= Fixed-volume capillary spreading in a cylindrical cusp
{title2=$w=[21\mu a(z_N^2-z^2)/(8\gamma t)]_+^{1/2}$}
For fixed volume $V$ and symmetric spreading, <conservation of mass> and the <cusp flow between touching cylinders> equation give width proportional to $t^{-1/8}$ and support length proportional to $t^{3/8}$. The source-type <similarity solution> has the displayed profile and $z_N=(8Va/\pi)^{1/4}(8\gamma t/(21\mu a))^{3/8}$. It is a formal outer lubrication solution; its microscopic nose requires a local description when the axial slope becomes large.
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