Abstract
An effective medium method (EMM) is developed to investigate the nonlinear propagation of acoustic waves for soft media containing air bubbles, which accounts for the effects of weak compressibility, viscosity, surrounding pressure, surface tension, and encapsulating shells. Based on the dynamics model of an individual bubble that has included these effects, the EMM is presented by employing a simple perturbation approach to "homogenize" the bubbly soft media. The equations describing the fundamental and the second harmonic waves are derived that applies to three-dimensional cases, and then solved in a one-dimensional case to obtain the effective acoustical parameters of a longitudinal wave. The EMM is compared with the previous theories in three representative cases regarded as simple models of significant practical applications. The results show that the EMM agrees well with the previous theories and can incorporate the additional effects, which may notably affect the accuracy of the results. The limitations of the EMM are also identified and stated.
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