Low Temperature Physics: 37, 975 (2011); https://doi.org/10.1063/1.3672821 (4 pages)
Fizika Nizkikh Temperatur: Volume 37, Number 11 (November 2011), p. 1221-1224 ( to contents , go back )
Metafluid with anisotropic dynamic mass
Universidad Popular Autónoma del Estado de Puebla, 21 Sur, #110, 72160, Mexico
Instituto de Fisica, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
Department of Physics, University of North Texas, 1155 Union Circle # 311427, Denton, TX 76203, USA
Received June 24, 2011
We show that a fluid filling the space between metallic cylinders arranged in a two-dimensional lattice exhibits anisotropic dynamic mass for sound waves propagating through the lattice, if its unit cell is anisotropic. Using the plane-waves expansion method we derive (in the long wavelength limit) a formula for the effective mass tensor of the metafluid. The proposed formula is very general — it is valid for arbitrary Bravais lattices and arbitrary filling fractions of the cylinders. We apply our method to a periodic structure with very high anisotropy, when other known methods fail. In particular, we calculate the effective mass tensor for sound waves in air with embedded lattice of aluminum cylinders having rectangular cross sections, and obtain excellent agreement with experiment. The proposed method of calculation may find numerous applications for tailoring of metafluids with prescribed anisotropy.
PACS: 62.65.+k Acoustical properties of solids;
Key words: sound waves, phononic crystal, homogenization, anisotropy.