Axial rotational resistance of eccentric nested spheres (source code)

= Axial rotational resistance of eccentric nested spheres
{title2=$\mathcal R_\Omega=\frac{2\pi\mu a^4}{\Delta\alpha^3}[2\alpha+(1-\alpha^2)\log\frac{1-\alpha}{1+\alpha}]$}

Rotation about the offset axis has azimuthal <Couette flow> and no pressure variation at leading <lubrication> order. Integrating the tangential traction gives torque $-\mathcal R_\Omega\Omega$ on the inner sphere. The concentric limit is $8\pi\mu a^4/(3\Delta)$ and the contact limit is finite, $4\pi\mu a^4/\Delta$, because the wall velocity vanishes at the closest pole.