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The coagulation of radioactive aerosols
J. Aerosol Sci., Vol. 23, Suppl. I, pp. SI45-S148, 1992 Printed in Great Britain.
0021-8502/92 $5.00 + 0.00 Pergamon Press Ltd
THE COAGULATION OF RADIOACTIVE AEROSOLS C.F. CLEMENT, R.A. CLEMENTt and R.G. HARRISOI~ Theoretical Studies, 424.4, AEA Industrial Technology, Harwell Laboratory, Oxon, OX11 OR.A, U.K. i" 15 Witan Way, Wantage, Oxon OX12 9EU, U.K. ~: Air Pollution Group, Centre for Environmental Technology, Imperial College, London SW7 2BX, U.K. ABSTRACT Radioactive aerosols can become charged by emitting charges during the decay process, and the resulting electrostatic forces will modify coagulation rates. For Brownian coagulation, calculations for nuclear containment aerosols show that rates averaged over charge distributions can be strongly reduced between particles of the same size, but that increases m average rates can occur for particles of different sizes. The increases arise from small, but significant, negative charging of non-radioactive and small-sized radioactive particles, and are sensitive to the asymmetry between the positive and negative ion mobilities. KEYWORDS Coagulation, radioactive aerosols, nuclear aerosols, electrical properties, aerosol charging. INTRODUCTION The emission of one or more electrons from a radioactive aerosol particle during each decay charges the particle, but the many positive and negative ions produced in the surrounding gas tend to neutralise it by diffusing back onto the aerosol. In a considerable extension to previous theory (Reed et al 1977), we have shown how resultant charge distributions on the aerosol may be calculated (Clement and Harrison, 1991, 1992). Here, we describe how to calculate modifications to mean coagulation rates for aerosol charge distributions. Calculations have been performed for various aerosols, including a highly radioactive aerosol containing 131Iin a reactor containment atmosphere. CHARGE DISTRIBUTIONS We are mainly interested in steady-state charge distributions reached by a ~decaying aerosol which are specified by three parameters (Clement and Harrison 1992). With eo as the permittivity of the vacuum, the size parameter for an aerosol of radius a, at temperature, T, is T = e2/( 87r ~ a k T)
(1)
To specify ionic charging by positive and negative ions, number concentrations n+,n. and mobilities g+,la-, respectively, we define the asymmetry ratio, x =
(2)
S145
S146
C . F . CLEMENT et al.
The third parameter expresses the aerosol self-charging in terms of its decay rate, Tl, per unit time: y = 11eo/(e It-n-)
(3)
Significant self-charging only occurs when recombination dominates the ion removal process when, with recombination rate, o~, ion pairs produced per decay, I, monodisperse aerosol number density, Z, and background ion production rate, q, the ionic density is approximately 1
n = [(Ir/Z +q)/c~]~.
(4)
The difference between the ion concentrations is specified by charge conservation in terms of the charge, ], on the aerosol, and in practice is found by iteration from calculations of using charge disuibutions obtained with parameters defined by equations (I)-(3). COAGULATION Using the electrostatic modification of Fuchs (1964), the average enhancement factor for Brownian coagulation between aerosol charge distributions N j, al), N j, (a2) for particles of radii al and a2 is t
K -=~= = Z N i Nj, JlJ2
Y exp Y - 1
/ZN~Nj,,
(5)
JlJ2
J'J2e2 V(a'j"azJ2) = 4~eokT(a, + a2)
(6)
Only steady-state charge distributions are needed for calculations if, as is possible to show for reactor containments, the timescale for ionic charging is much less than the agglomeration timescale: %ch= y/~ << %ag.
(7)
Results of calculations show that charging, when it occurs, always suppresses coagulation for aerosol particles of the same size, but that coagulation rates for particles of different sizes may be increased. This is illustrated here by two calculations relevant to radioactive aerosols in the atmosphere of a reactor containment. The first concerns coagulation between a largesized non-radioactive aerosol (y = 0) and a small-sized radioactive aerosol (y > 0). These types of aerosol could be typical of ones produced in possible accidents where large amounts of volatile non-radioactive material are involved. The results illustrated in Fig. 1 show an overall enhancement in the coagulation rates which increases with charging. This, and the unexpected sensitivity of the results to x, can be attributed to the wide charge distribution for the larger aerosol where the enhancement from its negatively charge part, which is greater if x < 1, outweighs the reduction from its positively charged part. The second calculation concerns a highly radioactive Cs ]31I aerosol (I = 7.7 103, xl = 350 (a(pm)/0.2)3), in a highly ionising containment atmosphere of a pressurized water reactor, where we estimate that radioactive Kr and Xe can produce a background ion production rate as high as q = 3.0 1018 s-lm -3. A larger size aerosol of density Z m "3 contributes to the ion
Coagulation of radioactive aerosols
I..
{01= 0"1 }.1111
.
O 2 = 1 "0 y m
S147
~[ ___1o,= o2~ o2= 2.0 jam
~c= 0-912
/ /
/..
K, t K
- -
/
+ /
oc=l
F 0
10
Y
20
30
Fig. 1, Enhancement in mean coagulation rates between aerosols of the two different radii shown as a function of the radioactive charging parameter, y. Results for two different asymmetry parameters, x.
KI 3 2 K
B
I
O
_ -0.3
m
J -0./.
m
o = 0-2~Jm C
100 80 B 6O m
T
=
~o
p
20 0 1012
,~--
I
1011
I
I
1010
i09
I
108
107
Z m "3
Fig. 2.
Mean charges, ], of 0.2 gm and 2}Jan radius Csl31I aerosols in a radioactive gas atmosphere, and their mutual mean coagulation rate enhancement, as functions of the number concentration, Z, of the 2gm aerosol.
Si48
C. F, CLEMENT et al. 10
K.-~. I 01 K
10-'
10
1012
Fig. 3.
1011
Z m'3
1010
109
Coagulation enhancement for a 2~a'n Csl31I aerosol in a radioactive gas atmosphere as a function of aerosol number density, Z.
production rate, and we calculate coagulation rates as a function of Z for itself and with small-sized Cs 131I particles. Results of calculations of mean charges and enhancements in coagulation rates for the two sizes of aerosol are shown in Figs. 2 and 3. Because of the large ion densities, the parameter x takes on its limiting value of g+/g. = 0.912. From the assumed dependence of rl on a, the values of y for the two sizes differ by a factor of 103, and the small-sized aerosol is slightly negatively charged from the asymmetry in the ion mobilities. At high number densities, the ions produced by decays from the 2grn aerosol effectively neutralise it and K'/K = 1. As Z is lowered, the 2pan aerosol becomes self-charged; coagulation with itself becomes strongly suppressed, but an enhancement takes place in the coagulation rate with the smaller aerosol. ACKNOWLEDGEMENT This work was funded as part of the General Nuclear Safety Programme undertaken by AEA Technology on behalf of the UK Department of Induslry. REFERENCES Clement, C.F. and R.G. Harrison (1991). Self charging of radioactive aerosols. J. Aerosol Sci., 22 Suppl. 1, $55-58. Clement, C.F. and R.G. Harrison (1992). The charging of radioactive aerosols. J. Aerosol Sci. (in press). Fuchs, N.A. (1964). The Mechanics of Aerosols. Pergamon, New York. Reed, L.D., H. Jordan and J.A. Gieseke (1977). Charging of radioactive aerosols. J. Aerosol Sci. 8, 457-463.
0021-8502/92 $5.00 + 0.00 Pergamon Press Ltd
THE COAGULATION OF RADIOACTIVE AEROSOLS C.F. CLEMENT, R.A. CLEMENTt and R.G. HARRISOI~ Theoretical Studies, 424.4, AEA Industrial Technology, Harwell Laboratory, Oxon, OX11 OR.A, U.K. i" 15 Witan Way, Wantage, Oxon OX12 9EU, U.K. ~: Air Pollution Group, Centre for Environmental Technology, Imperial College, London SW7 2BX, U.K. ABSTRACT Radioactive aerosols can become charged by emitting charges during the decay process, and the resulting electrostatic forces will modify coagulation rates. For Brownian coagulation, calculations for nuclear containment aerosols show that rates averaged over charge distributions can be strongly reduced between particles of the same size, but that increases m average rates can occur for particles of different sizes. The increases arise from small, but significant, negative charging of non-radioactive and small-sized radioactive particles, and are sensitive to the asymmetry between the positive and negative ion mobilities. KEYWORDS Coagulation, radioactive aerosols, nuclear aerosols, electrical properties, aerosol charging. INTRODUCTION The emission of one or more electrons from a radioactive aerosol particle during each decay charges the particle, but the many positive and negative ions produced in the surrounding gas tend to neutralise it by diffusing back onto the aerosol. In a considerable extension to previous theory (Reed et al 1977), we have shown how resultant charge distributions on the aerosol may be calculated (Clement and Harrison, 1991, 1992). Here, we describe how to calculate modifications to mean coagulation rates for aerosol charge distributions. Calculations have been performed for various aerosols, including a highly radioactive aerosol containing 131Iin a reactor containment atmosphere. CHARGE DISTRIBUTIONS We are mainly interested in steady-state charge distributions reached by a ~decaying aerosol which are specified by three parameters (Clement and Harrison 1992). With eo as the permittivity of the vacuum, the size parameter for an aerosol of radius a, at temperature, T, is T = e2/( 87r ~ a k T)
(1)
To specify ionic charging by positive and negative ions, number concentrations n+,n. and mobilities g+,la-, respectively, we define the asymmetry ratio, x =
(2)
S145
S146
C . F . CLEMENT et al.
The third parameter expresses the aerosol self-charging in terms of its decay rate, Tl, per unit time: y = 11eo/(e It-n-)
(3)
Significant self-charging only occurs when recombination dominates the ion removal process when, with recombination rate, o~, ion pairs produced per decay, I, monodisperse aerosol number density, Z, and background ion production rate, q, the ionic density is approximately 1
n = [(Ir/Z +q)/c~]~.
(4)
The difference between the ion concentrations is specified by charge conservation in terms of the charge, ], on the aerosol, and in practice is found by iteration from calculations of using charge disuibutions obtained with parameters defined by equations (I)-(3). COAGULATION Using the electrostatic modification of Fuchs (1964), the average enhancement factor for Brownian coagulation between aerosol charge distributions N j, al), N j, (a2) for particles of radii al and a2 is t
K -=~= = Z N i Nj, JlJ2
Y exp Y - 1
/ZN~Nj,,
(5)
JlJ2
J'J2e2 V(a'j"azJ2) = 4~eokT(a, + a2)
(6)
Only steady-state charge distributions are needed for calculations if, as is possible to show for reactor containments, the timescale for ionic charging is much less than the agglomeration timescale: %ch= y/~ << %ag.
(7)
Results of calculations show that charging, when it occurs, always suppresses coagulation for aerosol particles of the same size, but that coagulation rates for particles of different sizes may be increased. This is illustrated here by two calculations relevant to radioactive aerosols in the atmosphere of a reactor containment. The first concerns coagulation between a largesized non-radioactive aerosol (y = 0) and a small-sized radioactive aerosol (y > 0). These types of aerosol could be typical of ones produced in possible accidents where large amounts of volatile non-radioactive material are involved. The results illustrated in Fig. 1 show an overall enhancement in the coagulation rates which increases with charging. This, and the unexpected sensitivity of the results to x, can be attributed to the wide charge distribution for the larger aerosol where the enhancement from its negatively charge part, which is greater if x < 1, outweighs the reduction from its positively charged part. The second calculation concerns a highly radioactive Cs ]31I aerosol (I = 7.7 103, xl = 350 (a(pm)/0.2)3), in a highly ionising containment atmosphere of a pressurized water reactor, where we estimate that radioactive Kr and Xe can produce a background ion production rate as high as q = 3.0 1018 s-lm -3. A larger size aerosol of density Z m "3 contributes to the ion
Coagulation of radioactive aerosols
I..
{01= 0"1 }.1111
.
O 2 = 1 "0 y m
S147
~[ ___1o,= o2~ o2= 2.0 jam
~c= 0-912
/ /
/..
K, t K
- -
/
+ /
oc=l
F 0
10
Y
20
30
Fig. 1, Enhancement in mean coagulation rates between aerosols of the two different radii shown as a function of the radioactive charging parameter, y. Results for two different asymmetry parameters, x.
KI 3 2 K
B
I
O
_ -0.3
m
J -0./.
m
o = 0-2~Jm C
100 80 B 6O m
T
=
~o
p
20 0 1012
,~--
I
1011
I
I
1010
i09
I
108
107
Z m "3
Fig. 2.
Mean charges, ], of 0.2 gm and 2}Jan radius Csl31I aerosols in a radioactive gas atmosphere, and their mutual mean coagulation rate enhancement, as functions of the number concentration, Z, of the 2gm aerosol.
Si48
C. F, CLEMENT et al. 10
K.-~. I 01 K
10-'
10
1012
Fig. 3.
1011
Z m'3
1010
109
Coagulation enhancement for a 2~a'n Csl31I aerosol in a radioactive gas atmosphere as a function of aerosol number density, Z.
production rate, and we calculate coagulation rates as a function of Z for itself and with small-sized Cs 131I particles. Results of calculations of mean charges and enhancements in coagulation rates for the two sizes of aerosol are shown in Figs. 2 and 3. Because of the large ion densities, the parameter x takes on its limiting value of g+/g. = 0.912. From the assumed dependence of rl on a, the values of y for the two sizes differ by a factor of 103, and the small-sized aerosol is slightly negatively charged from the asymmetry in the ion mobilities. At high number densities, the ions produced by decays from the 2grn aerosol effectively neutralise it and K'/K = 1. As Z is lowered, the 2pan aerosol becomes self-charged; coagulation with itself becomes strongly suppressed, but an enhancement takes place in the coagulation rate with the smaller aerosol. ACKNOWLEDGEMENT This work was funded as part of the General Nuclear Safety Programme undertaken by AEA Technology on behalf of the UK Department of Induslry. REFERENCES Clement, C.F. and R.G. Harrison (1991). Self charging of radioactive aerosols. J. Aerosol Sci., 22 Suppl. 1, $55-58. Clement, C.F. and R.G. Harrison (1992). The charging of radioactive aerosols. J. Aerosol Sci. (in press). Fuchs, N.A. (1964). The Mechanics of Aerosols. Pergamon, New York. Reed, L.D., H. Jordan and J.A. Gieseke (1977). Charging of radioactive aerosols. J. Aerosol Sci. 8, 457-463.