Marginal regeneration in a horizontal film: Instability growth law in the nonlinear regime

Abstract

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Local origin of the visco-elasticity of a millimetric elementary foam

“…We show in Gros et al. (2021) that the tension difference between the film and the meniscus is positive even when is oriented toward the meniscus, and that at a given capillary number. The tension jump associated with a film motion toward the meniscus will thus be neglected.…”

“…Another possible failure of the model in compression at large velocity is the marginal regeneration instability, which has been shown to be triggered by a compression in Gros et al. (2021). This instability breaks the invariance along the meniscus and may modify the relationship between the tension difference and the velocity.…”

The Life of a Surface Bubble

“…They proposed scaling laws predicting the velocity at which the pinch thins and enlarges along time. Although this pinch has been observed in many different experimental studies (see for example [40][41][42]), its dynamics has never been compared to the theoretical prediction by Aradian. This is due to a fast destabilisation in many experimental studies, which will be discussed in the next section and to difficulties to measure the thickness with high enough accuracy.…”

“…Finally, in vertical soap films as well as in horizontal ones or in surface bubbles, the pinch instability and the subsequent marginal regeneration is expected for large enough characteristic sizes, in presence of standard surfactants [21,41,50,52] leading to low enough surface elasticity. Mysels already proposed that the dynamics of these thin films is crucial to understand the foam film thinning since thin patches tend to rise and replace thicker ones.…”

Instability of the one-dimensional thickness profile at the edge of a horizontal foam film and its Plateau border

“…This process is at the origin of the dimple shapes often observed in draining films [12]. In some cases, the pinched region is reported to destabilize into a necklace of thin spots [13][14][15], and this instability then evolves into a nonuniform flow dynamics along the meniscus [1,16,17], which controls the subsequent film drainage and its life time [10,[18][19][20]: regions of the film with a small thickness are emitted from the menisci, while thicker parts of the film flow into the menisci. In the presence of gravity, the thin regions migrate by buoyancy to the top of the film.…”