Turbulent Brownian Coagulation Model

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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


==

jiifnn

jiifnnDrDrKP

ji

jijjiiij

2...),,,,(


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=

=

M

ikikik

M

kji,kijij

kQPQPdt

dn

121 1 )(

=j ki



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TB KKK +=

)()(4 jijiB DDrrK ++=

ccajiT wwrrK *)()(3

8 22

2/1

++

=



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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

Turbulent Brownian Coagulation Model

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