Coagulation of fractal-like aerosols in the transition regime

E. Goudeli, M.L. Eggersdorfer and S.E. PratsinisParticle Technology Laboratory

ETH Zürich

2

IPCC, 2007

AerosolsRadiative Forcing - Emissions

Negative RadiativeForcing

• Larger error bar than greenhouse gases• Impact in global radiation budget by absorbing & scattering light• Investigate & regulate emissions from aerosol measurements

31. Eggersdorfer ML, Pratsinis SE. (2014) Adv. Powder Technol., 24, 71-90.

rm: mobility radius free molecular regime

DMA

rva: volume-equivalent radius

Filter weighingAPMTEOM

rg: radius of gyration

Light ScatteringMicroscopy

Agglomerate Characterizationrm: mobility radius continuum regime

Df 3 1

10g

va

rr

measurementsoverpredict emissionsby 1000 times

4

Understanding agglomerateGoal:

Motivation:• Connect emissions to aerosol size measurements

rva rg, rm

• Facilitate understanding of aerosol contribution in climateforcing (minimize hopefully error bar)

• Structure (relate to agglomerate mass)• Dynamics

in the free molecular, transition and continuum regime of aged aerosols in the atmosphere

Previous Work Brownian coagulation of spheres1,2

Non-spherical particlesdetermination of evolving structure3,4,5

collisional growth and dynamics6

on-line measurements of agglomerate size and structure7,8

3. Kostoglou M, Konstandopoulos AG (2001), J. Aerosol Sci., 32, 1399-1420.4. Schmid HJ, Al Zaitone B, Artelt C, Peukert W (2006), Chem. Eng. Sci., 61, 293-305.5. Eggerdorfer ML, Kadau D, Herrmann HJ, Pratsinis SE (2011), Langmuir, 27, 6358-6367.6. Thajudeen T, Gopalakrishnan R, Hogan CJ Jr. (2012), Aerosol Sci. Technol., 46, 1174-1186.7. Eggersdorfer ML, Gröhn AJ, Sorensen CM, McMurry PH, Pratsinis SE (2012), J. Colloid Interface Sci., 378,12-23.8. Gröhn AJ, Eggersdorfer ML, Pratsinis SE, Wegner K (2014), J. Aerosol Sci., 73, 1-13.

5

1. von Smoluchowski M. (1917), Z. Phys. Chem. Stoechiom. Verwandtschafts., 92, 129-168.2. Buesser B, Heine MC, Pratsinis SE (2009), J. Aerosol Sci., 40, 89-100.

6

SiO2 particles (like fly ash)T = 27 oC

DLCA

8 Bp

p

k Tum

Ballistic trajectories:

2. Heine MC, & Pratsinis SE. (2007). Langmuir, 23, 9882-9890.

Continuum regime: Langevin Dynamics 2

Free molecular regime: Event-driven method 1

BCCA

3. Eggersdorfer ML, Kadau D, Herrmann HJ, & Pratsinis SE. (2010). J. Colloid Interface Sci., 342, 261-268.

time

if N<N0/2double

if N<N0/2double

1. Allen MP, & Tildesley DJ. (1991). Computer Simulation of Liquids, Oxford University Press, New York.

72. Fuchs NA. (1964). Mechanics of Aerosols. Macmillan, New York.1. Dahneke, B. (1983). Academic Press, New York, 97‐133.

3. Gopalakrishnan R, Thajudeen T, Hogan CJ Jr. (2011).  J. Chem. Phys., 135, 054302‐1 – 054302‐9.

10-3 10-2 10-1 100 101 1020.3

1

5

10-3 10-2 10-1 100 101 1020.3

1

5

10-3 10-2 10-1 100 101 1020.3

1

5

10-3 10-2 10-1 100 101 1020.3

1

5

10-3 10-2 10-1 100 101 1020.3

1

5

β,10

-15 ,

m3 /s

Kn = λair/rp

Dahneke1

Fuchs2

Gopalakrishnan et al.3CMD-based β

7.34%

Free molecular

(Kn >10)

Continuum (Kn <0.1)

17.9%

Enhancement due to

polydispersity&

attainment of self-preserving size distribution

Validation – Full CoalescenceCollision Frequency Function, β

4. Husar RB, Whitby KT. (1973).  Environ. Sci. Technol., 7, 241 – 247.

r g (

), r m

( ),

r va(

), nm

time, s

n p(

)

Df ?

1. Eggersdorfer ML, Pratsinis SE. (2014) Adv. Powder Technol., 24, 71-90.

10-8 10-7 10-6 10-5 10-4100

101

102

10-8 10-7 10-6 10-5 10-410-1

100

101

102

103

104

Results – Agglomerate Size Evolution

50 nm

8

33 nm

13 nm

4a

g

v

rr

64 times overprediction

9

100 101 102 103 1041.5

2.0

2.5

3.0

Number of primary particles, np

Results – Agglomerate Structure EvolutionE

ffect

ive

fract

al d

imen

sion

, Df

PP radius:1 nm2 nm7 nm

15 nm100 nm500 nm

fD

gp n

p

rn k

r

10

Effe

ctiv

e fra

ctal

dim

ensi

on, D

f

1. Jullien R, Botet R. (1987). World Scientific, River Edge.2. Tence M, Chevalier JP, Jullien R. (1986). J Phys-Paris, 47, 1989–1998.

KnD,m = λp/rm10-3 10-1 101 103 105

1.5

2.0

2.5

3.0

10-3 10-1 101 103 1051.5

2.0

2.5

3.0

Df = 1.91 ± 0.03

Free molecular (BCCA)

Continuum (DLCA)

Df = 1.78 ± 0.05

Results – Agglomerate Structure Evolution

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

KnD,m = λp/rm1. Vemury S, Pratsinis SE. (1995). J. Aerosol Sci. 26: 175-185.

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σg,g,FM = 2.27

Results – Geometric Standard Deviationσ g

σg,vσg,v,C = 1.31(Df = 2)

σg,v,FM = 1.41

σg,v = 1.421

agglomeratesσg,g: rg-basedσg,m: rm-basedσg,v: rva-based

spheresσg,g: rg-basedσg,v: rva-based

σg,m

σg,g

σg,v

σg,g

, ,( )g g D mf Kn

σg,g,C = 1.95 σg,m,FM = 2.03

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

10-3 10-2 10-1 100 101 102 1031.0

1.5

2.0

2.5

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Conclusions

Structure• Transition regime: smooth shift of Df• FM regime: Df = 1.91 ± 0.03• Continuum regime: Df = 1.78 ± 0.05

Geometric Standard Deviation of Quasi-Self-PreservingSpheres Agglomerates

FM Continuum FM Continuum• σg,v 1.33 1.32 1.41 1.31• σg,m 1.46 1.44 2.03 -• σg,g 1.46 1.44 2.27 1.95 , ,( )g g D mf Kn

Agglomerate SizeFor np > 10 rg > rm , rva

overpredictemissions

Df evolution from spherical to fractal-like structures: ( )f pD f n

, 1v

g

va a

mrr

rr

,( )f D mD f Kn

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THANK YOU FOR YOUR ATTENTION!

Index

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