Wave Dynamics of a Gas Bubble Coated with a Hyperelastic Shell in a Viscoelastic Liquid

A modified Rayleigh–Lamb equation has been derived which takes account of the radial oscillations of a gas bubble coated with a hyperelastic shell and found in a viscoelastic liquid. The hyperelasticity of the shell is taken account of on the basis of the Mooney–Rivlin model, and the viscoelasticity of the liquid, according to the Zener model in whose particular cases the Kelvin–Voigt and Maxwell models are followed. Numerical calculations have been carried out. An analysis has been made of the influence of the dimension of the bubble′s shell and its rigidity, the shear modulus of the shell and the carrier liquid, and also the difference in rheological models on the radial dynamics of the gas bubble in the external acoustic field. A mathematical model has been constructed which determines the propagation of acoustic waves in the viscoelastic liquid with encapsulated gas bubbles. A study has been made of the difference in rheological models of the elastic carrier liquid, and also of the influence of the shell thickness on the dynamics of acoustic waves.