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The spontaneous puncture of thick liquid films

  • B. Néel (a1) and E. Villermaux (a1) (a2)

Abstract

We call thick those films for which the disjoining pressure and thermal fluctuations are ineffective. Water films with thickness $h$ in the $1{-}100~\unicode[STIX]{x03BC}\text{m}$ 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 $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ 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 $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}/a$ induces an inhomogeneous outward interstitial flow which digs the film within a time $\unicode[STIX]{x1D70F}_{0}\sim \sqrt{\unicode[STIX]{x1D70C}ha^{2}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}}$ , with $\unicode[STIX]{x1D70C}$ the density of the liquid. When the Péclet number $Pe=a^{2}/D\unicode[STIX]{x1D70F}_{0}$ 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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Corresponding author

Email address for correspondence: villermaux@irphe.univ-mrs.fr

References

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