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Light propagation model of titanium dioxide suspensions in water using the radiative transfer equation

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Title: Light propagation model of titanium dioxide suspensions in water using the radiative transfer equation
Authors: Fujii, Hiroyuki Browse this author →KAKEN DB
Yamada, Yukio Browse this author
Hoshi, Yoko Browse this author
Okawa, Shinpei Browse this author
Kobayashi, Kazumichi Browse this author →KAKEN DB
Watanabe, Masao Browse this author
Keywords: Light propagation in photocatalytic systems
Radiative transfer equation
Renormalization approach of the forward-directed phase function
Issue Date: Apr-2018
Publisher: Springer
Journal Title: Reaction kinetics, mechanisms and catalysis
Volume: 123
Issue: 2
Start Page: 439
End Page: 453
Publisher DOI: 10.1007/s11144-017-1328-2
Abstract: Constructions of numerical schemes for solving the radiative transfer equation (RTE) are crucial to evaluate light propagation inside photocatalytic systems. We develop accurate and efficient schemes of the three-dimensional and time-dependent RTE for numerical phantoms modeling aqueous titanium dioxide suspensions, in which the anisotropy of the forward-directed scattering varies and the strength of absorption is comparable to that of scattering. To improve the accuracy and efficiency of the numerical solutions, the forward-directed phase function is renormalized in the zeroth or first order with a small number of discrete angular directions. Then, we investigate the influences of the forward-directed scattering on the numerical solutions by comparing with the analytical solutions. The investigation shows that with the anisotropy factor less than approximately 0.7 corresponding to the moderate forward-directed scattering, the numerical solutions of the RTE using the both of the zeroth and first order renormalization approaches are accurate due to the reductions of the numerical errors of the phase function. With the anisotropy factor more than approximately 0.7 corresponding to the highly forward-directed scattering, the first order renormalization approach still provides the accurate results, while the zeroth order approach does not due to the large errors of the phase function. These results suggest that the developed scheme using the first order renormalization can provide accurate and efficient calculations of light propagation in photocatalytic systems.
Rights: This is a post-peer-review, pre-copyedit version of an article published in Reaction Kinetics, Mechanisms and Catalysis. The final authenticated version is available online at:
Type: article (author version)
Appears in Collections:工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 藤井 宏之

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