Phonon Transport in Anisotropic Scattering Particulate Media

Phonon Transport in Anisotropic Scattering Particulate Media

TitlePhonon Transport in Anisotropic Scattering Particulate Media
Publication TypeConference Paper
Year of Publication2003
AuthorsRavi S Prasher
Conference NameASME 2003 International Mechanical Engineering Congress and Exposition
Date Published11/2003
PublisherAmerican Society of Mechanical Engineers
KeywordsElectromagnetic scattering, particulate matter, Phonons, Radiation scattering
Abstract

Equation of phonon radiative transport (EPRT) is rewritten to include anisotropic scattering by a particulate media by including an acoustic phase function and an in-scattering term which makes EPRT exactly same as equation of radiative transport (ERT). This formulation of EPRT is called generalized EPRT (GEPRT). It is shown that GEPRT reduces to EPRT for isotropic scattering and is totally consistent with phonon transport theory, showing that transport cross section is different from the scattering cross section. GEPRT leads to same formulation for transport cross section as given by phonon transport theory. However GEPRT shows that transport cross section formulations as described by phonon transport theory are only valid for acoustically thick medium. Transport cross section is different for the acoustically thin medium leading to the conclusion that mean free path (m.f.p) is size dependant. Finally calculations are performed for two types of scatterers for acoustic waves without mode conversion: 1) Acoustically hard Rayleigh sphere 2) large sphere in the geometrical scattering regime. Results show that the scattering from these particles is highly anisotropic. It is also shown that for geometrical scattering case isotropic scattering leads to the conclusion of total internal reflection at the particle/medium interface.

DOI10.1115/IMECE2003-41033