Batut, S.

Desgroux, P.

Faccinetto, A.

Grimonprez, S

Petitprez, D.

Wu, J.

Yon, J.

English

Archive Ouverte en Sciences de l'Information et de la Communication

  
An Approach Based on κ-Kӧhler Theory for Calculating CCN Activation Curves that 
Considers the Dry Particle Size Distribution and Morphology 
 
J. Wu
1
, A. Faccinetto
1
, S. Grimonprez
1
, S. Batut
1
, J. Yon
2
, P. Desgroux
1
, D. Petitprez
1
 
 
1
Lille Univ., CNRS PC2A, 59000 Lille, France 
2
Normandie Univ., INSA Rouen, UNIROUEN, CNRS CORIA, 76000 Rouen, France 
 
Keywords: soot aerosol, cloud condensation nuclei, size distribution, morphology, electrical mobility 
Contact: alessandro.faccinetto@univ-lille.fr 
 
 
Introduction 
 To the present day, κ-Kӧhler theory (Petters 
and Kreidenweis, 2007) is still largely used to 
describe the formation of liquid cloud droplets and to 
understand the role of atmospheric aerosols as cloud 
condensation nuclei (CCN). κ-Kӧhler theory uses a 
Dirac delta distribution to model the density of ideal 
spherical point size dry particles and droplets, and 
therefore loses predictive power when applied to 
aerosol particle distributions with large geometric 
deviation or complex morphology, which are both 
very common cases for airborne particles. In this 
work, we propose a theoretical approach to account 
for the contribution of the size distribution and 
morphology of the dry particles that aims to make 
quantitative predictions on the activated fraction as a 
function of the supersaturation Fa(SS). 
 
Methods 
 To test the model, activation experiments are 
performed in water supersaturation conditions in a 
commercial CCNc-100 nucleation chamber and using 
two different aerosols as CCN. Lognormal aerosol 
size distributions with different mode and geometric 
deviation are compared to the experimental Fa(SS) 
calculated using the modified κ-Köhler theory for 
laboratory generated aerosols. Ammonium sulfate 
represents the simplest case tested herein that is well 
known in the literature for the non-aggregating, 
non-agglomerating, quasi spherical particles that can 
be generated by atomization (Rose et al., 2008). The 
more challenging case of fractal-like soot particles is 
then investigated to understand the effect of the 
morphology parameters on activation. Soot particles 
are generated by flame combustion, and then aged 
with ozone to obtain a measurable Fa. 
 
Results and conclusions 
 In order to make quantitative predictions on 
the activation curves in the simplest case of spherical, 
isolated dry aerosol particles, the dry particle volume 
equivalent diameter dve is approximated with the 
mobility diameter dm and a lognormal function that 
describes the particle size distribution is directly 
introduced in the analytical form of Fa(SS). This 
simple model, tested with ammonium sulfate 
aerosols, well reproduces activation experiments and 
clearly shows that the geometric standard deviation 
plays an important role on the shape of Fa(SS) for 
instance. However, soot particles are characterized 
by fractal-like morphology and require a more 
elaborated relation between dm and dve as well as 
detailed knowledge of their size distribution and 
morphology. The approach that we propose is based 
on the analysis of soot aggregate projections obtained 
from electron microscopy images in parallel to the 
measurement of their electrical mobility. In 
particular, dve can be related to dm through complex 
and/or empirical relations that require knowledge on 
the primary particle diameter and fractal dimension 
of the aggregates (Yon et al., 2015). 
 The effect of all morphology parameters on 
the activation curves are studied to provide a deeper 
understanding of the model, then this approach is 
applied to the calculation of Fa(SS) of soot aged by 
exposure to ozone as shown in Figure 1, and proved 
to be viable for κ > 5×10-5. 
0.0 0.4 0.8 1.2 1.6 2.0
0.0
0.2
0.4
0.6
0.8
1.0
Exposure / cm
-3
s
   --    0 (Kelvin limit)
 3.21×10
16
    1.2×10
-4
 5.37×10
16
    1.1×10
-3
 7.84×10
16
    3.0×10
-3
 10.2×10
16
    4.9×10
-3
 12.4×10
16
    6.3×10
-3
F
a
 /
 a
d
.
SS %
0.0 0.4 0.8 1.2 1.6 2.0
0.0
0.2
0.4
0.6
0.8
1.0
Exposure / cm
-3
s
   --       0 (Kelvin limit)   
 3.57×10
16
     --
 8.87×10
16
     --
 13.7×10
16
     --
 18.6×10
16
       6.0×10
-5
F
a
 /
 a
d
.
SS %
(b)
 
Figure 1. Experimental (data) and calculated (lines) 
activation curves of soot dry particles generated in a 
laboratory jet diffusion flame supplied with kerosene 
after exposure to ozone. 
 
Petters, M. D.; Kreidenweis, S. M. (2007). 
Atmospheric Chem. Phys. 7(8), 1961–1971. 
Rose, D., Gunthe, S. S., Mikhailov, E., Frank, G. P., 
Dusek, U., Andreae, M. O., Pöschl, U. (2008). 
Atmospheric Chem. Phys. 8(5), 1153–1179. 
Yon, J., Bescond, A., Ouf, F.-X. (2015). J. Aerosol 
Sci. 87, 28–37. 


An Approach Based on κ-Kӧhler Theory for Calculating CCN Activation Curves that Considers the Dry Particle Size Distribution and Morphology

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An Approach Based on κ-Kӧhler Theory for Calculating CCN Activation Curves that Considers the Dry Particle Size Distribution and Morphology

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