Intrinsic anisotropy of the effective acoustic properties in metafluids made of two-dimensional cylinder arrays

Within a unified theoretical framework, we extract the omnidirectional effective acoustic parameters for the metafluid consisting of isotropic fluid cylinders embedded in an isotropic fluid background. Besides the analytical formulas for the effective parameters reported previously, i.e., the bulk modulus and the mass density perpendicular to the cylinders, we also derive a simple expression for the effective mass density parallel to the cylinders. As expected, these two effective mass densities are not identical and constitute an anisotropic density tensor. Such intrinsic anisotropy can be engineered much stronger than the pure in-plane anisotropy induced by either anisotropic lattices or anisotropic scatterers.