Torque in rotational Stokes flow between concentric spheres
= Torque in rotational Stokes flow between concentric spheres
{c}
The torque transmitted across any concentric sphere is
$$
\mathbf G
=\frac{8\pi\mu a^3b^3}{b^3-a^3}\boldsymbol\Omega.
$$
It approaches $8\pi\mu a^3\boldsymbol\Omega$ when $a\ll b$, and for a thin gap $h=b-a\ll a$ it approaches
$$
\frac{8\pi\mu a^4}{3h}\boldsymbol\Omega.
$$