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

针对使用造影剂进行超声诊断的应用，在单个气泡的限制下理论上研究了封装气泡的动力学。在本文中，我们将单个气泡或一些气泡的理论扩展到许多气泡的理论，并从理论上研究超声在初始静止的不可压缩液体中的弱非线性传播，该液体均匀地包含许多被外壳包裹为粘弹性体的微气泡（Kelvin-福格特模型）。因此，我们推导出了低频长波的 Korteweg-de Vries-Burgers 方程，并阐明了壳会影响超声传播的平流、非线性和耗散（非色散）效应。特别是，壳刚度、表面张力和壳粘度增加了对流、非线性、