Applied Physics B

, Volume 104, Issue 2, pp 253–271 | Cite as

Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements

  • J. Yon
  • R. Lemaire
  • E. Therssen
  • P. Desgroux
  • A. Coppalle
  • K. F. Ren


The refractive index of soot is an essential parameter for its optical diagnostics. It is necessary for quantitative interpretation of LII (Laser Induced Incandescence) signals, light scattering or extinction measurements as well as for emissivity calculations. The most cited values have been determined by intrusive methods or without taking into account the soot size distribution and its specific morphology. In the present study, soot generated by the combustion of diesel and diesel/rapeseed methyl ester (RME) mixture (70% diesel and 30% RME) are extensively characterized by taking into account the morphology, the aggregate size distribution, the mass fraction and the spectral dispersion of light. The refractive index m for wavelengths λ between 300 and 1000 nm is determined for diesel and diester fuels by both in-situ and ex-situ methods. The ex-situ method is based on the interpretation of extinction spectra by taking into account soot sizes and fractal morphology with the RDG-FA (Rayleigh–Debye–Gans for Fractal Aggregate) theory. The in-situ approach is based on the comparison of the LII signals obtained with two different excitation wavelengths. The absorption function E(m) and the scattering function F(m) are examined. This study reveals similar optical properties of soot particles generated by both studied fuels even at ambient and flame temperatures. The function E(m) is shown to reach a maximum for λ=250 nm and to tend toward a plateau-like behavior close to E(m)=0.3 for higher wavelength (600<λ (nm)<1000). The function F(m) is found to be quite constant for 400<λ (nm)<1000 and equal to 0.31.


Diesel Diester Soot Particle Extinction Spectrum Soot Volume Fraction 
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Constant used for Single Scattering Albedo characterization

B m−1

Constant used for Single Scattering Albedo characterization

c ms−1

Speed of the light

Cabs m2

Absorption parameter used in RDG-FA

Cs kg m−3

Particles mass concentration (TEOM measurement)

Csca m2

Scattering parameter used in RDG-FA

D m

Diaphragm/flame distance D in LII setup


Fractal dimension

Dg m

Soot particle gyration diameter

Dp m

Soot primary particles (monomer) diameter (mode of the distribution)

Dm m

Electrical mobility diameter of the particle (SMPS measurement)

e C

Electron charge


Absorption function, derive from optical index

Elaser J

Total energy of the laser pulse radiation

Ep J

Total energy absorbed by a single soot particle


Scattering function, derive from optical index

f laser Jm−2

Laser fluence (taken at 1/e 2)


Volume fraction

gi s−1

Damping constants of bound electrons

gc s−1

Damping constants of bound and free electrons

h J s

Planck constant


Absorbed power of a single soot particle

kB J K−1

Boltzmann constant


Dimensionless extinction coefficient

Kext m−1

Extinction coefficient


Fractal prefactor

l m

Mean free path of conduction electrons

L m

Optical path length

La m

Aggregate maximum projected length on TEM pictures


Optical index

m kg

The effective electron mass

mv kg

The electron mass in vacuum

Mabs m−3

Mean number of primary particle/momentum used for absorption calculation

Msca m−3

Quasi-momentum used for scattering calculation

Nagg m−3

Number of particles by unit volume

nc m−3

Free electron number density

ni m−3

Bound electron number density

nt m−3

Total number densities


Number of primary particles in an aggregate


Soot absorption efficiency

qλ W m−2

Laser irradiance

Rg=Dg/2 m

Particle gyration radius

Rp=Dp/2 m

Soot primary particle radius

Slaser m2

Laser pulse cross-sectional area


Flame temperature

Tp K

Particle temperature

x,y,z m

Spatial coordinates



Diesel/RME mixture


Dilution ratio of the aerosol sampling in flame


Diffusion Limited Cluster-Cluster Aggregation


Fine Particle Sampling system


Height Above the Burner


Laser Induced Fluorescence


Laser Induced Incandescence


Polycyclic Aromatic Hydrocarbon


Rayleigh-Debye-Gans for Fractal Aggregate


Rapeseed Methyl Ester


Scanning Mobility Particle Sizer


Single Scattering Albedo


Transmission Electron Microscopy

λem m

The particle emission wavelength

Δλem m

Detection spectral-range of the measured LII signal

Δt s

Laser pulse duration


Mass concentration correction factor


Permittivity constant in vacuum

λ m

Detection wavelength (ex-situ method)

λlaser, λi, λj m

Wavelength of the laser light (in-situ method)

ρ kg m−3

The soot material density

σλ m2

Absorption cross-section at a given wavelength

σp m

Standard deviation of the Gaussian primary particle size distribution

σs m2 kg−1

Soot specific extinction

ω s−1

Excitation frequency

ωi s−1

Natural frequency of bound electrons


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • J. Yon
    • 1
  • R. Lemaire
    • 2
    • 3
  • E. Therssen
    • 2
    • 4
  • P. Desgroux
    • 2
    • 4
  • A. Coppalle
    • 1
  • K. F. Ren
    • 1
  1. 1.CNRS UMR 6614—CORIAUniversité et INSA de RouenSaint Etienne du RouvrayFrance
  2. 2.Université Lille Nord de FranceLilleFrance
  3. 3.EMDouai, EIDouaiFrance
  4. 4.CNRS UMR 8522—PC2AUniversité Lille1Villeneuve d’AscqFrance

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