Acoustic nonlinearity of liquid containing encapsulated microbubbles

Recently, a high value nonlinear parameter of liquid containing contrast agents (encapsulated microbubbles) has been reported by some measurements, however an effective way to study it theoretically has not been found so far. In this paper, an approach, based on the concept of the equivalent nonlinear parameter is presented to estimate the nonlinear property of such media. The liquid containing encapsulated microbubbles is treated as a homogenous liquid with a equivalent nonlinear parameter. An experimental approximate linear relationship for attenuation and nonlinear parameter with bubble volume is confirmed from our calculation. It is also found that when a microbubble is encapsulated by a shell, the nonlinear oscillation of the bubble is restrained; the second and higher harmonics are generated not so effectively compared to a free bubble. Naturally this causes the nonlinear parameter of such a liquid to decrease greatly. Favorable agreement between the theory and Wu et al.’s experiments shows this approach could effectively estimate the nonlinearity of encapsulated bubbly liquid. Finally, some applicable limitations for this approach are also mentioned.