Nonlinear ultrasound propagation through coated microbubbles:Influence of shell constitutive laws

The use of microbubbles encapsulated by membranes as contrast agents has generated considerable interest owing to their potential to enhance image resolution. Numerous theoretical studies have investigated the mechanics of these membranes, revealing that they play a crucial role in microbubble oscillation, for example, by significantly increasing attenuation. While several membrane materials have been examined for their mechanical properties, theoretical studies on the behavior of multiple microbubbles remain limited, despite their frequent use in both practical and experimental contexts. This gap highlights the importance of understanding ultrasound propagation through liquids containing multiple microbubbles. In this study, the foundational work of Tsiglifis and Pelekasis (J. Acoust. Soc. Am., 123, 2008), which analyzed the oscillation of a single microbubble, is extended to examine ultrasound propagation through multiple microbubbles using three distinct constitutive laws. These laws describe varying stress–strain relationships that characterize membrane elasticity. The singular perturbation method was applied to the governing equations for bubbly liquids to derive a one-dimensional nonlinear wave equation that captures the second-order ultrasound nonlinearity. The analysis shows that variations in the constitutive laws significantly affect the nonlinearity of ultrasound propagation. The findings suggest potential applications in enhancing the accuracy of ultrasound models and guiding the development of new contrast agents.