The impact of diffusion on confined oscillated bubbly fluid

TL;DR

This paper investigates how high-frequency oscillations influence the distribution and stability of bubbles in a confined fluid, revealing frequency-dependent accumulation patterns and stability conditions.

Contribution

It introduces a time-averaged model that captures bubble diffusion and mutual coupling, showing new steady states and stability behaviors under oscillatory conditions.

Findings

Bubbles accumulate near walls at low frequencies

Central bubble accumulation occurs at high frequencies

Steady states are unstable at low frequencies and stable at high frequencies

Abstract

We consider the dynamics of monodisperse bubbly fluid confined by two plane solid walls and subjected to small-amplitude high-frequency transversal oscillations. The frequency these oscillations is assumed to be high in comparison with typical relaxation times for a single bubble, but comparable with the eigenfrequency of volume oscillations. A time-averaged description accounting for mutual coupling of the phases and 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 oriented parallel to the walls is detected. These one-dimensional states are shown to be unstable. At relatively high frequencies the bubbles accumulate at the central plane and the solution is stable.