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International Journal of Antennas and Propagation
Volume 2016, Article ID 1785751, 7 pages
http://dx.doi.org/10.1155/2016/1785751
Research Article

A Modeling Method for Small Packing Particles in Electromagnetic Simulation

Fundamental Science on Extreme High Frequency Laboratory, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 28 August 2015; Revised 12 February 2016; Accepted 29 February 2016

Academic Editor: Luciano Tarricone

Copyright © 2016 Yi Cheng Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Looyenga, “Dielectric constants of heterogeneous mixtures,” Physica, vol. 31, no. 3, pp. 401–406, 1965. View at Publisher · View at Google Scholar · View at Scopus
  2. J. C. Santamarina, A. Klein, and M. A. Fam, “Soils and waves: particulate materials behavior, characterization and process monitoring,” Journal of Soils and Sediments, vol. 1, no. 2, p. 130, 2001. View at Publisher · View at Google Scholar
  3. M. Meng and F. Wang, “Theoretical analyses and experimental research on a cement concrete dielectric model,” Journal of Materials in Civil Engineering, vol. 25, no. 12, pp. 1959–1963, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Lambot, I. Van den Bosch, B. Stockbroeckx, P. Druyts, M. Vanclooster, and E. Slob, “Frequency dependence of the soil electromagnetic properties derived from ground-penetrating radar signal inversion,” Subsurface Sensing Technologies and Applications, vol. 6, no. 1, pp. 73–87, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. M. I. Mishchenko and L. Liu, “Electromagnetic scattering by densely packed particulate ice at radar wavelengths: exact theoretical results and remote-sensing implications,” Applied Optics, vol. 48, no. 13, pp. 2421–2426, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Transactions on Instrumentation and Measurement, vol. 19, no. 4, pp. 377–382, 1970. View at Publisher · View at Google Scholar · View at Scopus
  7. Y.-J. Cheng, Z.-X. Xia, L. Wang, and Y. Fan, “Frequency reconfigurable microwave reaction experiment apparatus for coal desulphurization,” Journal of the University of Electronic Science and Technology of China, vol. 43, no. 1, pp. 31–35, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. J. Cheng and X. L. Liu, “W-band characterizations of printed circuit board based on substrate integrated waveguide multi-resonator method,” IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 2, pp. 599–606, 2016. View at Google Scholar
  9. D. A. Robinson and S. P. Friedman, “The effective permittivity of dense packings of glass beads, quartz sand and their mixtures immersed in different dielectric backgrounds,” Journal of Non-Crystalline Solids, vol. 305, no. 1–3, pp. 261–267, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. A. M. Shutko and E. M. Reutov, “Mixture formulas applied in estimation of dielectric and radiative characteristics of soils and grounds at microwave frequencies,” IEEE Transactions on Geoscience and Remote Sensing, vol. 20, no. 1, pp. 29–32, 1982. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Y. Chernyak and H. Heimann, Dielectric Methods for Investigating Moist Soils, Israel Program for Scientific Translations, Jerusalem, Israel, 1967.
  12. G. C. Topp, J. L. Davis, and A. P. Annan, “Electromagnetic determination of soil water content: measurements in coaxial transmission lines,” Water Resources Research, vol. 16, no. 3, pp. 574–582, 1980. View at Publisher · View at Google Scholar · View at Scopus
  13. D. A. Robinson and S. P. Friedman, “Electrical conductivity and dielectric permittivity of sphere packings: measurements and modelling of cubic lattices, randomly packed monosize spheres and multi-size mixtures,” Physica A: Statistical Mechanics and its Applications, vol. 358, no. 2–4, pp. 447–465, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. X. Xia, Y. J. Cheng, and Y. Fan, “Frequency-reconfigurable TM010-mode reentrant cylindrical cavity for microwave material processing,” Journal of Electromagnetic Waves and Applications, vol. 27, no. 5, pp. 605–614, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. B. Sareni, L. Krähenbühl, A. Beroual, and C. Brosseau, “Effective dielectric constant of periodic composite materials,” Journal of Applied Physics, vol. 80, no. 3, pp. 1688–1696, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Sareni, L. Krähenbühl, A. Beroual, and C. Brosseau, “Effective dielectric constant of random composite materials,” Journal of Applied Physics, vol. 81, no. 5, pp. 2375–2383, 1997. View at Publisher · View at Google Scholar · View at Scopus
  17. K. K. Karkkainen, A. H. Sihvola, and K. I. Nikoskinen, “Effective permittivity of mixtures: numerical validation by the FDTD method,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 3, pp. 1303–1308, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Suzuki and T. Oshima, “Verification of a model for estimating the void fraction in a three-component randomly packed bed,” Powder Technology, vol. 43, no. 2, pp. 147–153, 1985. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Oger, J. P. Troadec, D. Bideau, J. A. Dodds, and M. J. Powell, “Properties of disordered sphere packings I. Geometric structure: statistical model, numerical simulations and experimental results,” Powder Technology, vol. 46, no. 2-3, pp. 121–131, 1986. View at Publisher · View at Google Scholar · View at Scopus
  20. P. R. Rios, “Comparison between a computer simulated and an analytical grain size distribution,” Scripta Materialia, vol. 40, no. 6, pp. 665–668, 1999. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Al-Raoush and M. Alsaleh, “Simulation of random packing of polydisperse particles,” Powder Technology, vol. 176, no. 1, pp. 47–55, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Elimelech, J. Gregory, and X. Jia, Particle Deposition and Aggregation: Measurement, Modelling and Simulation, Butterworth-Heinemann, 2013.
  23. D. He, N. N. Ekere, and L. Cai, “Computer simulation of random packing of unequal particles,” Physical Review E, vol. 60, no. 6, pp. 7098–7104, 1999. View at Google Scholar · View at Scopus
  24. G. D. Scott, “Packing of spheres: packing of equal spheres,” Nature, vol. 188, no. 4754, pp. 908–909, 1960. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Konakawa and K. Ishizaki, “The particle size distribution for the highest relative density in a compacted body,” Powder Technology, vol. 63, no. 3, pp. 241–246, 1990. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Rodríguez, C. H. Allibert, and J. M. Chaix, “A computer method for random packing of spheres of unequal size,” Powder Technology, vol. 47, no. 1, pp. 25–33, 1986. View at Publisher · View at Google Scholar · View at Scopus
  27. L. D. Landau, J. Bell, M. Kearsley, L. Pitaevskii, E. Lifshitz, and J. Sykes, Electrodynamics of Continuous Media, Elsevier, Philadelphia, Pa, USA, 1984.
  28. J. A. Reynolds and J. M. Hough, “Formulae for dielectric constant of mixtures,” Proceedings of the Physical Society, Section B, vol. 70, no. 8, pp. 769–775, 1957. View at Publisher · View at Google Scholar · View at Scopus
  29. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philosophical Transactions of the Royal Society of London, vol. 203, no. 359–371, pp. 385–420, 1904. View at Publisher · View at Google Scholar
  30. Ć. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” Journal of Applied Physics, vol. 102, no. 6, Article ID 064101, 2007. View at Publisher · View at Google Scholar · View at Scopus
  31. C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization, Elsevier Science, Philadelphia, Pa, USA, 1978.
  32. W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proceedings of the IEEE, vol. 62, no. 1, pp. 33–36, 1974. View at Publisher · View at Google Scholar · View at Scopus