Revisiting independent versus dependent scattering regimes in suspensions or aggregates of spherical particles

Galy, Tiphaine; Huang, Di; Pilon, Laurent

doi:10.1016/j.jqsrt.2020.106924

Cited by 32 publications

(22 citation statements)

References 36 publications

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“…Radiation transfer through scattering and absorbing colloidal suspensions has often been simulated by solving the radiative transfer equation (RTE) to predict the local radiation intensity field. − To do so, the absorption and scattering coefficients of the suspensions were predicted as the sum of the contributions from all constitutive particles . This approach is based on the so-called “independent scattering” approximation and holds when the particles are sufficiently dilute and distant from one another . If the particles are spherical, the Lorenz-Mie theory can be used to predict the absorption and scattering cross sections of individual particles and their scattering phase function .…”

Section: Introductionmentioning

confidence: 99%

“…If the particles are spherical, the Lorenz-Mie theory can be used to predict the absorption and scattering cross sections of individual particles and their scattering phase function . Independent scattering prevails if (i) the suspension is dilute so that particles are separated by a distance larger than several wavelengths depending on their size, (ii) the observation point resides sufficiently far from any particle; (iii) the number of particles in the suspension is very large; (iv) all particles move randomly and independently of each other in the medium; (v) the physical state of each particle is independent of its position and of the states and positions of all the other particles; and (vi) the particle ensemble is fully ergodic, that is, its average characteristics can be deducted from sufficiently large samples randomly collected from the system . For example, Mishchenko et al observed experimentally that the independent scattering assumption was valid for randomly dispersed spherical latex particles, 700 nm in diameter and suspended in water for particle volume fraction smaller than 2% at wavelengths 595 and 696 nm.…”

Section: Introductionmentioning

confidence: 99%

“…As the particle concentration in the suspension increases, dependent scattering may prevail depending on the particle size parameter x s and some measure of the particle proximity . Tien and Drolen reviewed the different analytical models developed prior to 1987 to account for dependent scattering in packed beds and fluidized beds. − Dependent scattering was accounted for by expressing the average scattering efficiency factor Q sca D of a single particle in the form Q sca D ( x s , m , f v , c /λ) = F ( f v , c /λ) Q sca M ( x s , m ), where F ( f v , c /λ) is a form factor depending on the volume fraction f v and the ratio c /λ of the clearing distance c between adjacent particles and the wavelength λ.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, an alternative regime map was proposed to identify the dependent vs independent scattering regimes in terms of x s versus /λ so as to reflect these new developments . Moreover, different transition criteria from dependent to independent scattering regimes were obtained for Q sca D and g D of ensembles of nonabsorbing particles …”

Section: Introductionmentioning

confidence: 99%

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Dependent Scattering in Thick and Concentrated Colloidal Suspensions

et al. 2022

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This study demonstrates numerically and experimentally that dependent scattering occurs in colloidal suspensions and can, counterintuitively, cause their transmittance to increase with increasing particle volume fraction. Radiation transfer through colloidal suspensions has been modeled with the radiative transfer equation (RTE) assuming independent scattering. Then, the effective absorption and scattering coefficients of the disperse medium are predicted as the sum of the cross sections of all particles divided by the volume of suspension. However, this approach is not valid when the average interparticle distance is on the same order of magnitude as the wavelength, corresponding to large particle concentrations. The latter situation is referred to as dependent scattering. Rigorously accounting for dependent scattering requires solving Maxwell’s equations, but is limited to relatively thin suspensions. Here, we extend the Radiative Transfer with Reciprocal Transactions (R2T2) method to predict the normal-hemispherical transmittance of thick and concentrated plane-parallel slabs of nonabsorbing nanoparticle suspensions and to rigorously account for dependent scattering effects. The radiation characteristics of a large number of particle ensembles were estimated using the superposition T-matrix method and the RTE was solved using Monte Carlo method combined with strategies for sampling the previously computed radiation characteristics. A wide range of particle size parameter, volume fraction, and optical properties as well as colloidal suspension thickness were investigated. Dependent scattering effects were found to prevail for particle volume fractions as low as 1% depending on the particle size and refractive index. Evidences of dependent scattering were also observed experimentally in the visible normal-hemispherical transmittance of 10 mm thick colloidal suspensions of silica nanoparticles with diameter between 16 and 30 nm and particle volume fraction ranging from 2% to 15%. Moreover, good agreement was found between experimental measurements and numerical predictions from the R2T2 method. By contrast, assuming independent scattering underestimated systematically the normal-hemispherical transmittance, especially for large particle volume fraction. As such, this paper presents, for the first time, experimental validation of the R2T2 method and its ability to account for dependent scattering.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dependent Scattering in Thick and Concentrated Colloidal Suspensions

et al. 2022

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“…In the case of independent scattering, each particle is in the far-field zones of all other particles and scattering by individual particles is incoherent. The hypothesis of independent scattering is usually true when the distance between randomly positioned particles is greater than both the particle size and the wavelength [44][45][46][47][48][49]. It is highly likely that the last of these conditions is not satisfied during the main part of the melting period of copper samples.…”

Section: Light Pressure Of Probe Laser Beam On a Copper Nanoparticlementioning

confidence: 99%

Interaction of a Low-Power Laser Radiation with Nanoparticles Formed over the Copper Melt in Rarefied Argon Atmosphere

Dombrovsky

Mendeleyev

2020

Thermo

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Two effects have been recently observed by the authors for the copper sample melted in a rarefied argon atmosphere. The first of these effects is a strong decrease in the normal reflectance of a copper sample with time just after the beginning of melting. A partially regular crystal structure was also formed on the surface of the solid sample after the experiment. Both effects were explained by generation of a cloud of levitating nanoparticles. Additional experiments reported in the present paper show that the rate of decrease in reflectance increases with pressure of argon atmosphere and the surface pattern on the solid sample after the experiment depends on the probe laser radiation. It is theoretically shown for the first time that the dependent scattering effects in the cloud of copper nanoparticles are responsible for the abnormal decrease in normal reflectance and also for the observed significant role of light pressure in deposition of nanoparticles on the sample surface. The predicted minimum of normal reflectance is in good agreement with the experimental value.

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