Effective dynamic properties of random complex media

A core-shell, self-consistent effective medium mode is employed to estimate the effective dynamic bulk modulus and density for random media consisting of particles in a viscous host fluid. Analytical expressions are obtained for the effective bulk modulus and mass density, incorporating the viscous nature of the fluid host into the core-shell model through wave mode conversion phenomena. The effective density is derived in terms of particle concentration, particle and host densities, particle size, and the acoustic and shear wavenumbers of the liquid host. The analytical expressions obtained agree with prior known results in the limit of both static and inviscid cases; the bulk modulus is found to be quasi-static. Numerical calculations demonstrate the dependence of the effective mass density on frequency, particle size (from nano- to micro-regime) and concentration.