Use of acoustic excitation to enhance the mobility of buoyancy driven bubbles inside a viscoplastic material.

The ability to control the mobility of bubbles inside a viscoplastic material can be crucial in a wide range of engineering applications. Here, we provide a detailed theoretical study of the dynamics of the buoyancy-driven rise of a bubble inside a viscoplastic material when subjected to an acoustic pressure field. We develop a simplified model based on Lagrangian formalism assuming a pulsating bubble with spherical shape. Moreover, to account for the effects of a deformable bubble, we also perform detailed 2D axisymmetric simulations. Qualitative agreement, to some extent, is found between the simplified approach and the detailed numerical simulations. Our results reveal that the acoustic excitation enhances the mobility of the bubble, by increasing the size of the yielded region that surrounds the bubble, thereby decreasing the effective viscosity of the liquid and accelerating the motion of the bubble. Interestingly, it is shown that for frequencies near resonance, the bubble motion takes place even for Bingham (Bn) numbers that can be orders of magnitude higher than the critical Bn for bubble entrapment in the case of a static pressure field.