Metafluid with anisotropic dynamic mass

Abstract

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.