Shape stability of a microbubble in a power-law liquid

The onset of non-spherical oscillations of a microbubble in an unbounded power-law liquid, important for biomedical ultrasound applications, is studied. Two sets of evolution equations are obtained from the equation of motion: a Rayleigh Plesset-type equation for the spherical oscillations and an equation for the non-spherical oscillations. The non-spherical oscillations are modeled using the perturbation method via the Legendre polynomials. Two kinds of instabilities, namely parametric and Rayleigh-Taylor instabilities, are investigated. A higher power-law index causes the damping of the oscillations for both spherical and non-spherical oscillations. The power-law index damping effect depends on the ultrasonic drive frequency. At natural frequency, the amplitude of the perturbations is high compared to the non-resonant cases. At a low consistency index, the damping effect of the power-law index decreases. Unlike Newtonian liquids, the viscosity of power-law liquids is affected by the frequency of the acoustic field, thereby affecting Rayleigh-Taylor instability.