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Foam on troubled water: Capillary induced finite-time arrest of sloshing waves

Author(s): Viola, F; Brun, PT; Dollet, B; Gallaire, F

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Abstract: Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid’s oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.
Publication Date: 1-Sep-2016
Electronic Publication Date: 13-Sep-2016
Citation: Viola, F, Brun, PT, Dollet, B, Gallaire, F. (2016). Foam on troubled water: Capillary induced finite-time arrest of sloshing waves. Physics of Fluids, 28 (9), 10.1063/1.4961260
DOI: doi:10.1063/1.4961260
ISSN: 1070-6631
EISSN: 1089-7666
Type of Material: Journal Article
Journal/Proceeding Title: Physics of Fluids
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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