Rotational Stokes flow between concentric spheres

For concentric spheres of radii $a<b$, with the inner sphere rotating at angular velocity $\mathbf{\Omega }$ and the outer sphere fixed, the Stokes velocity isThe pressure is constant, and may be set to zero.

The torque transmitted across any concentric sphere isIt approaches $8\pi \mu a^3\mathbf{\Omega }$ when $a\ll b$, and for a thin gap $h=b-a\ll a$ it approaches