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.
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Foam on troubled water: Capillary induced finite-time arrest of sloshing waves
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September 2016
Letter|
September 13 2016
Foam on troubled water: Capillary induced finite-time arrest of sloshing waves
Francesco Viola;
Francesco Viola
1Laboratory of Fluid Mechanics and Instabilities,
EPFL
, 1015 Lausanne, Switzerland
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P.-T. Brun;
P.-T. Brun
2Department of Mathematics,
Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
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Benjamin Dollet;
Benjamin Dollet
3Institut de Physique de Rennes, UMR CNRS 6251,
Université Rennes 1 Bâtiment 11A
, Campus de Beaulieu, 35042 Rennes Cedex, France
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François Gallaire
François Gallaire
a)
1Laboratory of Fluid Mechanics and Instabilities,
EPFL
, 1015 Lausanne, Switzerland
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a)
Electronic mail: francois.gallaire@epfl.ch
Physics of Fluids 28, 091701 (2016)
Article history
Received:
June 03 2016
Accepted:
August 05 2016
Citation
Francesco Viola, P.-T. Brun, Benjamin Dollet, François Gallaire; Foam on troubled water: Capillary induced finite-time arrest of sloshing waves. Physics of Fluids 1 September 2016; 28 (9): 091701. https://doi.org/10.1063/1.4961260
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