= Solution
Take the upward direction as $\mathbf e_z$, with polar angle $\theta$ measured from it. The liquid is quiescent at infinity. On a translating clean inviscid bubble, the <kinematic boundary condition> is $(\mathbf u-U\mathbf e_z)\cdot\mathbf n=0$, and the <stress-free boundary condition> is zero tangential traction. The normal traction must balance uniform gas <pressure> and any constant-curvature surface-tension jump.
For a vertical <Stokeslet> of strength $F$, the radial <velocity> is $u_r=F\cos\theta/(4\pi\mu r)$. Its traction on a concentric <sphere> is purely normal, so zero tangential traction is automatic. The kinematic condition at $r=a$ gives
$$
\boxed{F=4\pi\mu aU.}
$$
The singularity is only a device for generating the exterior solution; there is no liquid point <force> inside the actual bubble. The integrated dynamic traction on the bubble is $-F\mathbf e_z$, giving the <clean-bubble Stokes drag>. The upward <buoyancy> is $4\pi\rho ga^3/3$, hence <force> balance gives
$$
\boxed{U=\frac{\rho ga^2}{3\mu}.}
$$
The normal stress also shows that <surface tension> is not required for this particular spherical solution. Let the ambient <hydrostatic pressure> at the bubble centre be $p_c$, so on its surface $p_h=p_c-\rho ga\cos\theta$. Adding the Stokeslet's dynamic normal traction gives
$$
\sigma_{nn}^{\rm total}=-p_c+
\left(\rho ga-\frac{3F}{4\pi a^2}\right)\cos\theta=-p_c,
$$
where the terminal <buoyancy> value of $F$ cancels the dipole. This is the <spherical clean bubble without surface tension> balance: \b[an initially spherical bubble can remain spherical in this ideal steady Stokes solution even when <surface tension> is zero]. With uniform <surface tension> $\gamma$, choose gas <pressure> $p_b=p_c+2\gamma/a$; with $\gamma=0$, $p_b=p_c$. This proves compatibility of the spherical shape, not stability of arbitrary deformations or validity when inertia matters.
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