 Draining viscous film on a finite horizontal plate

With $K=\rho g/(3\mu )$ and formal edge conditions $h(\pm L,t)=0$, the lubrication theory equation is $h_t=K(h^3{h}_x{)}_x$. Its positive separated long-time profile hasWriting $C=B(4/5,1/2)$ in terms of the beta function, the centre height is $h_0^3=10\mu L^2/(\rho g{C}^{2}t)$. The edge region of a draining viscous film determines how the singular outer profile matches the flow over the physical edge.