The spontaneous puncture of thick liquid films

We call thick those films for which the disjoining pressure is ineffective. Water films with thickness $h$ in the 1-10 $\mu$m range are thick, but it is also known that, paradoxically, they nucleate holes spontaneously. We have uncovered a mechanism solving the paradox. Most natural films are dirty to some extent, and we show that if a spot of dissolved substance lowers locally the surface tension of the liquid, the corresponding Marangoni stress may lead to a self-sustained instability triggering film rupture. When deposited with size $a$, the spot dissipates by molecular diffusion (coefficient $D$) along the film in a time $a^2/D$. Before doing so, the surface tension gradient $\Delta\sigma/a$ between the spot center (tension $\sigma-\Delta\sigma$) and the rest of the film (tension $\sigma$) induces an inhomogeneous outward interstitial flow which digs the spot, and reinforces the tension gradient. Hence the instability, which occurs within a timescale $\tau\sim\sqrt{\rho a^2 h/\Delta \sigma}$, with $\rho$ the liquid density. When the Péclet number $Pe=a^2/D\tau$ is small, diffusion regularizes the film, which remains flat: clean films don’t break, while for $Pe>1$, the film punctures. This new scenario will be illustrated by several experiments.