Scattering of Phonons by Nano and Micro Particles

Scattering theory for the scattering of phonons by particulate scatterers is developed in this paper. Recently the author introduced the generalized equation of phonon radiative transport (GEPRT) in particulate media which included a phase function to account for the anisotropic scattering of phonons by particulate scatterer. Solution of the GEPRT showed that scattering cross section is different than the thermal transport cross section. In this paper formulations for the scattering and transport cross section for horizontally shear (SH) wave phonon or transverse wave phonon without mode conversion is developed. The development of the theory of scattering and the transport cross section is exactly analogous to the Mie scattering theory for photon transport in particulate media. Results show that transport cross section is very different than the scattering cross section. It is also shown that for SH (horizontally shear) phonons the scattering and transport cross sections are proportional to ω8 rather than the well accepted value of ω4 in the Rayleigh regime where ω is the frequency of the SH phonons. The theory of phonon scattering developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems such as nano composites, nano-micro particle laden systems and etc.