On the absence of marginal pinching in thin free films

Abstract

This paper concerns the drainage of a thin liquid lamella into a Plateau border.
Many models for draining soap films assume that their gas-liquid interfaces are effectively immobile. Such models predict a phenomenon known as `marginal pinching', in which the film tends to pinch in the margin between the lamella and the Plateau border. We analyse the opposite extreme, in which the gas-liquid interfaces are assumed to be stress-free. We show that no marginal pinching occurs in this case: the film always approaches a monotonic profile at large times.