Using analytical results for viscous dissipation in phononic crystals, we calculate the decay coefficient of a sound wave propagating at low frequencies through a two-dimensional phononic crystal with a viscous fluid background. It is demonstrated that the effective acoustic viscosity of the phononic crystal may exceed by two to four orders of magnitude the natural hydrodynamic viscosity of the background fluid. Moreover, the decay coefficient exhibits dependence on the direction of propagation; that is, a homogenized phononic crystal behaves like an anisotropic viscous fluid. Strong dependence on the filling fraction of solid scatterers offers the possibility of tuning the dissipative decay length of sound, which is an important characteristic of any acoustic device. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
Keywords: homogenization; phononic crystals; viscosity.