A continuum model for liquids with vapour bubbles including micro-configurational forces

"Bubble dynamics has been widely studied since the very origin of the mechanics of fluids, to deal with problems such as bubbly flows—cavitating or boiling—or sound propagation. Applications span today a broad class of different problems, considering materials such as water, oils, inks, fuels, metals, advanced materials and manufacturing processes, or heat-transfer fluids close to their boiling conditions. Lord Rayleigh’s solution of 1917 to the problem of determining the size of a spherical bubble in an infinite medium where pressure is applied at the boundary, led in the sixties to the generalized Rayleigh- Plesset equation. Continuummodels were then introduced looking heuristically at the liquidwith bubbles as a mixture: the size of bubbles—a continuous field—changes driven by the local value of the pressure field as if pressure were applied on each bubble in Rayleigh’s conditions. The approach proves accurate in the main and versatile in practice. Limits derive nonetheless from the soft boundary condition used to get the local model: any bubble interacts with the rest of the mixture where it is embedded as if the latter were perfectly soft, regardless of the real behaviour of it. The choice entails the uncoupling of the macro from the micromotion