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Coagulation of soot particles and fractal dimension
J Aerosol ScL Vol. 30. Suppl. I, pp. $445-$446. 1999 O 1999 Published by Elsevier Science Ltd. All rights r e , f r e d Printed in Gve.atBritain 0021-8502/9915- see front matter
Pergamon
COAGULATION OF SOOT PARTICLES AND FRACTAL DIMENSION B. Gorbunov, A.G. Clarke + and R.S. Hamilton Urban Pollution Research Centre, Middlesex University Bounds Green Road, London N11 2NQ, UK; +Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, UK KEYWORDS agglomerates, diesel, mobility radius, aerosol size distribution Coagulation of soot aerosols generated by a FORD 1.81 turbo diesel engine has been studied in a Teflon bag (540 1 volume; 4.4 m2 surface) under 50% RH and temperature 25.2 ° C. Aerosol size distributions were measured every 5 rain with the SMPS system (TSI model 3934). A diesel exhaust sample was diluted approximately 14 fold in the bag. It was found that initially the aerosol size distribution is a log-normal one with the radius of the maximum in the distribution at R= = 74 nm and the standard geometrical deviation o'g = 1.7 (Figure 1). The total number concentrations of particles at the beginning was 5.8x105 e m "3. 18000
18000
12000 ~ 10000 8000
/1111
oooo
/ 20o0
//Ai I
0
0
0.5
1
1.5
2
2.5
3
Log(R), R -nm
Figure I. Aerosol number size distributionsmeasured every 5 rain.dN =f(R,t)dlogR,where f(R,t) is the aerosol size distribution at the time t. R is the mobility radius.
A novel integrating method is suggested for calculation of the fraetal dimension of soot aggregates that is based on the approximation of a constant fraetal dimension D f in the size range of the interest. The new approach enables the link between the mass of a particle m and the mobility radius to he expressed as follows: (Rp)
(1)
where Rp - the radius of the primary particles and rap - its mass. N0 is the average number of the primary particles in the smallest aggregate for which the expression (1) is still valid. The fraetal dimension was calculated from the integral equation:
$445
$446
Abstracts of the 1999 EuropeanAerosolConference
M(,): Nora. oS -~t R. )
(R,,)<.og . '
(2)
where M(t) is the mass concentration of aerosol. The mass concentration of soot aerosol was measured gravimetdcally. These data were paramcterised employing a linear approximation. It was obtained that M(O = A-Bt, where A = 870 lag m"3 and B = 2.417 ~tg m-3 min -i. Thus loses of particles due to deposition onto the walls of the bag was taken into account. The main advantage of this approach is that it is an integrating method. Both parameters Dr and the combination of N0, Ro and mo (Nom~Rp"Df) can be obtained using equation (2) with relatively high accuracy. Equation (2) was solved for every couple of aerosol size distributions (Figure l) measured at the time that differs for 15 min. It was found that both the ffactal dimension and No do not depend on time during the first 80 min. The average values for this period of time were found: D/= 1.92 + 0.08 and No = 2.5+0.6. The density of a primary particle was accepted to be 1.5 g cm3 and the radius of a primary particle - 12.5 nm (Weingartner et al., 1997). This approach enables the deposition of aerosol particles to be investigated. The mass concentration of aerosols in a container is influenced by the deposition rate D(R) and the ratio of the surface to the volume of the container (S/V): ,
M(t)=Mo-No(t)m_ f a r
®
( n ~ °I(~)
fdlogR| ~-~-|
"'o _:
tR,)
f(R,r)¢D(R) S v
,
(3)
Where ~ is the geometrical factor that is responsible for the shape of the container. Usually, it is close to unity. Equation (3) makes it possible to evaluate the deposition rate of particlesas well as their diffusivity.Alternatively, if the deposition rate is known the change in the mass concentration could be obtained. It was found that during first25 rain the coagulation rate was much higher than the deposition rate and the deposition could be neglected (the fastcoagulation).During that time itis possible to assume M(t) to be a constant. This enables the solutions of equation (2) to be found without n~asuring the mass concentration. The accuracy of finding the fractaldin~nsion in this way is relativelyhigh and the additionalerror due to neglecting the deposition is lessthan 10%. The coagulation of aerosol particleswas also calculated using the coagulation kernel reported by Dahneke (1983). It was found that calculated size distributionsare transformed more slowly than measured ones. There was no asymmetry to be found in calculated distributions.All calculated distributionswere close to log-normal shape. Thus, a conventional coagulation kernel cannot be used to describe the coagulation of soot particles. ACKNOWLEDGEMENT: The authors would like to acknowledge Dr. V. Scheer (Ford Research Centre, Aachen, Germany) for the providing the size distributions and assistance to the work. REFERENCES Dakhneke B. (1983) Simple kinetic theory of Brownian diffusion in vapours and aerosols. In Theory of dispersed multiphase flow (R.E. Meyer, Ed.) Acad. Press, N.-Y., pp. 97-138. Weingartner E., Burtscher H. and Baltensperger U. (1997) Hygroscopic properties of carbon and diesel soot particles. Atmos. Environ., 31,2311-2327.
Pergamon
COAGULATION OF SOOT PARTICLES AND FRACTAL DIMENSION B. Gorbunov, A.G. Clarke + and R.S. Hamilton Urban Pollution Research Centre, Middlesex University Bounds Green Road, London N11 2NQ, UK; +Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, UK KEYWORDS agglomerates, diesel, mobility radius, aerosol size distribution Coagulation of soot aerosols generated by a FORD 1.81 turbo diesel engine has been studied in a Teflon bag (540 1 volume; 4.4 m2 surface) under 50% RH and temperature 25.2 ° C. Aerosol size distributions were measured every 5 rain with the SMPS system (TSI model 3934). A diesel exhaust sample was diluted approximately 14 fold in the bag. It was found that initially the aerosol size distribution is a log-normal one with the radius of the maximum in the distribution at R= = 74 nm and the standard geometrical deviation o'g = 1.7 (Figure 1). The total number concentrations of particles at the beginning was 5.8x105 e m "3. 18000
18000
12000 ~ 10000 8000
/1111
oooo
/ 20o0
//Ai I
0
0
0.5
1
1.5
2
2.5
3
Log(R), R -nm
Figure I. Aerosol number size distributionsmeasured every 5 rain.dN =f(R,t)dlogR,where f(R,t) is the aerosol size distribution at the time t. R is the mobility radius.
A novel integrating method is suggested for calculation of the fraetal dimension of soot aggregates that is based on the approximation of a constant fraetal dimension D f in the size range of the interest. The new approach enables the link between the mass of a particle m and the mobility radius to he expressed as follows: (Rp)
(1)
where Rp - the radius of the primary particles and rap - its mass. N0 is the average number of the primary particles in the smallest aggregate for which the expression (1) is still valid. The fraetal dimension was calculated from the integral equation:
$445
$446
Abstracts of the 1999 EuropeanAerosolConference
M(,): Nora. oS -~t R. )
(R,,)<.og . '
(2)
where M(t) is the mass concentration of aerosol. The mass concentration of soot aerosol was measured gravimetdcally. These data were paramcterised employing a linear approximation. It was obtained that M(O = A-Bt, where A = 870 lag m"3 and B = 2.417 ~tg m-3 min -i. Thus loses of particles due to deposition onto the walls of the bag was taken into account. The main advantage of this approach is that it is an integrating method. Both parameters Dr and the combination of N0, Ro and mo (Nom~Rp"Df) can be obtained using equation (2) with relatively high accuracy. Equation (2) was solved for every couple of aerosol size distributions (Figure l) measured at the time that differs for 15 min. It was found that both the ffactal dimension and No do not depend on time during the first 80 min. The average values for this period of time were found: D/= 1.92 + 0.08 and No = 2.5+0.6. The density of a primary particle was accepted to be 1.5 g cm3 and the radius of a primary particle - 12.5 nm (Weingartner et al., 1997). This approach enables the deposition of aerosol particles to be investigated. The mass concentration of aerosols in a container is influenced by the deposition rate D(R) and the ratio of the surface to the volume of the container (S/V): ,
M(t)=Mo-No(t)m_ f a r
®
( n ~ °I(~)
fdlogR| ~-~-|
"'o _:
tR,)
f(R,r)¢D(R) S v
,
(3)
Where ~ is the geometrical factor that is responsible for the shape of the container. Usually, it is close to unity. Equation (3) makes it possible to evaluate the deposition rate of particlesas well as their diffusivity.Alternatively, if the deposition rate is known the change in the mass concentration could be obtained. It was found that during first25 rain the coagulation rate was much higher than the deposition rate and the deposition could be neglected (the fastcoagulation).During that time itis possible to assume M(t) to be a constant. This enables the solutions of equation (2) to be found without n~asuring the mass concentration. The accuracy of finding the fractaldin~nsion in this way is relativelyhigh and the additionalerror due to neglecting the deposition is lessthan 10%. The coagulation of aerosol particleswas also calculated using the coagulation kernel reported by Dahneke (1983). It was found that calculated size distributionsare transformed more slowly than measured ones. There was no asymmetry to be found in calculated distributions.All calculated distributionswere close to log-normal shape. Thus, a conventional coagulation kernel cannot be used to describe the coagulation of soot particles. ACKNOWLEDGEMENT: The authors would like to acknowledge Dr. V. Scheer (Ford Research Centre, Aachen, Germany) for the providing the size distributions and assistance to the work. REFERENCES Dakhneke B. (1983) Simple kinetic theory of Brownian diffusion in vapours and aerosols. In Theory of dispersed multiphase flow (R.E. Meyer, Ed.) Acad. Press, N.-Y., pp. 97-138. Weingartner E., Burtscher H. and Baltensperger U. (1997) Hygroscopic properties of carbon and diesel soot particles. Atmos. Environ., 31,2311-2327.