“Marginal pinching” in soap films

We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance λ( t ), due to the formation of a well-localized pinched region of thickness h ( t ) and extension w ( t ). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilities set in. We find λ( t ) ∼ t 1/4 , and for the pinch dimensions, h ( t ) ∼ t −1/2 and w ( t ) ∼ t −1/4 . These results may play a useful role for the discussion of later instabilities leading to a global film thinning and drainage, as first discussed by K. Mysels under the name "marginal regeneration".