WAVE DYNAMICS OF A GAS BUBBLE COATED WITH A HYPERELASTIC SHELL IN A VISCOELASTIC LIQUID

A modifi ed 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 infl uence of the dimension of the bubble′s shell and its rigidity, the shear modulus of the shell and the carrier liquid, and also the diff erence in rheological models on the radial dynamics of the gas bubble in the external acoustic fi eld. 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 diff erence in rheological models of the elastic carrier liquid, and also of the infl uence of the shell thickness on the dynamics of acoustic waves.
A modifi ed 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 infl uence of the dimension of the bubble′s shell and its rigidity, the shear modulus of the shell and the carrier liquid, and also the diff erence in rheological models on the radial dynamics of the gas bubble in the external acoustic fi eld. 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 diff erence in rheological models of the elastic carrier liquid, and also of the infl uence of the shell thickness on the dynamics of acoustic waves.
Author:  Yu. V. Fedorov, R. N. Gafi yatov, D. D. Gubaidullina
Keywords:  acoustic fi eld, gas bubble, hyperelastic shell, viscoelastic liquid, forced oscillations, dispersion equation
Page:  1277