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On the aerodynamic behavior of fractal agglomerates
Pergamon
J. Aerosol Sci. V o l . 28, Suppl. 1, pp. $ 5 1 3 - S 5 1 4 . 1997 © 1 9 9 7 E l s e v i e r S c i e n c e Ltd. A l l r i g h t s reserved Printed in Great Britain
PII:SO021-8502(97)O0305-4
~21-s50~97 $17.~+0.~
On the Aerodynamic Behavior of Fractal Agglomerates Charles C.-K. C h o u I and Chung-Te Lee 2 l Center for Industrial Safety and Health Technology, Industrial Technology Research Institute, 11F, Bldg. 51,195-10 Sec. 4 Chung-Hsing Rd. Chutung, Hsinchu, Taiwan, R.O.C. 2 Graduate Institute of Environmental Engineering, National Central University, Chungli 32054, Taiwan, R.O.C. KEYWORDS fractal aggregates, aerodynamics, shape factor, electrical mobility METHODS
Based on the electrical mobility of aerosol agglomerates, an experimental system was installed to generate agglomerates of ultrafine silver particles, and measuring the fractal dimension (Dr) and volume equivalent radius (R~) of the agglomerates. The instrumental setup in this work is modified from that developed by Schmidt-Ott (1988). sheath air
sheath air
thermometer | , ~-gsl
500K :
~
Section 2 Section3 , Section4 , C o o l i n g Electrostatic i Collapsing' Chamber' Classifier ' Furnace '
acuum ump
;pcl p
J
monodisperse aerosol 'i Section 1 Aerosol Generator
!
Section 5 Scanning Mobility Particle Sizer
Figure 1. Schematic diagram of the experimental setup. The experimental setup in this study is shown on Figure 1. Silver particles were generated from homogeneous nucleation of silver vapor in a tube-furnace. Fractal agglomerates were produced subsequently after going through agglomeration of the monomers. Due to the instability of the agglomeration structure against heat (Koch and Friedlander, 1990), the agglomerates would collapse somewhat to result in the change of the corresponding fractal dimensions. By varying the temperatures in the furnace-1 from 1100 to 1225 °K, agglomerates with different degrees of compactness and Df can be produced. An electrostatic classifier (TSI Model 3071A, MN) was used to selected agglomerates with a certain electrical mobility and the hydrodynamic radius (Rm) can be determined. The selected agglomerates were introduced into the second tube furnace with a temperature of 500 °K and collapsed to form completely compact clusters but kept their mass unchanged (Koch and Friedlander, 1990; Schmidt-Ott, 1988). The
S513
S514
Abstracts of the 1997 European Aerosol Conference
clusters were directed into a SMPS (Scanning Mobility Particle Sizer, TSI Model 3934, MN) system to measure P~ of the selected agglomerates. Thus, the Df of agglomerates can be calculated from Eq.(1), --oc R0
(1)
and the aerodynamic shape factor (K) of agglomerates can be calculated from the ratio of R~ and
R~. RESULTS By adjusting the temperature in the furnace-1, aerosol agglomerates with Df in a range from 2.65 _+ 0.05 ( l l 0 0 ° K ) to 2.87 -+ 0.04 (1225°K) were generated. The experimental results showed that the electrical mobility for several agglomerates with similar volume (and mass) was increased with the increasing of De. Besides, the ~c values were found to be decreased with the increasing of Dr. It implies that the aerodynamic behavior of an agglomerate with higher Df is more similar to that of a spherical particle. Figure 2 illustrates the relationship of K and De The structure of the agglomerate was loose and branched to result in a Df at 2.6 and ~ at 1.24_+0.02. In contrast, the more compact agglomerate was with a Df of 2.9 and a lower K value at 1.05_+0.01. Linear regression model between K and Df was also shown on the figure. Based on the fitted line, a 1< of 1.03 is obtained for an ideal sphere (Df =3), a value of only 3% higher than the theoretical one. This work demonstrates a possible link between Df and K for an agglomerate. 1.5
-
1.4
1~ =-o.53Di + 2.62! !
R2 = 0.8378 -
1.3 i 1.2 1.1 I
E .
1
2.5
.
.
.
.
.
±
2.6
_
.
J .
.
.
.
J _
2.7
2.8
_
_
I
2.9
3
Df Figure 2. Linear regression model of the aerodynamic shape factor of fractal agglomerates ACKNOWLEDGMENTS The authors acknowledge financial support from the Nation Science Council under Grant NSC 83-0410-E-008-026 in Taiwan, R.O.C. REFERENCES
Koch, W. and Friedlander, S. K. (1990) Particle growth by coalescence and agglomeration, J. Aerosol Sci. 21, $73-$76. Schmidt-Ott, A. (1988) In situ measurement of the fractal dimensionality of ultrafine aerosol particles, Appl. Phys. Lett. 52, 954-956.
J. Aerosol Sci. V o l . 28, Suppl. 1, pp. $ 5 1 3 - S 5 1 4 . 1997 © 1 9 9 7 E l s e v i e r S c i e n c e Ltd. A l l r i g h t s reserved Printed in Great Britain
PII:SO021-8502(97)O0305-4
~21-s50~97 $17.~+0.~
On the Aerodynamic Behavior of Fractal Agglomerates Charles C.-K. C h o u I and Chung-Te Lee 2 l Center for Industrial Safety and Health Technology, Industrial Technology Research Institute, 11F, Bldg. 51,195-10 Sec. 4 Chung-Hsing Rd. Chutung, Hsinchu, Taiwan, R.O.C. 2 Graduate Institute of Environmental Engineering, National Central University, Chungli 32054, Taiwan, R.O.C. KEYWORDS fractal aggregates, aerodynamics, shape factor, electrical mobility METHODS
Based on the electrical mobility of aerosol agglomerates, an experimental system was installed to generate agglomerates of ultrafine silver particles, and measuring the fractal dimension (Dr) and volume equivalent radius (R~) of the agglomerates. The instrumental setup in this work is modified from that developed by Schmidt-Ott (1988). sheath air
sheath air
thermometer | , ~-gsl
500K :
~
Section 2 Section3 , Section4 , C o o l i n g Electrostatic i Collapsing' Chamber' Classifier ' Furnace '
acuum ump
;pcl p
J
monodisperse aerosol 'i Section 1 Aerosol Generator
!
Section 5 Scanning Mobility Particle Sizer
Figure 1. Schematic diagram of the experimental setup. The experimental setup in this study is shown on Figure 1. Silver particles were generated from homogeneous nucleation of silver vapor in a tube-furnace. Fractal agglomerates were produced subsequently after going through agglomeration of the monomers. Due to the instability of the agglomeration structure against heat (Koch and Friedlander, 1990), the agglomerates would collapse somewhat to result in the change of the corresponding fractal dimensions. By varying the temperatures in the furnace-1 from 1100 to 1225 °K, agglomerates with different degrees of compactness and Df can be produced. An electrostatic classifier (TSI Model 3071A, MN) was used to selected agglomerates with a certain electrical mobility and the hydrodynamic radius (Rm) can be determined. The selected agglomerates were introduced into the second tube furnace with a temperature of 500 °K and collapsed to form completely compact clusters but kept their mass unchanged (Koch and Friedlander, 1990; Schmidt-Ott, 1988). The
S513
S514
Abstracts of the 1997 European Aerosol Conference
clusters were directed into a SMPS (Scanning Mobility Particle Sizer, TSI Model 3934, MN) system to measure P~ of the selected agglomerates. Thus, the Df of agglomerates can be calculated from Eq.(1), --oc R0
(1)
and the aerodynamic shape factor (K) of agglomerates can be calculated from the ratio of R~ and
R~. RESULTS By adjusting the temperature in the furnace-1, aerosol agglomerates with Df in a range from 2.65 _+ 0.05 ( l l 0 0 ° K ) to 2.87 -+ 0.04 (1225°K) were generated. The experimental results showed that the electrical mobility for several agglomerates with similar volume (and mass) was increased with the increasing of De. Besides, the ~c values were found to be decreased with the increasing of Dr. It implies that the aerodynamic behavior of an agglomerate with higher Df is more similar to that of a spherical particle. Figure 2 illustrates the relationship of K and De The structure of the agglomerate was loose and branched to result in a Df at 2.6 and ~ at 1.24_+0.02. In contrast, the more compact agglomerate was with a Df of 2.9 and a lower K value at 1.05_+0.01. Linear regression model between K and Df was also shown on the figure. Based on the fitted line, a 1< of 1.03 is obtained for an ideal sphere (Df =3), a value of only 3% higher than the theoretical one. This work demonstrates a possible link between Df and K for an agglomerate. 1.5
-
1.4
1~ =-o.53Di + 2.62! !
R2 = 0.8378 -
1.3 i 1.2 1.1 I
E .
1
2.5
.
.
.
.
.
±
2.6
_
.
J .
.
.
.
J _
2.7
2.8
_
_
I
2.9
3
Df Figure 2. Linear regression model of the aerodynamic shape factor of fractal agglomerates ACKNOWLEDGMENTS The authors acknowledge financial support from the Nation Science Council under Grant NSC 83-0410-E-008-026 in Taiwan, R.O.C. REFERENCES
Koch, W. and Friedlander, S. K. (1990) Particle growth by coalescence and agglomeration, J. Aerosol Sci. 21, $73-$76. Schmidt-Ott, A. (1988) In situ measurement of the fractal dimensionality of ultrafine aerosol particles, Appl. Phys. Lett. 52, 954-956.