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 from 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 from the scattering cross section. The theory of phonon scattering developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems, such as nanocomposites, nano-micro-particle-laden systems, etc.

Issue Section:
Radiative Heat Transfer
Keywords:
Mie scattering, phonons, nanoparticles, thermal conductivity
Topics:
Electromagnetic scattering, Particulate matter, Phonons, Radiation scattering, Scattering (Physics), Scattering theory, Waves
1.
Majumdar
,
A.
,
1993
, “
Microscale Heat Conduction in Dielectric Thin Films
,”
ASME J. Heat Transfer
,
115
, pp.
7
–
16
.
2.
Prasher
,
R. S.
,
2003
, “
Generalized Equation of Phonon Radiative Transport
,”
Appl. Phys. Lett.
,
83
(
1
), pp.
48
–
50
.
3.
Prasher
,
R. S.
,
2003
, “
Phonon Transport in Anisotropic Scattering Particulate Media
,”
ASME J. Heat Transfer
,
125
, pp.
1156
–
1162
.
4.
Callaway
,
J.
,
1959
, “
Model of Lattice Thermal Conductivity at Low Temperatures
,”
Phys. Rev.
,
113
(
4
), pp.
1046
–
1051
.
5.
Ziman, J. M., 1996, Electrons and Phonons, Oxford Press, London.
6.
Sverdrup
,
P. G.
,
Ju
,
Y. S.
, and
Goodson
,
K. E.
,
2001
, “
Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors
”
ASME Journal of Heat Transfer
,
123
, pp.
130
–
137
.
7.
Chen
,
G.
,
1997
, “
Size and Interface Effects on Thermal Conductivity of Supperlattices and Periodic Thin-Film Structures
,”
ASME J. Heat Transfer
,
119
, pp.
220
–
229
.
8.
Song
,
D.
, and
Chen
,
G.
,
2004
, “
Thermal Conductivity of Periodically Microporous Silicon Films
,”
Appl. Phys. Lett.
,
84
, pp.
1883
–
1885
.
9.
Keblisnki
,
P.
,
Phillpot
,
S. R.
,
Choi
,
S. U. S.
, and
Eastman
,
J. A.
,
2002
, “
Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluids)
,”
Int. J. Heat Mass Transfer
,
45
, pp.
855
–
863
.
10.
Dresselhaus, G., Dresselhaus, M. S., Sun, X., Zhang, Z., and Chen, G., 1998, “Modeling Thermoelectric Behavior in Bi Nano-Wires,” Proceedings of 17th International Conference on Thermoelectrics, Nagoya, Japan, pp. 43–46.
11.
Cahill
,
D. G.
,
Ford
,
W. K.
,
Goodson
,
K. E.
,
Mahan
,
G. D.
,
Majumdar
,
A.
,
Maris
,
H. J.
,
Merlin
,
R.
, and
Phillpot
,
S. R.
,
2003
, “
Nanoscale Thermal Transport
,”
J. Appl. Phys.
,
93
(
2
), pp.
793
–
818
.
12.
Bohren, C. F., and Huffman, D. R., 1983, Absorption and Scattering of Light by Small Particles, Wiley, New York.
13.
Van De Hulst, H. C., 1981, Light Scattering by Small Particles, Dover Publication, New York.
14.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw Hill, Inc., New York.
15.
Ying
,
C. F.
, and
Truell
,
R.
,
1956
, “
Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid
,”
J. Appl. Phys.
,
27
(
9
), pp.
1086
–
1097
.
16.
Hinders
,
M. K.
,
1991
, “
Plane-Elastic-Wave Scattering From an Elastic Sphere
,”
Nuovo Cimento B
,
106
(
7
), pp.
799
–
818
.
17.
Morochnik
,
V. S.
,
1983
, “
The Scattering of Elastic S-Waves on a Low-Contrast Spherical Inclusion
,”
Izv. Earth Phys.
,
19
(
6
), pp.
460
–
465
.
18.
Prasher, R. S., 2004, “Thermal Transport Due to Transverse Phonons in Nano and Micro Particulate Media,” J. of Applied Physics (submitted).
19.
Prasher, R. S., 2004, “Thermal Transport Cross Section and Phase Function of Longitudinal Phonons for Scattering by Nano and Micro Particles,” J. of Applied Physics, 96 (submitted).
20.
Arfken, G. B., and Weber, H. J., 1995, Mathematical Methods for Physicists, Academic Press, San Diego.
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