Buoyancy of an aerated liquid (${\rho }_{\mathrm{mix}}=(1-\alpha ){\rho }_{\ell }+\alpha {\rho }_g$)

For a quasihydrostatic bubbly mixture with gas void fraction $\alpha$, volume averaging gives the displayed mass density. A body displacing mixture volume $V$ has approximate buoyant force ${\rho }_{\mathrm{mix}}gV$. A floating body of mass $m$ therefore needs $V=m/{\rho }_{\mathrm{mix}}$; gas release can increase its draft until the required displacement exceeds its available watertight volume. This mechanism explains a possible loss of flotation without making sinking inevitable in every gas plume. Upward liquid flow, turbulence and nonuniform bubble distributions require additional hydrodynamic forces beyond this simple mixture model.