle Size Analysis in Estimating the Significance of Airborne Contamination. International Atomic Energy Agency. Vienna, Austria. John, W. and Vincent, J. H. (1985) Review--static electrification of workplace aerosols: a perspective. Ann. occup. Hyg. 29, 285-288. Johnston, A. M., Vincent, J. H. and Jones, A. D. (1985) Measurement of electric charge for workplace aerosols. Ann. occup. HYg. 29, 271-284. Melandri, C., Tarroni, G., Prodi, ¥., DeZaiacomo, T., Formignani, M. and Lombardi, C. C. (I983) Deposition of charged particles in the human airways. J. Aerosol Sci. 14, 657--669. Prodi, V. and Muiaroni, A. (1985) Electrostatic lung deposition experiments with humans and animals. Ann, occup. Hyg. 29, 229-240.
Electrostatic charge on uranium ore dust
297
Vincent, J. H., Johnston, W. B., Jones, A. D. and Johnston, A. M. (1981) Static electrification of airborne asbestos: a study of its causes, assessment and effects on deposition in the lung of rats. Am. Ind. Hyg. Assoc. J. 42, 711-721. Yu, C. P. (1985) Theories of electrostatic lung deposition of inhaled aerosols. Ann. occup. Hyg. 29, 219-227. APPENDIX:
MATHEMATICAL
AND
STATISTICAL
ISSUES
The mathematical form of A, (1) Consider first the positively charged particles with diameters in the range (D, D + dD). There are NF+f(D)dD of them, with a uniform spread of initial distances across the elutriator (between zero and Z). On deposition, this results in a uniform spread of these particles over an initial rectangular strip of electrode. According to equation (4), this has length: I . . ( D ) = b/D
(13)
where b = 3QZ~l/Y C VK e. Thus if l < I=,(D), an infinitesimal strip of surface of dimensions dl x Y at distance I will have
NF +F(D)dD (dl/lm,(D)) = NF +f(D)(D/b)dDdl
(14)
of these particles deposited on it, each contributing Ot/6)DapA= to the strip's total activity. Such a strip's total activity, At(l ) Ydl [by definition of At(l)], is obtained by adding over all diameters with l=,(D)>l. Thus, bile
A,(I) Y d L = a } D+f(D)dD Ydl,
(15)
0
where a = (~/6)p Am NF +.(Y/b). This integral can be rewritten, after some rearrangement, as follows:
A~(l) = a/54 P(-(lnl-ln(b/D4.s))/¢)
(16)
+oo
where P(z)= 1/2~ j
exp ( - t 2 / 2 ) dt is the standard normal cumulative distribution function, D,. e = e x p ( # + 4 ~ 2)
-ao
and/54 = exp (4/~ + 8~ 2) (IAEA, 1978). When a logarithmic scale is used for the I axis, A,(l) takes the form of a reversed sigmoidal curve, increasing to a /54 as In/---*- oo (l--,0), equalling 50% at its maximum when l = b/D,,.v and decreasing to 0 as I increases. Using the natural length scale compresses the left half of the reversed sigmoid into the finite interval between 1=0 and l = b/D,. v including the curve's only inflection point (at 1= b/Ds. ,), while the right half assumes a stretched out form (see the fitted curve in Fig. 2a, b). Note that the limiting value at zero, a/5", is as specified in equation (8).
Estimating K from the observed shape of A s (1) The data available for estimation of K comprises: (i) Experimental data for A,(I ) at a chosen range of distances 11. . . . . In. (ii) Estimates of the size distribution parameters D3. s and ~ (obtained from an independent experiment). Taking D3, s and tT~ as given, K becomes the only unknown in equation (16). Under these conditions, a good estimate of K is the value which minimizes the sum of the squared differences between the observed experimental activities and their theoretical predictions from equation (16). In other words, the parameter K is chosen to optimize the least-squares fit of the theoretical As(l ) curve to the data. Because equation (16) is non-linear in K, an iterative search on a computer is required to find best fitting values of K. The values reported in this paper were found by applying the non-linear regression commands in the statistical package GENSTAT (Alvey et al., 1985).
0021-8502/90 $3.00+0.00 © 1990 Pergamon Press plc.
ELECTROSTATIC CHARGE ON U R A N I U M ORE DUST JIRI KVASNICKA* a n d GEOFF RILEY'~ *Department of Mines and Energy, PO Box 2901, Darwin NT 0801, Australia tSIROMATH Pty Ltd, 8/154 Hampden Road, Nedlands, WA 6009, Australia
(Received 21 April 1989; and in final form 4 August 1989) Al~tract--A system of four electrostatic elutriators was constructed in order to estimate the median charge on airborne uranium ore (U-ore) dust particles generated during the drilling in the open pit of the Ranger Uranium Mines in the Northern Territory of Australia. The surface alpha activity of the electrodes was measured as a function of distance from the elutriator's inlet. By analysing this data along with the measured activity mean aerodynamic diameter of airborne U-ore dust, a median electrostatic charge of about 33 electrons was calculated for a 1 #m particle. The above charge has a negligible effect on the lung deposition of U-ore dust generated by drilling of the U-ore body.
NOMENCLATURE Am
As A, a,(O,) a(O) At
B
C D D* Do, I
03. s Da3. s e
E
~qd) F l lmax m
M N k K Kr He
P q qm
O t t~
V u Y Z
Specific alpha activity (Bq kg-1) Surface alpha activity (Bq m-2) Air volume alpha activity (Bq m-3) Density distribution of air-borne alpha activity with respect to particle equivalent aerodynamic diameter Particle's alpha activity (Bq) Total alpha activity (Bq) Particle mechanical mobility (B = C/3mID) Slip correction factor Particle diameter (/~m) Particle equivalent aerodynamic diameter (/~m) Particle geometric mean diameter (/am) Activity mean diameter (/~m) Activity mean aerodynamic diameter (AMAD) (/~m) Elementary charge (e = 1.602 x 10-19C) Electric field strength (V m-~) Probability density function of the distribution of particle diameters Charge normalization factor (F + + F - + F ° = 1) Distance of particle deposition in the elutriator (m) Maximum distance of particle deposition from the entrance of the elutriator (m) Particle mass (kg) Electrical mobility (M = qC/3n~lD) Particle number concentration Ratio Da/D Proportionality constant (K = q/eD2n) Resistance shape factor Number of elementary charges on a particle (no = Iq/el) Penetration probability of particles through the elutriator Charge on particle (C) Median charge (C) Volumetric flow rate (m 3 s- ~) time (s) Electric drift velocity (v = CqE/3n~ID) Potential difference (V) Flow velocity (m s- 1) Width of the elutriator (m) Distance between the electrodes (m)
Greek letters r/ p po ~t
Viscosity of air (m 2 s- 1) Specific density of a particle (kg m- 3) Unit density (kg m- 3) Shape factor Surface density of particles (m- 2) # Mean of the log-normal distribution (#o=ln Do,s or ~ur.s=ln D,,8) tr8 Geometric S.D. of the log-normal distribution tr S.D. (o=lnor) 289
290
J. KVASNICKAand O. RH.EV INTRODUCTION
Surface charge density on airborne dust particles causes enhanced lung deposition of inhaled aerosols. A theoretical basis for calculation of electrostatic enhancement of deposition in the lung of inhaled aerosols was given by Yu (1985). Theoretical conclusions were supported by experimental results on humans (Melandri et al., 1983) and animals (Vincent et al., 1981). These studies have shown an increase of charged aerosol deposition in the lung. For fine particles this increase is mainly related to an enhanced deposition in the alveolar region of the lung. However, for each particle size, there exists a threshold charge level, qc(e), below which lung deposition increase is negligible (Melandri et al., 1983; John and Vincent, 1985; Yu, 1985). Assuming the unit specific density of inhaled aerosols Yu (1985) derived that Gle) is equal to 12, 30 and 54 unit charges, respectively, for 0.3, 0.6 and 1 pm particles in diameter, respectively. Calculated increase of total lung deposition vs charge, q, for unit density particles increases approximately linearly with charge (Melandri et al., 1983; Prodi and Mularoni, 1985; Yu, 1985).
Dust charging The general mechanism of electrostatic charging of aerosols is the breaking of contacts between materials or triboelectric effects. This for instance happens when powder is blown from a surface made out of different material than powder. Aerosols may be also charged in an electrostatic field, by u.v. and ionizing radiation, by corona discharge, etc. In the mining industry the charging of Uranium-ore (U-ore) dust will be mostly associated with drilling, crushing and conveying of U-ore. The situation in the uranium mining industry is different from most of the other industries because of handling of radioactive materials. Uranium-ore has very high equilibrium concentrations of electrons and holes trapped by structural defects presented in the minerals forming the U-ore. This is proportional to the dose rate inside the U-ore body or concentration of U. These localized high concentrations of electrons and holes within the microstructure of U-ore minerals are a new parameter which might have an effect on the magnitude of electrostatic charge on U-ore dust particles generated in the course of drilling of U-ore. The main goal of this study was to assess the median magnitude of the charge carried by a 1 #m diameter U-ore dust particle generated by drilling in open pit of Ranger Uranium Mines (in the Northern Territory of Australia).
EXPERIMENTAL In order to estimate the amount of electrostatic charge on the U-ore dust particles, a set of electrostatic elutriators was constructed (Vincent et al., 1981; Hochrainer, 1985). The system had been designed in such a way that U-ore dust could be sampled in parallel by up to four such elutriators operating at different d.c. voltages (Fig. 1). Each elutriator consisted of a pair of flat electrodes made of 4 era-thick perspex glass sheet. One side of the sheet was covered by mylar foil having one conductive surface. A wooden spacer was used to maintain the chosen distance Z ( Z = 6.5 ram) between the positive and negative electrodes. The width of the elutriator channel, Y, was 106 ram. The elutriator was vertical during the sampling to eliminate the gravitation effect. The vertical air stream through the channel of the elutriator had a flow rate, Q, of 5 1rain- 1. A fibre glass filter placed under the elutriator was used to collect the U-ore dust not attached to either of the two electrodes by the electric field force. After sampling, 3 x 3 cm 2 pieces of foil were cut and carefully stripped from the centre of each electrode. The total long lived alpha activity of the radioactive dust on each piece was assessed by a low-background alpha counter (DAYBREAK, by Nuclear and Medical Systems, Inc., CT, U.S.A.). With this experimental configuration, the dependence of surface alpha activity, As, on the distance, 1, from the top of the electrode, could be measured for elutriators with different d.c. potentials.
Electrostatic charge on uranium ore dust
291
I
Fig: 1. Electrostaticelutriator. The elutriator with both electrodes at zero potential was used to evaluate the total amount of the U-ore dust entering the flat channel when the trajectories of the charged dust particles were not affected by an electric field. The total alpha activity of the U-ore dust entering the elutriator is the sum of any alpha activity of U-ore particles deposited on the zero potential electrodes and the alpha activity on the collecting filter at the bottom of the flat channel. Airborne dust particles are usually log-normally distributed in size. Provided that the total alpha activity of the particle, A(D), is purely a function of the diameter of the particle (A(D) = 1/6nD3pAm), the alpha activity will also be log-normally distributed, with geometric S.D. equal to the cube of that applying to the particle diameters. The parameters (activity mean aerodynamic diameter, D~.g, and geometric standard deviation, as), of the log-normal distribution of the alpha activity of airborne U-ore particles with respect to particle diameters were assessed by Sierra Series 230 High Volume Cascade Impactors Sampler which was running parallel with the elutriator sampling. THEORY The median charge, qm, of the airborne U-ore dust may be assessed by the electrostatic elutriator and the activity mean aerodynamic diameter is usually measured by the cascade impactor. These are the main inputs for the estimation of enhanced deposition in the lung of inhaled charged U-ore dust. The theory of charged U-ore dust particle deposition inside the elutriator and formalism for evaluation of the electric charge on U-ore dust will be described in detail as there was a need to derive such theory for radioactive dust and the type of elutriator used.
Deposition of charged particles inside the elutriator When the air stream with charged U-ore dust particles passes through the flat channel of the electrostatic elutriator the electric drift velocity, v, is the product of the charge of the
292
J. KVASNICKAand G. RILEY
particle, q, the particle mechanical mobility, B, and the electric field strength, E, i.e. (1)
v=qEB,
where q B = M is the electrical mobility of the particle. The dependence of the particle charge or the particle diameter, D, can be written in the general form q = AD", where A and n are constant coefficients, and n usually lies between 1 and 2 (Johnston et al., 1985). Assuming that the U-ore dust particles have predominantly a spherical shape and the electrostatic charge on those particles is proportional to the particle surface, the following equation may give the link between the surface charges and diameter of a particle q=rcKeD 2. (2) The proportionality constant, K, is an unknown value which has to be assessed in order to quantify the electrostatic charge of U-ore airborne dust of known distribution. It is the median magnitude of charge (in equivalent electrons) carried by a surface area of 1 #m 2 of a particle. The deposition distance of a charged spherical particle with its initial trajectory parallel with the electrode surface can be calculated according to the formula z 3urlz l(D)=u - = v CEDKe
(3)
where z is the distance of the particle from the electrode in consideration on entry to the elutriator channel. By substituting Q~ YZ for u and the ratio V/Z for E, in equation (3), one may write 3Qqz l(O)= Y C V O K e"
(4)
Let us now consider the deposition of positive particles inside the elutriator. The positive particles in a stream of particles of a given diameter, D, move due to the electric force towards that negative electrode and are theoretically deposited onto the negative electrode with a constant surface density, ~b, which is given by Nf(D)F + q~(D)= Y lmax(D)"
(5)
The top part of the fraction is the total concentration of positively charged particles of diameter, D, which entered the elutriator (N is the particle number concentration entering the elutriator, f(D) is the fraction of particles with the diameter D, and F + is the fraction of positively charged particles). The bottom part is the area of particle deposition, the product of the width, Y, of the elutriator and the maximum distance, Imu, of particle deposition in the elutriator. By substituting the right hand side of equation (4) for lm~x(D) (the maximum distance of deposition) in equation (5), we can write 49(D) = Nf(D) D F +C V K e
3(2,7z
(6)
where Z is the distance between the electrodes. The link between particle density and activity
As the air volume alpha activity and the surface alpha activity of U-ore dust particles on the negative electrode are to be found, and not the surface density of particles, equation (6) has to be modified to satisfy the experiment's aims. This can be achieved by multiplication of both sides of equation (6) by the particle's alpha activity, A(D)= 1/6r~D3pA,,, of a nominallyspherical particle of diameter, D. Thus As(D)=6AmPf(D)D4 F + C V K e 3QrlZ
(7)
Electrostatic charge on uranium ore dust
293
By integrating equation (7), the extrapolated surface alpha activity A,(I--,O) at the entry to the elutriator on the negative electrode can be calculated for the log-normal particle size distribution of airborne U-ore dust +oo
As(I__.0)=NAm~Z p f f(lnD)D4d(lnD)F+ C VK e
3QZtl
(8)
After integration, equation (8) can be written in the form As(/__.0) =
AtDo gexp (3.51n2as)F + CV_~K e
(9)
where At(At= 1/6 NAmnpD],s) is the total alpha activity detected on the collecting filter at the bottom of the elutriator with both electrodes at zero potential, corrected for activity attached to both electrodes (IAEA, 1978). Because the activity mean diameter, D3,g (respective activity mean aerodynamic diameter D~, g) is measured, and Do, g is not, the Do, g in equation (9) must be replaced by an expression in D3, 8" D3, 8 can be expressed as a function of Do, s (IAEA, 1978), thus 1 •
D3. 8 = ~D3.8=Do.8 exp
(31n2o8).
(10)
The constant k is the ratio D'/D which in practice may be regarded as a separate particle shape factor: k =~-
=
Po Ka
.
(11)
If the density of U-ore dust (p = 2.6 g cm-3) and ~/Ka = 0.52 for a spherical particle (IAEA, 1978) are substituted in equation (11), k= 1.61 can be calculated. (Note: K R is a resistance shape factor related to the diameter, D.) If Do, 8 from equation (10) is then substituted in equation (9), the constant K is obtained:
K= A~(I--*O) 3Q Z~l kexp(-O.51n2as) At
F+C Ve
D ~3,g
(12)
The above formula may give an approximate value for K if an extrapolated A,(l~O) figure is used. A more accurate solution can be derived from the mathematical form of A,(/) as described in the Appendix. RESULTS The activity mean aerodynamic diameter of the U-ore airborne dust was found to be 3.69 #m and the geometric S.D. was % = 5.42. The surface alpha activities of the elutriators' collecting electrodes are presented in Table 1 for both negative and positive electrodes at 605 and 918 V. The surface alpha activity of electrodes on zero potential is also presented in Table 1. The total alpha activity which entered the elutriator was 14.7 Bq. The ratio of positive and negative U-ore dust particle activity was calculated to be F +IF- = 0.84. This ratio is equal to the ratio of the total alpha activity on the negative and the positive electrode of the elutriator at 605 V (Table 1). The surface alpha activity at the elutriator inlet A,(l~O) ,-, 2000 B q m -2 was found by extrapolating experimental results in Table 1 for the elutriator at 605 V potential. This figure was used to calculate the constant K according to equation (12) (K--- 8.3 x 1012e m - 2 or 8.3 e #m - 2). Numerical values substituted for parameters in equation (12) are summarized in Table 2. As the calculation of the constant K according to equation (12) is regarded as a very approximate one, due to the uncertainty in finding the exact value A,(l--,O), the more appropriate procedure described in the Appendix was followed. A non-linear least-squares
0.513 Bq
32 22 18 18 12 10 9.1 7.8 10 7.2 6.6 8.1
A~(0V) (Bq m 2)
5.08 Bq
572 374 191 119 91.0 71.2 52.6 41.4 27.7 24.0 20.8 13.0
- Electrode A~(605 V) - A~(0 V) (Bq m 2)
6.06 Bq
562 436 284 185 129 88.7 67.6 39.4 36.1 33.7 25.3 18.1
+ Electrode A~(605 V ) - A~(O V) (Bq m -2)
5.44 Bq
695 530 149 87.0 68.5 44.0 36.8 28.6 34.0 17.0 14.8 9.4
- Electrode A~(918V)-As(0V) (Bq m -2)
5.99 Bq
721 606 206 113 78.7 43.8 40.9 21.0 20.7 14.2 10.7 7.1
+ Electrode A~(918V)--A~(0V) (Bq m -2)
* Total alpha activity attached to the electrode is calculated by multiplying the sum in a column by a factor (0.03 x 0.106) which is the product of the width of the mylar foil strip and the width of the elutriator channel.
At* attached to the electrode
2 5 8 11 14 17 20 23 26 29 32 35
Ixl0 2 (m)
Table 1. Surface alpha activity of the elutriator electrodes as a function of distance from the air inlet
F-
295
Electrostatic charge on uranium ore dust Table 2. Input data for calculation of the constant K A t
F+/F C e
= 14.7 Bq = 0.84
Z Y
= 6 . 5 x 10 -3 m
=1
(2
= 8 . 3 3 x 1 0 - S m a s -1 = 3.69/~m = 5.42/~m = 1.61
=
=
1.6x I 0 - 1 9 C 1.88 x 1 0 - s k g m - 1 s - 1 (at 35°C)
]ll)O I
i
I
$
I0
I
=0.106 m
D~, 8 a= k
I
I
I
~3
I|
|0
3000
~E
2400
I~
llOO
100
0
, 0
n I|
n
410
I ( m ) xlO =
3100
30QO~J
'E
~400 -
0"
llO0 -
1200-
I00
0
,
I(m)xlO z Fig. 2. Graphical presentation of the surface alpha activities on the negative electrode vs distance from the air inlet of the elutriator at (a) 605 V potential and (b) 908 V potential.
procedure was used to choose K to minimize the sum of squared deviations between observed and fitted activities. Results of the least-squares procedure can be seen from Figs 2a, b, 3a and b, where the solid curves present the model calculation results and the points are the measured alpha activities of positively charged particles attached to the negative electrodes. The average constant K calculated from experimental results was 10.6 x 1012 e m-2. This average surface charge density may be used to calculate the number of elementary charges carried by a 1/+m particle: this was 33 electrons. Considering the error of experimental results and assumptions used in the theory, the accuracy of the final results is about +50%.
296
J, KVASNICKAand G. RILEY 3500
i
t
i
n
t L E
$000
E an v
~400
II00
i
I~O0
800
] i
o
1 -(0
-~!s
-~!0
*~'$
-Z'O
-I'll
-Iro
-'a'~
I
i
r
-I0
-0!
log I(m)
3100
i
,
j
I
JO00 -
)[:::
2100 -
g I100-
1200 -
IO0
• ¢0
-] 5
-50
-~.5
-LO
-I 5
-0.0
log I(m) Fig. 3. Dependence of the surface alpha activity on the negative electrode vs distance from the air inlet of the elutriator at (a) 605 V potential (b) 908 V potential. The graph is the result of a non-linear least-squares procedure to choose K.
CONCLUSIONS It has been assessed that the surface charge on a 1 # m U - o r e a i r b o r n e d u s t particle g e n e r a t e d in the course of drilling in U - o r e b o d y in the o p e n pit is u n d e r the t h r e s h o l d of 50 electrons a b o v e which electrostatic charge affects lung deposition. F u r t h e r s t u d y is p l a n n e d to estimate the charge on U - o r e dust in a crushing p l a n t a n d o n U - p r o d u c t dust in a p a c k a g i n g plant. Acknowledgements--The authors wish to thank Ranger Uranium Mines Pty Ltd for the help with assessing AMAD
of uranium ore dust and Mr K. L Mu for his assistance with the alpha counting of samples.
REFERENCES Alvey et al. (1985) GENSTAT, a General Statistical Program, Version 4:04b. Numerical Algorithms Group, Oxford, U.K. Hochrainer, D. (1985) Moasurement mothods for electric charges on aerosols. Ann. occup. Hyg, 29, 241-249. IAEA Technical Report Series No. 179 (1978) Particle Size Analysis in Estimating the Significance of Airborne Contamination. International Atomic Energy Agency. Vienna, Austria. John, W. and Vincent, J. H. (1985) Review--static electrification of workplace aerosols: a perspective. Ann. occup. Hyg. 29, 285-288. Johnston, A. M., Vincent, J. H. and Jones, A. D. (1985) Measurement of electric charge for workplace aerosols. Ann. occup. HYg. 29, 271-284. Melandri, C., Tarroni, G., Prodi, ¥., DeZaiacomo, T., Formignani, M. and Lombardi, C. C. (I983) Deposition of charged particles in the human airways. J. Aerosol Sci. 14, 657--669. Prodi, V. and Muiaroni, A. (1985) Electrostatic lung deposition experiments with humans and animals. Ann, occup. Hyg. 29, 229-240.
Electrostatic charge on uranium ore dust
297
Vincent, J. H., Johnston, W. B., Jones, A. D. and Johnston, A. M. (1981) Static electrification of airborne asbestos: a study of its causes, assessment and effects on deposition in the lung of rats. Am. Ind. Hyg. Assoc. J. 42, 711-721. Yu, C. P. (1985) Theories of electrostatic lung deposition of inhaled aerosols. Ann. occup. Hyg. 29, 219-227. APPENDIX:
MATHEMATICAL
AND
STATISTICAL
ISSUES
The mathematical form of A, (1) Consider first the positively charged particles with diameters in the range (D, D + dD). There are NF+f(D)dD of them, with a uniform spread of initial distances across the elutriator (between zero and Z). On deposition, this results in a uniform spread of these particles over an initial rectangular strip of electrode. According to equation (4), this has length: I . . ( D ) = b/D
(13)
where b = 3QZ~l/Y C VK e. Thus if l < I=,(D), an infinitesimal strip of surface of dimensions dl x Y at distance I will have
NF +F(D)dD (dl/lm,(D)) = NF +f(D)(D/b)dDdl
(14)
of these particles deposited on it, each contributing Ot/6)DapA= to the strip's total activity. Such a strip's total activity, At(l ) Ydl [by definition of At(l)], is obtained by adding over all diameters with l=,(D)>l. Thus, bile
A,(I) Y d L = a } D+f(D)dD Ydl,
(15)
0
where a = (~/6)p Am NF +.(Y/b). This integral can be rewritten, after some rearrangement, as follows:
A~(l) = a/54 P(-(lnl-ln(b/D4.s))/¢)
(16)
+oo
where P(z)= 1/2~ j
exp ( - t 2 / 2 ) dt is the standard normal cumulative distribution function, D,. e = e x p ( # + 4 ~ 2)
-ao
and/54 = exp (4/~ + 8~ 2) (IAEA, 1978). When a logarithmic scale is used for the I axis, A,(l) takes the form of a reversed sigmoidal curve, increasing to a /54 as In/---*- oo (l--,0), equalling 50% at its maximum when l = b/D,,.v and decreasing to 0 as I increases. Using the natural length scale compresses the left half of the reversed sigmoid into the finite interval between 1=0 and l = b/D,. v including the curve's only inflection point (at 1= b/Ds. ,), while the right half assumes a stretched out form (see the fitted curve in Fig. 2a, b). Note that the limiting value at zero, a/5", is as specified in equation (8).
Estimating K from the observed shape of A s (1) The data available for estimation of K comprises: (i) Experimental data for A,(I ) at a chosen range of distances 11. . . . . In. (ii) Estimates of the size distribution parameters D3. s and ~ (obtained from an independent experiment). Taking D3, s and tT~ as given, K becomes the only unknown in equation (16). Under these conditions, a good estimate of K is the value which minimizes the sum of the squared differences between the observed experimental activities and their theoretical predictions from equation (16). In other words, the parameter K is chosen to optimize the least-squares fit of the theoretical As(l ) curve to the data. Because equation (16) is non-linear in K, an iterative search on a computer is required to find best fitting values of K. The values reported in this paper were found by applying the non-linear regression commands in the statistical package GENSTAT (Alvey et al., 1985).