= Capillary collapse of an annular viscous cylinder
For equal internal and external <pressures>, zero <axial strain rate> and positive <surface tension>, <annular viscous extension> gives constant $A=R_e^2-R_i^2$ and thickness $D(t)=R_e(0)-R_i(0)+\gamma t/(2\mu)$. Since $R_i=(A/D-D)/2$, the central hole closes at
$$
t_* =\frac{2\mu}{\gamma}\left[\sqrt{A(0)}-R_e(0)+R_i(0)\right].
$$
The formula holds until closure and requires a genuine initial annulus; the subsequent topology has no inner cylindrical interface.
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