  We investigate the radial oscillations of small gas bubbles trapped in
yield-stress fluid and driven by an acoustic pressure field. We model the
rheological behavior of the yield-stress fluid using the recently developed
elasto-visco-plastic (EVP) constitutive equation that takes into account the
elastic and visco-plastic deformations of the material [P. Saramito, J.
NonNewton. Fluid Mech. 158 (1-3) (2009) pp.154-161]. Assuming that the bubble
remains spherical during the pressure driving, we reduce the problem to a set
of ODEs and an integrodifferential equation, which we solve numerically for the
case of two yield-stress fluids, a sot Carbopol gel and a stiffer Kaolin
suspension. We find that, depending on the amplitude and frequency of the
pressure field, the radial oscillations of the bubble produce elastic stresses
that may or may not suffice to yield the surrounding material. We evaluate the
critical amplitude of the acoustic pressure required to achieve yielding and we
find a good agreement between numerical simulations and an analytical formula
derived under the assumption of linear deformations. Finally, we examine the
bubble oscillation amplitude for a very wide range of applied pressures both
below and above the critical value to assess the impact of yielding on the
bubble dynamics. This analysis could be used to identify a signature of
yielding in experiments where the radial dynamics of a bubble is measured. More
generally, these results can be used to rationalize the optimal conditions for
pressure-induced bubble release from yield-stress fluids, which is relevant to
various biomedical and industrial applications, including oil industry and food
processing.
