Effective medium of periodic fluid-solid composites

An analytic solution of the effective mass density and bulk modulus of a periodic fluid-solid composite is obtained by using the multiple-scattering theory in the long-wavelength limit. It is shown that when the concentration of solid inclusions is high, the effective mass density is structure dependent and differs significantly from the leading-order dipole solution, whereas Wood's formula is accurately valid, independently of the structures. Numerical evaluations from the analytic solution are shown to be in excellent agreement with finite-element simulations. In the vicinity of the tight-packing limit, the critical behavior of the effective mass density is also studied and it is independent of the lattice symmetry.