= Buoyancy of an aerated liquid
{title2=$\rho_{\rm mix}=(1-\alpha)\rho_\ell+\alpha\rho_g$}
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> $\rho_{\rm mix}gV$. A floating body of <mass> $m$ therefore needs $V=m/\rho_{\rm mix}$; 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.
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