turbulent brownian coagulation model
TRANSCRIPT
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INTRODUCTION
MEAN FIELD COAGULATION
MODEL
RESULTS
CONCLUSIONS
TOPICS
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diffusion
coagulation
nucleation
condensation
sedimentation
INTRODUCTION
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Brownian motion (~ 0.001 a 1 m)Turbulent motion (~ 1 a 10 m)
Differential sedimentation ( > 10 m )
COAGULATION
Process by which some of the aerosol particles collide with each
other and they join to form larger particles
=+
=i
kiikkji
jiijk
nnnndt
dn
21
Monodisperse sizedistribution
All the particles are
spherical
Only binary collisions
These collisions conserve mass andvolume
All collisions produce coagulation
Smoluchowsky (1917)
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=
jk
i
0
50
100
150
200
Diameter intervals
0.001 0.01 0.02 0.03 0.04 0.08 0.16 0.32 0.64 1.28 2.56 5 10
- Only binary collisions, conservemass and volume
- Polydisperse size distribution
- Aerosol particles are spherical
- All collisions coagulation
MEAN FIELD COAGULATION MODEL (MFC)
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The probability that one collision takes place in the system.
The probability that such collision involves particles of
particular intervals i and j
The probability Qijk that such collision produces a particle
in a given interval k
MEAN FIELD COAGULATION MODEL (MFC)
==
jiifnn
jiifnnDrDrKP
ji
jijjiiij
2...),,,,(
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=
=
M
ikikik
M
kji,kijij
kQPQPdt
dn
121 1 )(
=j ki
MEAN FIELD COAGULATION MODEL (MFC)
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TB KKK +=
)()(4 jijiB DDrrK ++=
ccajiT wwrrK *)()(3
8 22
2/1
++
=
MEAN FIELD COAGULATION MODEL (MFC)
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RESULTS
Kim et al., 2003
NaCl aerosol
Diameters: 0.050, 0.115 m
Duration: 1800 3000 s
Sample time: 300 350 s.
Rooker and Davies, 1979
CaCO3 aerosol
Diameter interval: 0.005 0.030 m
Duration: 1800 s
Sample time: 300 - 400 s.
Simulation of brownian coagulation
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SIMULATION OF BROWNIAN COAGULATIONKim et al., 2003
Experimental data MFC model - Brownian Kernel
0 1000 2000 3000
TIME (s)
0
0.2
0.4
0.6
0.8
1
N/No
0.050 m
0 400 800 1200 1600
TIME (s)
0.2
0.4
0.6
0.8
1
N
/No
0.115 m
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0 400 800 1200 1600 2000
TIME (s)
0.6
0.7
0.8
0.9
1
N
/No
C50
0 400 800 1200 1600 2000
TIME (s)
0.2
0.4
0.6
0.8
1
N
/No
C90
Rooker and Davies, 1979
Experimental data MFC model - Brownian Kernel
SIMULATION OF BROWNIAN COAGULATION
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Experimental data MFC model - Turbulent Kernel by Kruis and Kusters (1997)
0 100 200 300
TIME (s)
0
0.2
0.4
0.6
0.8
1
N
/No
1800 rpm
= 810,000 cm2 s-3
c= 3.5
SIMULATION OF TURBULENT BROWNIAN
COAGULATION
0 100 200 300 400 500
TIME (s)
0
0.2
0.4
0.6
0.8
1
N
/No
600 rpm
= 30,000 cm2 s-3
c= 1.0
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CONCLUSIONS
The Mean Field Coagulation model (MFC) simulates, in asimple form, the coagulation of polydispersed aerosols.
The simulation experiments showed that the MFC modelreproduces satisfactorily the experimental data of pure
brownian and brownian turbulent coagulation.
The MFC model takes into account the polydisperse nature ofthe aerosol. It is simulated with a probability function, Qij
k,that conserves the aerosol volume.
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Thank you for your attention
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Kim D. S., Park S. H., Song Y. M., Kim D. H., Lee K. W. (2003).
Brownian coagulation of polydisperse aerosols in the transitionregime. Journal of Aerosol Science, Vol. 34(7):859-868.
Kruis F. E., Kusters K. A. (1997). The collision rate of particles
in turbulent flow. Chem. Eng. Comm., Vol. 158:201-230.
Okuyama K. Kousaka Y., Kida Yoshinori y Yoshida Tetsuo.
(1977). Turbulent coagulation of aerosols in a stirred tank.
Journal of Chemical Engineering of Japan, Vol. 10(2):142-147.
Rooker S. J., Davies C. N. (1979). Measurement of thecoagulation rate of a high Knudsen number aerosol withallowance for wall losses. Journal of Aerosol Science, Vol.10:139-150.
REFERENCES