Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence

Liu, Fengshan; Daun, Kyle J.; Snelling, David R.; Smallwood, Gregory J.

doi:10.1007/s00340-006-2194-1

Cited by 137 publications

(102 citation statements)

References 58 publications

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“…Here, l MFP is the mean free path of air molecules and was fixed at 65.1 nm (300 K and 1 atm). The harmonic interpolation method (Sherman 1963;Liu et al 2006) is adopted to calculate heat and mass flux in the transition regime. According to the interpolation method, flux q v (i. e., mass, heat, and momentum) in the transition regime can be expressed as…”

Section: Model Descriptionmentioning

confidence: 99%

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Effects of Mixing State on Black Carbon Measurements by Laser-Induced Incandescence

Moteki

Kondo

2007

Aerosol Science and Technology

291

300

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Laboratory experiments and theoretical calculations were made to characterize the performance of a Single Particle Soot Photometer (SP2) manufactured by Droplet Measurement Technologies (DMT), which was designed to measure the mass and the mixing state of individual black carbon (BC) or elemental carbon (EC) particles, based on the laser-induced incandescence (LII) technique. In this study, graphite was used as a surrogate of EC. Graphite particles with mass equivalent diameters of 110-200 nm were layered with organic liquids (glycerol and oleic acid) to produce coated graphite with diameters up to 650-800 nm. These were sampled by the SP2 to measure the waveforms (i.e., time development) of the LII and scattering signals. The peak temperature and the peak LII signal of graphite particles were independent of the coating thickness or the coating material to within experimental errors. These results indicate that the mass of EC can be measured by using peak LII signal without interference by the coating conditions. It was also shown that the difference between the times of the scattering and LII peaks can be used as an indicator of coating on EC with thicknesses larger than about 100-200 nm. LII and scattering waveforms were calculated using a newly developed theoretical model that takes into account the physical processes controlling the temperature and evaporation rate of the coated graphite particle in the laser beam. The calculations reproduced the general features of observed waveforms of LII and scattering signals, providing a firm theoretical basis for the interpretation of the SP2 data.

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Section: Model Descriptionmentioning

confidence: 99%

“…Details of the derivation of Equation (15) from (14) are described by Liu et al (2006). G is the geometry-dependent transfer factor,…”

Section: Model Descriptionmentioning

confidence: 99%

Effects of Mixing State on Black Carbon Measurements by Laser-Induced Incandescence

Moteki

Kondo

2007

Aerosol Science and Technology

291

300

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“…The model used to describe the heat and mass transfer process of laser-heated soot particles is based on that proposed by Melton (1984) and further developed by Snelling et al (2000a) and Liu et al (2006a). According to the RayleighDebye-Gans theory for fractal aggregates (RDG-FA) (Koylu and Faeth, 1992), the absorption and radiation of aggregates can be expressed as the sum of the same processes for individual primary particles.…”

Section: Signal Evolutionmentioning

confidence: 99%

“…The terms on the right side are the rate of laser energy absorption by the aggregate, the soot sublimation, the rate of heat loss by conduction from the aggregate to the surrounding gas, and thermal radiation, respectively. The parameter N p represents the number of primary soot particles within the aggregate, d p is the primary soot particle diameter, ρ s and c s denote the soot particle density and specific heat, which are set to the values used by Liu et al (2006a), and T p and t are the laser-heated soot particle temperature and time, respectively. The variable E(m) in the first term on the right-hand side represents the refractive index function, and λ and q(t) are the excitation wavelength and pulsed laser temporal intensity, respectively.…”

Section: Signal Evolutionmentioning

confidence: 99%

“…This model was found to be the most accurate to define the heat conduction process of spherical nanoparticles in a wide range of the Knudsen (Kn) number (Liu et al, 2006a). It is a two-layer model where the space surrounding the particle is divided into inner and outer regions separated by a limiting sphere, as detailed by Liu et al (2006a).…”

Section: Signal Evolutionmentioning

confidence: 99%

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Particle Size Distribution of Soot from a Laminar/Diffusion Flame

Chen

Zhou

et al. 2017

Aerosol Air Qual. Res.

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A practical method is proposed to determine the inflame soot particle size distribution via an explicit solution derived from time-resolved laser-induced incandescence (TiRe-LII). Three appropriate time intervals are selected from the TiRe-LII decay signal. The equivalent mean sizes as well as relative ratios of number densities for three classes of monodisperse particles are determined with the mono-exponential fit to each interval, which allows an explicit solution for the particle size distribution. Simulations show that inversed log-normal distributions from the explicit solution are coincident with the input parameters in terms of trend, and there exist critical time intervals where inversed results are most insensitive to the variation of interval length. The error of inversion is critically dependent on the geometric standard deviation but weakly dependent on the count median particle diameter. Influences of experimental conditions on the inversed error are additionally evaluated. The results show that flame temperature has a significant impact on the error of inversion. Thus, a database of the error as a function of flame temperature at a fixed aggregate size is established. The error database allowed the inversed results from experimental TiRe-LII signals to be readily corrected at various flame locations by interpolation. The corrected inversed log-normal distributions were consistent in trend with those determined from the established nonlinear regression method, and the modeling LII signals reproduced agree with the experimental data. The small deviation of the results potentially stemmed from the statistical noise contained in recorded LII signals.

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Optical Particle Characterization

Onofri¹,

Barbosa²

2012

Laser Metrology in Fluid Mechanics

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Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence

Cited by 137 publications

References 58 publications

Effects of Mixing State on Black Carbon Measurements by Laser-Induced Incandescence

Effects of Mixing State on Black Carbon Measurements by Laser-Induced Incandescence

Particle Size Distribution of Soot from a Laminar/Diffusion Flame

Optical Particle Characterization

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