Instability of the 1D thickness profile at the edge of a horizontal foam film and its Plateau border*

The stability of soap bubbles and hence of liquid foams is a set by the film thinning, which is known to occur locally: rounds patches of thin films appear at the edges of the film before moving to the top of the film by buoyancy. This phenomenon, called the marginal regeneration, has been observed for decades, but its origin hasn't yet been established. It involves the appearance of a localized pinched region between the film and the meniscus, which dynamics has been entirely characterized by assuming its invariance in the direction of the meniscus. We identify a limit in which the bulk drainage and the surface rearrangements are decoupled, the film thus evolving in a sliding-puzzle-like dynamic. In this frame, we study theoretically and numerically the stability of this straight pinched region, and show that it is unstable to long wavelengths. We predict a critical wavelength of fastest destabilization and a thickness ratio between the thin and thick parts of the film, both in good agreement with experimental observations.