An analytic solution of the effective mass density and bulk modulus of a periodic fluid-solid composite is obtained by using the multiple-scattering theory in the long-wavelength limit. It is shown that when the concentration of solid inclusions is high, the effective mass density is structure dependent and differs significantly from the leading-order dipole solution, whereas Wood's formula is accurately valid, independently of the structures. Numerical evaluations from the analytic solution are shown to be in excellent agreement with finite-element simulations. In the vicinity of the tight-packing limit, the critical behavior of the effective mass density is also studied and it is independent of the lattice symmetry. © 2012 Europhysics Letters Association.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors would like to thank Profs. PING SHENG and ZHAOQING ZHANG for discussions. This work was supported by National Natural Science Foundation of China (Grant No. 10804086) and the PhD Programs Foundation of Ministry of Education of China (Grant No. 200804861018), the Fundamental Research Funds for the Central Universities (Grant No. 2012ZZ0077), KAUST Start-up Package, and Hong Kong RGC grant HKUST 604207.
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- Physics and Astronomy(all)