= Axisymmetric squeeze-film pressure
{title2=$p=3\mu\dot h(r^2-R^2)/h^3$}
For liquid between spatially uniform parallel plates with gap $h(t)$ and circular material rim $R(t)$, <lubrication theory> gives $\overline u_r=-h^2p_r/(12\mu)$ and $\dot h+r^{-1}(rh\overline u_r)_r=0$. Bounded pressure at zero excludes the logarithmic solution, and $p(R)=0$ gives the displayed pressure. Then $\overline u_r=-r\dot h/(2h)$ and rim advection implies $(R^2h)'=0$, expressing volume conservation. Closing plates have positive gauge pressure; opening requires suction, whose validity can be limited by <cavitation> or air invasion. Negative gauge pressure is not in itself a contradiction.
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