Oscillatory behavior of a gas bubble growing (or collapsing) in viscoelastic liquids

A theoretical study was carried out to achieve a better understanding of the oscillatory behavior of a gas bubble growing (or collapsing) in a viscoelastic liquid, by taking into account both the hydrodynamic and diffusion effects. The Zaremba‐DeWitt model was chosen to represent the rheological properties of the suspending medium. The finite difference method was employed to solve the governing system equations. The computational results show that, in the case of very fast diffusion (i.e., constant bubble pressure), the oscillatory behavior of a bubble takes place only when the ratio of the initial pressure difference between the gas bubble and the liquid phase to the elastic modulus of the suspending medium is below a certain critical value. On the other hand, in the case of very slow diffusion, the oscillatory behavior of a bubble persists, regardless of the magnitude of the rheological properties of the suspending medium. Our study indicates further that the diffusivity of a gas has a profound influence on the occurrence of oscillatory behavior, that the elastic property of the suspending medium enhances oscillatory behavior while its viscosity plays the opposite role, and that even a Newtonian medium can give rise to an oscillatory pattern of bubble growth (or collapse), although it dampens out very quickly.