Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell

Abstract Aimed towards an application of ultrasound diagnosis using contrast agents, the dynamics encapsulated bubbles has been theoretically investigated under restriction a single bubble. In this paper, we extend theory for bubble or some to that many bubbles, and investigate weakly nonlinear propagation in initially quiescent incompressible liquid, uniformly containing microbubbles by shell as viscoelastic body (Kelvin–Voigt model). As result, derived Korteweg–de Vries–Burgers equation low-frequency long wave clarified affects advection, nonlinear, dissipation (not dispersion) effects propagation. particular, rigidity, surface tension, viscosity increased effects, respectively.