Dynamics of free gas bubbles immersed in an unbounded viscoplastic fluid subject to an acoustic field

In the present work, the effect of an acoustic pressure field is numerically investigated on the dynamics of a free gas bubble suspended in a viscoplastic media obeying the bi-viscous model. This model can represent yield-stress fluids obeying the bi-viscous Bingham material for a certain range of parameters. We have relied on the general Rayleigh–Plesset equation in order to derive the ODE representing the dynamics of the bubble. The integro-differential equation governing the bubble dynamics was then solved numerically using Gauss–Laguerre quadrature (GLQ) method. It has been demonstrated that at sufficiently low yield stresses, the bubble behavior s harmonic response can be observed, and a fluid’s yield stress is predicted to hamper bubble growth and suppress the emergence of the harmonics. The yield stress is also predicted to affect the rise of second harmonics which is a useful feature when bubbles are used as contrast agent boosters in sonography.