ACOUSTIC BAND-GAPS IN COMPOSITES OF SOLIDS AND VISCOUS-LIQUIDS

The propagation of sound in three dimensional periodic lattices of sol id-solid and solid-liquid composites is determined by calculating the acoustic band structure. Inclusion of viscous damping in the liquid is essential in understanding the acoustical properties of the solid-liq uid composite when the characteristic length scale of the system match es the viscous penetration depth in the liquid. By using complex sound velocities to model the visco-elastic properties of the liquid we sho w that the solid-viscous liquid composite displays acoustic band gaps. These results are consistent with the hydrodynamic analysis of viscoe lastic modes in porous media, binary mixtures and with a stratified la yer model. As a characteristic example the ultrasonic band structure o f silica spheres in ice and of colloidal crystals of silica in glycero l/water mixture are presented. Both systems display gaps under experim entally obtainable conditions. (C) 1998 Elsevier Science Ltd.