= Spherical clean bubble without surface tension
{title2=$\rho ga-3F/(4\pi a^2)=0$}
A buoyantly rising inviscid bubble in otherwise quiescent unbounded liquid has an exterior <Stokeslet> with $F=4\pi\mu aU=4\pi\rho ga^3/3$. Its tangential traction vanishes on the <sphere>. The dynamic normal traction is $-3F\cos\theta/(4\pi a^2)$, while the hydrostatic normal-traction variation is $\rho ga\cos\theta$. Their dipoles cancel at the terminal <velocity>, leaving a constant total normal stress compatible with uniform gas <pressure> even when <surface tension> is zero. This is an exact spherical solution in the stated Stokes model, not a proof of shape stability under arbitrary perturbations.
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