Acoustic band gaps for a two-dimensional periodic array of solid cylinders in viscous liquid

We investigated the absolute acoustic band gaps for two-dimensional periodic arrays of silica cylinders in viscous liquid. Acoustic band structures, which have complex eigenfrequencies for these systems, are calculated with the plane wave expansion method. They show that when the viscous penetration depth is comparable to the structural length scale, the structures possess large absolute acoustic band gaps compared with those without viscosity. We also found that the magnitude of the viscosity plays an important role in these band gaps.