= Squeeze resistance of eccentric nested spheres
{title2=$\mathcal R=\frac{6\pi\mu a^4}{\Delta^3\alpha^3}[\frac{2\alpha}{1-\alpha^2}+\log\frac{1-\alpha}{1+\alpha}]$}
For an inner sphere of radius $a$, outer radius $a+\Delta$, and signed offset $\alpha\Delta$ along a fixed axis, the leading <lubrication pressure> generated by offset speed $V=\Delta\dot\alpha$ is $p=3\mu a^2V/[\alpha\Delta^3(1-\alpha\cos\theta)^2]+\text{constant}$. Its force on the inner sphere is $-\mathcal R V$ along that axis. Remove the spatially constant divergent term before taking $\alpha\to0$; the resistance then tends to $8\pi\mu a^4/\Delta^3$. As $\alpha\to1$, it is $6\pi\mu a^4/[\Delta^3(1-\alpha)]$ to leading order.
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