The spontaneous puncture of thick liquid films
Résumé
We call thick those films for which the disjoining pressure and thermal fluctuations are ineffective. Water films with thickness h in the 1-100 m m range are thick, but are also known, paradoxically, to nucleate holes spontaneously. We have uncovered a mechanism solving the paradox, relying on the extreme sensitivity of the film to surface tension inhomogeneities. The surface tension of a free liquid film is lowered by an amount Delta sigma over a size a by chemical or thermal contamination. At the same time this spot diffuses (within a time a(2)/D, with D the diffusion coefficient of the pollutant in the substrate), the Marangoni stress Delta sigma/a induces an inhomogeneous outward interstitial flow which digs the film within a time tau 0 similar to root rho ha(2)/Delta sigma with rho the density of the liquid. When the Peclet number Pe = a(2)/D tau(0) is larger than unity, the liquid substrate motion reinforces the surface tension gradient, triggering a self-sustained instability insensitive to diffusional regularisation. Several experimental illustrations of the phenomenon are given, both qualitative and quantitative, including a precise study of the first instants of the unstable dynamics made by controlled perturbations of a Savart sheet at large Pe.
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