The impact of bubble diffusivity on confined oscillated bubbly liquid

We consider the dynamics of monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency transverse oscillations. The period of these oscillations is assumed small in comparison with typical relaxation times for a single bubble but comparable with the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles and for the diffusivity of bubbles is applied. We find nonuniform steady states with the liquid quiescent on average. At relatively low frequencies, accumulation of bubbles either at the walls or in planes parallel to the walls is detected. These one-dimensional states are shown to be unstable. At relatively high frequencies, this accumulation is found at the central plane and the solution is stable.