= Transport limit of a rotating-cylinder coating film
{title2=$\alpha_c=4/27$}
In the leading steady coating model, $Q=Uh-gh^3\cos\theta/(3\nu)$ and $H=Uh/Q$ obey $(H-1)/H^3=\alpha\cos\theta$, where $\alpha=gQ^2/(3\nu U^3)$. The left side reaches its positive maximum $4/27$ at $H=3/2$. This gives the largest globally continuous finite wall-entrained branch, with critical thickness $3Q/(2U)$. It is an algebraic transport-capacity result; full temporal stability needs the corresponding time-dependent free-surface model.
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