Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 66 / 3 / ii / Solution

Balance the two terms in the planar viscous-sheet stretching equations over the transition. The velocity changes by $O(U)$ on length $\delta$, and $h_{xxx}=O(h_0/{\delta }^3)=O(1/(a\delta ))$. ThusUsing the geometric transition length givesThis balances capillary forcing with planar extensional viscous stress, not the no-slip Poiseuille resistance appropriate to a film bounded by rigid walls.