paper

"Marginal pinching" in soap films

arXiv:cond-mat/0105318 · doi:10.1209/epl/i2001-00356-y

Abstract

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 lambda(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 instabilitites set in. We find lambda(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 instabilitites leading to a global film thinning and drainage, as first discussed by K. Mysels under the name ``marginal regeneration''.

7 pages, 2 figures

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