Transport limit of a rotating-cylinder coating film (${\alpha }_c=4/27$)

In the leading steady coating model, $Q=Uh-g{h}^3\cos \theta /(3\nu )$ and $H=Uh/Q$ obey $(H-1)/H^3=\alpha \cos \theta$, where $\alpha =g{Q}^2/(3\nu U^3)$. 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.