Size Determination of Micron-Nano Scale Carbon Particulates Based on Time-resolved
Laser-induced Incandescence
CHEN Linghong1, ZUO Lei1, JIANG Yiqi1, Jiao Li2, GREHAN Gérard3, CEN Kefa1
1
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
Hangzhou Environmental Monitoring Center, Hangzhou 310007, China
3
LESP, UMR 6614/CORIA, CNRS/Universit´eet INSA de ROUEN, 76800 Saint Etienne du Rouvray, France
2
ABSTRACT
Micron-nano scale carbon particulates resulting from the incomplete combustion of fossil fuel are highly related
to the combustion efficiency, atmospheric environment and human health, etc. Time-resolved laser-induced
incandescence (LII) was proved to be a potential useful tool to measure carbon particulate concentration and
primary particulate size in combustion, particulate synthesis, and environmental applications. LII involves heating
particulates with a high power pulsed laser and measuring the radiative emission. Using LII technique for
quantitative determination of particulate concentration and size requires a detail understanding of the heat- and
mass-transfer mechanisms in the process. Two mass- and energy-balance models were established to simulate
different sizes of laser-heated carbon particulates during the laser-heated and subsequent cooling process. A
uniform internal temperature was assumed in model N while internal temperature gradient was considered in
model M. The simulated LII signal profiles using two models were compared for different particulates sizes. The
results showed that models N and M could fit together when the particulate diameter was in the range between 1.0
and 2.5μm. The magnitude of LII curve using model M was significantly lower than using model N when the
particulate diameter was less than 0.1μm. This could be explained that the tradition heat transfer mechanism was
not fit in this size region. The results showed that the internal temperature gradient could not be neglected when
the particulate diameter was larger than 5.0μm. In addition, experiments of pointwise (0D) and imaging (2D) LII
applications on a methane flame were set up. The measured temporally LII signals were compared to theoretical
calculations. The results indicated that the carbon particulate size was of 1-2nm in flame. Simultaneously
extinction measurement showed that the carbon particulate concentration was lower than 3ppm along the flame
height.
KEYWORDS
Micron-nano scale; Carbon particulate; Laser-induced incandescence; Concentration; Particulate-size
NOMENCLATURE
D particulate diameter, cm;
1
D0
Dm
r
t
M
T0
T
T*
Qabs
q(t)
F
ka
l
G
ΔHv
Ws
Wv
P
ρs
Cs
ks
αs
R
σ
c1
c2
λ
λem
initial particulate diameter, cm;
mean particulate diameter, cm;
radial coordinate, cm;
time, s;
particulate mass, g;
initial flame temperature, K;
particulate temperature, K;
temperature in K at which carbon vapor pressure p = p* (p = 1 atm T* = 3915K);
absorption efficiency factor;
laser temporal power density, W/cm2;
laser fluence, J/cm2;
thermal conductive of air, = 5.83×10-5(T/273)0.82 W/(cm·K);
mean free path, =2.355×10-8·T cm for air at 1 atm;
geometry-dependent heat transfer factor, = 53.33;
heat of sublimation of carbon, = 7.68×105 J/mol;
molecular weight of solid carbon, = 12 g/mol;
molecular weight of vapor taken at 36 g/mol;
vapor pressure of carbon;
solid carbon density, = 2.26 g/cm3;
specific heat of carbon, = 2.41 J/(g·K);
thermal conductivity of graphitic carbon, = 1.5 W(cm·K);
thermal diffusivity of graphitic carbon, = 0.275 cm2/s;
gas constant, = 8.31 J/(K·mol)
Stefan-Boltzman constant, =5.67×10-12 W/(cm2·K4);
Planck First radiation constant, = 3.7419×10-16 W·m2;
Planck Second radiation constant, = 1.4388×10-2 m·K;
wavelength of incident light, μm;
emission wavelength, nm;
1. INTRDUCTION
Black carbon is one of the most important pollutants emitting from a variety of combustion processes and is
found throughout the Earth system. Black carbon has a unique and important role in the Earth’s climate system
because it absorbs solar radiation, influences cloud processes, and alters the melting of snow and ice cover [1]. In
addition, carbon particulates will carry plenty of toxicants (such as heavy metal and organic matter) because of its
high absorption. These particulates with diameters from 10nm to 100nm can be breathed into alveolus, which can
harm breath system of human [2,3]. Besides, carbon particulates from the incomplete combustion will reduce
combustion efficiency significantly [ 4 ]. Thus, developing carbon particulates measurement techniques is
important to the understanding of physical and chemical mechanisms of carbon formation and the validation of
carbon formation models, which ultimately helps to increase combustion efficiency and decrease pollutant
emission.
Laser-induced incandescence (LII) has proven to be a useful tool for carbon particulate concentration and
primary particulate size measurements in combustion, particulate synthesis, and environmental applications. LII
involves heating particulates with a high power pulsed laser and measuring the radiative emission. The magnitude
2
of the LII signal depends on the particulate volume fraction, and the decay rate of the LII signal is mainly
governed by the specific surface of the particulates, which in turn depends on primary size [5]. Using such
measurements for quantitative determinations of particulate volume fraction and size requires a detailed
understanding of experimental parameters and physical mechanisms that control the LII signal.
One approach to developing such a description of LII signals generation involves modeling the processes that
control signal production. A first mathematical model of the laser-induced incandescence phenomenon, based on
the energy- and mass-balance equations to predict temporal response of the particulate to pulsed laser heating, has
been developed by Eckbreth and Melton [6,7]. Subsequently considerable effort has been devoted to developing
models capable of predicting LII signals over a range of fluences [8]. Some models have been optimized to fit LII
signal decay curves for inferring particulate size distributions [9,10] and aggregate size distributions [11], whereas
others have been used primarily to understand the influence of factors such as experimental parameters [12,13,14],
particulate characteristics [15,16], and particulate phase changes during particulate heating and cooling [17]. As
the evolution of LII emission is often a combination of the size-dependent LII decay of the different particulate
size classes, it is critical to detection small particulates in the presence of large ones. Bladh and Bengtsson [18]
investigated the impact of Gaussian and lognormal size distributions of different width on temporal LII-signal
behavior. The result is a significant bias towards larger particulate sizes because of the higher influence of the
larger particulates on the LII signal. Allouis et al. [19] extended Melton model for different kinds of large
carbonaceous particulate assuming a temperature profile inside. The theoretical calculations showed a good
agreement compared to the temporally resolved LII emissions in a diesel oil spray flames, but the accuracy of the
model needed to be drastically improved [20].
Our motivation in this paper is to demonstrate an appropriate model applying to size measurement of
micron-nano scale carbon particulates. Firstly, we will establish the differential equations for the spatial- and
time-dependence of the temperature and diameter of a laser-heated spherical particulate with different classes of
particulate sizes. Then a detailed analysis of the particulate-size that determines the uncertainty of LII technique
will be present. Finally, the carbon particulate concentration and size distribution in a methane flame will be given
through the fitting of theoretical calculations of the model.
2. METHODOLOGY
2.1 Model description
For a carbon particulate, the mass balance can be written as follows [6]:
 s
2W
dD
 P ( v )1 2
dt
RT
(1)
where P is the vapor pressure of carbon, which is given by the Clapeyron equation:
P  P* exp[
H v (T  T * )
]
RTT *
(2)
3
However, the form of energy balance equation between a spherical particulate and its surroundings varies from
different classes of particulate sizes. This depends on the form of heat flux due to Kundsen number [21]:
continuum region (Kn < 0.1), transition region (0.1 < Kn < 2.0), slip region (2.0 < Kn < 10), free molecular region
(Kn > 10). The Kundsen number represents the ratio between mean free path of heat-transfer medium and
particulate diameter. Basing on different classes of particulate diameter, heat flux between the particulate and
surrounds and inside the particulate varies and ultimately affects the temperature profile appears inside the
particulate. The nano-scale carbon particulates may be assured to have a uniform internal temperature since the
laser, which is assumed to have a triangular pulse of 10ns FWHM (Full Width Half Maximum), is much longer
than the characteristic time for internal gradient dissipation of 10-3ns for a diameter D = 10nm [7]. In contrast, a
particulate with a diameter of 10μm has a characteristic diffusion time, tD, of about 24ns. This time rises with the
second power of the particulate diameter, as predicted by the boundary layer approximation [22]. Therefore, a
spatial- and time-dependent temperature profiles appears inside the micron-scale particulates. Here we gave the
description of two different models due the different shapes of temperature profiles inside the particulates.
(1)Model N
The particulates are assumed to have a uniform internal temperature in the process of heating by laser
absorption and cooling by conduction to surrounding atmosphere, sublimation of carbon clusters, and radiative
emission. The energy balance is expressed as a function of time, temperature, mass, and primary particulate
diameter:
2k a
1
dT Qabs q(t ) PH v Wv 1/2
 s Cs D


(
) 
(T  T0 )   (T 4  T04 )
6
dt
4
Ws 2 RT
D  Gl
(3)
The terms on the right of the equation are the laser energy absorption per second, the energy expended in
sublimation of the carbon, the rate of heat transfer to the surrounding atmosphere (taken to be air at temperature
T0) and the rate of energy loss by black-body radiation respectively. The thermal conductivity must be corrected
considering the particulates are smaller compared to the mean free path.
(2)Model M
An internal temperature gradient is considered inside the particulate in this model. The energy balance is given
by the heat diffusion equation in spherical coordinates:
T  s  2 T

(r
)
t r 2 r
r
The initial condition is
at
t = 0,
D = D0
The boundary conditions are
r  D/2
ks
(4)
and
T = T0∀ r
T Qabs q(t ) PH v Wv 1/2 2ka


(
) 
(T  T0 )   (T 4  T04 )t
r
4
Ws 2 RT
D
4
(5)
r 0
T
 0t
r
2.2 Absorption efficiency factor
Equation (3) and (5) involved the calculation of Qabs, which represents the absorption efficiency factor and is a
function of the complex refractive index (m = n - ik). Chang and Charalmpopoulos gave the values of n and k of
carbon particulate [23]:
n  1.811  0.1263ln   0.027 ln 2   0.0417 ln 3 
(6)
k  0.5821  0.1213ln   0.2309 ln 2   0.01ln 3 
(7)
Given the complex indices of refraction for the medium and the particulate, Qabs can be computed from the Mie
equations. A FORTRAN program was used to compute Qabs. Instead of using the Rayleigh approximation to
calculate the absorption efficiency factor as in the previous works [8], we adopt the full Lorenz-Mie theory when
the particulate size is beyond the Rayleigh size limit.
2.3 Prediction of LII signals
The radiation emitted by one particulate follows the Planck law and the LII signal can be expressed as follows
at any time during the laser pulse heating and cooling process [24]:

c  ( ) D 2 
c2
RCAL (em , T )  1 em 5
)  1
exp(
4em
emT


1
(8)
During these processes the LII signal rises very fast, becomes limited by the energy going into sublimation and
then falls with a time constant appropriate thermal conduction to the medium. The magnitude of the signal
depends on the particulate volume fraction and the signal decay rate depends on the primary particulate size.
3. EXPEIMENTAL PROCEDURE
Experiments on a methane flame of pointwise (0D) and imaging (2D) LII applications have been set up to
illustrate the accuracy of the present models. Figure 1 shows schematics of the apparatus arrangements. A Nd:
YAG laser generating 10ns pulses at 1064nm with a repetition rate of 10Hz is used for LII. A 1064nm laser is
used rather than at 532nm because: (i) At longer excitation wavelengths, the generation of electronically excited
C2 fragments is less pronounced [25], (ii) laser-induced fluorescence (LIF) of polycyclic aromatic hydrocarbons
(PAH) is induced with excitation in the visible and the UV [26], which is not easily separated with detection
filters from LII signal. The experiments proceed under an incident laser pulse fluence of 0.1J/cm2.
Figure 1a presents the two-dimensional measurement of the LII from the carbon particulates in a methane flame.
To form the laser sheet, two lenses, cylindrical (f = -75mm) and spherical (f = +300m), are installed at the laser
output. The laser sheet is 30mm in width and 1mm in thickness. An ICCD camera is located perpendicularly to
5
the laser sheet, allowing the best view of 2D LII images. The camera is synchronized with the laser pulse through
the camera control unit. The LII signal has a long temporal decrease and therefore a 30ns delay after laser pulse
permits to eliminate light scattered by carbon particulates [26].A 100ns gate width is chosen to have enough LII
signal [27]. Furthermore, LII signal is detected at 600nm to achieve a good signal-to-noise ratio and avoid signal
disturbances [5].
To calibrate the LII signal, an extinction measurement through the flame is made. A semiconductor laser at
532nm coupled with a photodiode with a 532nm filter is applied to the extinction measurement. According to the
Beer-Lambert law, the carbon volume fraction is calculated by the ratio between the initial intensity I0 and
decayed intensity I transmitted through the flame [28]. Given by the LII distribution at the detected height, the
temporal ratio on the optical depth provides the absolute carbon volume fraction along the width in flame.
Figure 1b shows the simultaneous pointwise measurement of the LII and light absorption along the flame height.
A homogeneous laser light sheet (3mm×3mm) is formed by an aperture. The signal is collected by a PMT with a
narrow pass bond filter at 600nm and recorded on an oscilloscope.
Figure 1 Experimental apparatus for carbon particulate measurement in a methane flame with LII
4. SIMULATION RESULTS AND DISCUSSION
4.1 Calculation of Qabs
Figure 2 demonstrates the effects of particulate size on the particulates’ emissivity based on theoretical
calculations. With increasing particulate diameter the absorption efficiency factor increases, then decreases slowly
and finally approaches a constant when the diameter goes forward beyond 3μm. It is as if that Qabs becomes more
size-dependent effect for smaller particulates (D < 0.5μm) and less size-dependent effect for larger particulates (D
> 1μm). Compared with curves of different wavelengths of incident light, the effect of wavelength seems to be
less pronounced when the wavelength is chosen at the infrared range.
6
FIGURE 2
Calculated absorption efficiency factor Qabs for spheres carbon particulates with primary diameter
of 0-5μm. The wavelength of incident light was in a wide regime from the ultraviolet range to the infrared range
(λ = 355, 532 and 1064nm). The refractive index was assumed to be independent of wavelength.
4.2 Comparisons between Model N and M
In order to elaborate which model would be suitable to use in an accurate classes of particulates, comparisons
between Model N and M were performed under the same laser temporal profile, wavelength and fluences. It is a
well-known fact that LII signal first increases with the laser fluence and then reaches a plateau. With increasing
laser fluence carbon sublimation during the laser pulse increases and evaporative cooling and mass loss cause the
maximum LII signal to remain constant [12]. In our case, we will consider laser intensities causing excessive
sublimation, i.e. laser fluence F = 3.0J/cm2 would be sufficient for different classes of particulates to approach
carbon sublimation temperature.
7
FIGURE 3
Comparisons of LII signal emit from one carbon particulate between model N and M with different
initial diameters. Calculations were perform for a fluence of 3.0J/cm2, at λ = 1064nm and FWHM = 10ns; T0 =
2000K, λem = 600nm.
To better understand the differences between model N and M, it is useful to compare the results calculated from
the two model types having the same particulate size. Combined effects on the LII signal profiles of the different
particulates are represented in Figure 3, it seems that signal curves of the two model types could fit together in a
restrict condition, i.e. D = 1.0-2.5μm demonstrated in Figure 3b and Figure 3c. In Figure 3a, the signal of Model
N first rises, approaches the peak and then falls with a time constant appropriate thermal conduction to the
medium, compared to lower curve of Model M. The reason why the signal calculated in Model M are weird is that
the surface heat flux of particulate in Model M is calculated by Fourier’s law, which cannot be applied in
nano-scale heat transfer. The thermal conductivity of carbon of nano-scale is significantly lower than the values in
the conventional scale [21], which results in rapid rise and decay rate of LII signals emit from nano-scale carbon
particulates. In contrast, the signal data from Model N is much lower than Model M in Figure 3d. This is because
particulate in Model N is assumed to have a uniform temperature since the laser pulse, but in fact the internal
temperature gradient could not be neglected of particulate of micron-scale. As a consequence Model N calculates
the mean temperature of a heated-particulate, which is definitely lower than the surface temperature. These
behaviors affect directly the time evolution of the LII signal, which strongly depends on particulate surface
temperature.
In general, Model N suits the calculation of nano-scale particulates while Model M is appropriate to use in
micron-scale particulates. Both Model types are adapted in the calculation of particulate size of 1.0-2.5μm. As
fine (D < 2.5μm) particulates is of special interest of our study, Model N is capable to use in the simulation on the
measurement of carbon particulates of PM2.5 with LII technology.
4.3 Effect of carbon particulate size on LII signals
As we are seizing a way to measure carbon particulate size with LII technique, it is critical to discuss the effect
of particulate size on LII signals. Figure 4 shows the dependence of the temperature and normalized LII signal on
time of different particulate sizes (D = 0.1, 1.0 and 2.5μm). Figure 4a indicates that small carbon particulates
approaches higher temperature-addition rate than large ones. With increasing particulate size of nano-scale the
final temperature increases, and then drops down tardily when particulate size moves forward in the range of
8
micron-scale. This is because when the particulate is sufficiently large, the energy is better distributed and cooling
goes on rapidly because of the higher exchange surface, which limits the particulate temperature goes higher. As
shown in Figure 4b, it is as if LII signal decay rates keep the same at the beginning and then vary from different
particulate sizes. When particulate temperature is sufficient to enable the incandescence phenomenon which
occurs around 4000K, sublimation of carbon particulate contributes significantly to signal decay rate. When
temperature drops down under 4000K, signal decay rate depends primarily on conductive cooling rate. Therefore,
the larger the particulates, the lower their signal decay rates.
FIGURE 4
Calculated values of (a) the temperature and (b) the normalized LII signal using Model N on
dependence of time for different particulate sizes. Of the normalized LII signal time t=0 was fixed to correspond
to the peak position of the signal for each size of particulate. Calculations were performed for a fluence of
3.0J/cm2, at λ = 1064nm and FWHM = 10ns; T0 = 2000K, λem = 600nm.
5. EXPERIMENTAL MEASUREMENTS
5.1 2D LII signals
Figure 5 shows a relationship between the instantaneous photograph of a methane flame and its corresponding
two-dimensional LII image. Figure 5a reveals two different structures of the flame in height, i.e. a stable triangle
shape of laminar flame below 80mm compared with relative streaky turbulent flame above 80mm, which is in
coincidence with the image of ICCD, present in Figure 5b. As it is well known that the LII signal intensity is
proportional to the carbon volume fraction [7], the intensity of LII signals recorded in the 2D ICCD image
indicates the spatial distribution of carbon particulates. A very high LII intensity around the outer edge of the
flame implies a very high carbon concentration. In contrast with low intensity within the flame, it seems that
carbon particulates generate at the burning region. The luminosity is highlighted around the surface of the
turbulent flame, which suggests amount of carbon particulates aggregating at the top of flame in the consequence
of flame movement and propagation.
9
FIGURE 5
Direct photograph (exposure time: 1/50s) of a methane flame (a) and its corresponding
two-dimensional distribution of LII signals (b). The flame was generated by a gaseous burner with methane at
1L/min. The instantaneous photograph of the methane flame shows its structure is 130mm in height and 15mm in
width.
5.2 Particulate concentration measurement
The 2D distribution of LII signals from the ICCD image at different heights is calibrated by the simultaneous
measurement of optical extinction, as shown in Figure 6. It seems the absolute carbon particulate concentration
grows with increasing measurement height in the flame, limiting in 3ppm. The trend of the particulate distribution
varies from different heights, as a typical bimodal distribution moving towards a unimodal distribution. However
measurements from light absorption may cause the underestimation of the carbon volume fraction. This is because
in optical extinction measurement the absorption of a carbon aggregate is lower than the sum of the total
absorptions of its constituent primary particulates, and thus leads to a result of lower carbon volume fraction.
10
Carbon volume fraction (ppm)
4
Flame height (mm)
60
90
120
3
2
1
0
-10
-5
0
5
10
Radial distance (mm)
Figure 6 Carbon volume fraction profiles calibrated by the simultaneous measurement of light absorption in the
radial direction at different heights.
5.3 Particulate-size measurement
For point measurements the entire LII decay curve can be used to obtain primary particulate-size information
from fits of numerical simulation to the experimental decay curve. Figure 7 demonstrates experimental LII signal
with the best fitting simulation curve in flame height. A mean particulate diameter represents the size distribution,
which cannot be evaluated since normalized LII signals can biased towards particulate sizes. It seems the mean
carbon particulate size remains at a region of 1-2nm in the flame and gets larger in height. The results accord with
the conclusion reported in the literature that during the early stage of carbon formation carbon particulates are
very big molecules with diameters less than 2nm [29].
11
Figure 7 Experimental LII signal and its respective fitting simulation curve in flame height. The LII signals were
detected at 600nm for a fluence of 0.1J/cm2.
6. CONCLUDION
Two mass- and energy-balance models were established to simulate different sizes of laser-heated carbon
particulates during the laser-heated and subsequent cooling process. A uniform internal temperature was assumed
in model N while internal temperature gradient was considered in model M. The simulated LII signal profiles
using two models were compared for different particulates sizes. The results showed that models N and M could
fit together when the particulate diameter was in the range between 1.0 and 2.5μm. The magnitude of LII curve
using model M was significantly lower than using model N when the particulate diameter was less than 0.1μm.
This could be explained that the tradition heat transfer mechanism was not fit in this size region. The results
showed that the internal temperature gradient could not be neglected when the particulate diameter was larger than
5.0μm. In addition, experiments of pointwise (0D) and imaging (2D) LII applications on a methane flame were set
up. The measured temporally LII signals were compared to theoretical calculations. The results indicated that the
carbon particulate size was of 1-2nm in flame. Simultaneously extinction measurement showed that the carbon
particulate concentration was lower than 3ppm along the flame height.
12
ACKNOWLEDGEMENT
This work is supported by the National Basic Research Program of China (grants 2009CB219802), the National
Science Foundation (51206144), the Natural Science Foundation of Zhejiang province (LY12E06003), the
Program of Introducing Talents of Discipline to University (B08026).
REFERENCES
[1] Bond T C, Doherty S J, Fahey D W, et al. Bounding the role of black carbon in the climate system: a
scientific assessment[J]. Journal of Geophysical Research: Atmospheres, 2013.
[2] Dumka U C, Moorthy K K, Kumar R, et al. Characteristics of aerosol black carbon mass concentration over a
high altitude location in the Central Himalayas from multi-year measurements[J]. Atmospheric Research,
2010, 96(4): 510-521.
[3] Lou L, Luo L, Wang W, et al. Impact of black carbon originated from fly ash and soot on the toxicity of
pentachlorophenol in sediment[J]. Journal of hazardous materials, 2011, 190(1): 474-479.
[4] Al-Omari S A B, Kawajiri K, Yonesawa T. Soot processes in a methane-fueled furnace and their impact on
radiation heat transfer to furnace walls[J]. International journal of heat and mass transfer, 2001, 44(13):
2567-2581.
[5] Schulz C, Kock B F, Hofmann M, et al. Laser-induced incandescence: recent trends and current questions[J].
Applied Physics B, 2006, 83(3): 333-354.
[6] Eckbreth A C. Effects of laser‐modulated particulate incandescence on Raman scattering diagnostics[J].
Journal of Applied Physics, 1977, 48(11): 4473-4479.
[7] Melton L A. Soot diagnostics based on laser heating[J]. Appl. Opt, 1984, 23(12): 2201-2208.
[8] Michelsen H A, Liu F, Kock B F, et al. Modeling laser-induced incandescence of soot: a summary and
comparison of LII models[J]. Applied physics B, 2007, 87(3): 503-521.
[9] Lehre T, Jungfleisch B, Suntz R, et al. Size distributions of nanoscaled particulates and gas temperatures
from time-resolved laser-induced-incandescence measurements[J]. Applied optics, 2003, 42(12): 2021-2030.
[10] Krüger V, Wahl C, Hadef R, et al. Comparison of laser-induced incandescence method with scanning
mobility particulate sizer technique: the influence of probe sampling and laser heating on soot particulate size
distribution[J]. Measurement Science and Technology, 2005, 16(7): 1477.
[11] Liu F, Smallwood G J, Snelling D R. Effects of primary particulate diameter and aggregate size distribution
on the temperature of soot particulates heated by pulsed lasers[J]. Journal of Quantitative Spectroscopy and
Radiative Transfer, 2005, 93(1): 301-312.
[12] Michelsen H A, Witze P O, Kayes D, et al. Time-resolved laser-induced incandescence of soot: the influence
of experimental factors and microphysical mechanisms[J]. Applied optics, 2003, 42(27): 5577-5590.
[13] Charwath M, Suntz R, Bockhorn H. Influence of the temporal response of the detection system on
time-resolved laser-induced incandescence signal evolutions[J]. Applied Physics B, 2006, 83(3): 435-442.
[14] Wang F, Yan J, Ma Z Y, et al. Simulation on soot concentration measurement with laser induced
incandescence[C]. Zhongguo Dianji Gongcheng Xuebao (Proceedings of the Chinese Society of Electrical
Engineering). 2006, 26(7): 6-11
[15] Therssen E, Bouvier Y, Schoemaecker-Moreau C, et al. Determination of the ratio of soot refractive index
function E (m) at the two wavelengths 532 and 1064 nm by laser induced incandescence[J]. Applied Physics
B, 2007, 89(2-3): 417-427.
[16] Liu F, Smallwood G J. The effect of particulate aggregation on the absorption and emission properties of
mono-and polydisperse soot aggregates[J]. Applied Physics B, 2011, 104(2): 343-355.
13
[17] Michelsen H A. Understanding and predicting the temporal response of laser-induced incandescence from
carbonaceous particulates[J]. The Journal of chemical physics, 2003, 118: 7012.
[18] Bladh H, Bengtsson P E. Characteristics of laser-induced incandescence from soot in studies of a
time-dependent heat-and mass-transfer model[J]. Applied Physics B, 2004, 78(2): 241-248.
[19] Allouis C, Rosano F, Beretta F, et al. A possible radiative model for micronic carbonaceous particulate sizing
based on time-resolved laser-induced incandescence[J]. Measurement Science and Technology, 2002, 13(3):
401-410.
[20] Allouis C, Beretta F, D’Alessio A. Sizing soot and micronic carbonaceous particulate in spray flames based
on time resolved LII[J]. Experimental thermal and fluid science, 2003, 27(4): 455-463.
[21] Liu J. Micro/nano scale heat transfer[M]. Science Press, 2001: 179.
[22] Bird R B, Stewart W E, Lightfoot E N. Transport phenomena[M]. Wiley, 2006: 357.
[23] Chang H, Charalampopoulos T T. Determination of the wavelength dependence of refractive indices of flame
soot[J]. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1990,
430(1880): 577-591.
[24] Snelling D R, Smallwood G J, Liu F, et al. A calibration-independent laser-induced incandescence technique
for soot measurement by detecting absolute light intensity[J]. Applied optics, 2005, 44(31): 6773-6785.
[25] Vander Wal R L, Weiland K J. Laser-induced incandescence: development and characterization towards a
measurement of soot-volume fraction[J]. Applied Physics B, 1994, 59(4): 445-452.
[26] Moreau C S, Therssen E, Mercier X, et al. Two-color laser-induced incandescence and cavity ring-down
spectroscopy for sensitive and quantitative imaging of soot and PAHs in flames[J]. Applied Physics B, 2004,
78(3-4): 485-492.
[27] Hebert D, Coppalle A, Talbaut M. 2D soot concentration and burning rate of a vertical PMMA slab using
Laser-Induced Incandescence[J]. Proceedings of the Combustion Institute, 34(2013): 2575-2582.
[28] Hofmann M, Bessler W G, Schulz C, et al. Laser-induced incandescence for soot diagnostics at high
pressures[J]. Applied optics, 2003, 42(12): 2052-2062.
[29] Haynes B S, Wagner H G. Soot formation[J]. Progress in Energy and Combustion Science, 1981, 7(4):
229-273.
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