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How the contact line damp liquid oscillations

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Controlling liquid oscillations in a tank, so-called sloshing, is important in industrial applications (stability of ships or satellites) as well as in daily life. However, the influence on sloshing of the triple line between the liquid, the wall and the air remains poorly understood. Researchers from two teams at LIPhy (MODI and DyFCoM), in collaboration with the Laboratory of Fluid Mechanics and Instabilities at EPFL in the frame of a PICS program from CNRS, have just unravelled the role of this triple line.

Most of us know that it is easier to spill coffee than beer. This highlights the influence of interfaces on the damping of sloshing; here, the beer froth strongly dissipates the motion owing to the friction of bubbles sliding along the glass walls. However, in the seemingly simple case of a triple line between the liquid, the wall and the ambient air, the influence of this interface between different phases on the damping of motion remains elusive. Two researchers from LIPhy, Benjamin Dollet and Elise Lorenceau, in collaboration with François Gallaire, Professor at EPFL, have unravelled the role of the triple line on the simplest case of liquid oscillations, that of a liquid column in a U-shaped tube. They evidenced that dissipation strongly increases in the so-called partial wetting regime, as the triple line slides over a dry wall with a finite contact angle. Moreover, dissipation associated with such a sliding motion displays original nonlinear features, in particular an arrest of the oscillations in finite time, in sharp contrast with the classical vision of a harmonic oscillator, which is exponentially damped by viscous effects. They proved that this dissipation originates from contact angle hysteresis, i.e. the fact that an advancing line has a lower contact angle than a receding line. Contact angle hysteresis, responsible e.g. of the pinning of rain drops on a glass window, acts as an effective solid friction which adds to viscous effects within the liquid column.
This study may eventually help to optimise the damping of sloshing in tanks, and illustrates the potential of interdisciplinary studies at the border between macroscopic fluid mechanics and the physics of interfaces.
Reference : B. Dollet, E. Lorenceau & F. Gallaire, Transition from exponentially damped to finite-time arrest liquid oscillations induced by contact line hysteresis, à paraître dans Physical Review Letters.

DOI: 10.1103/PhysRevLett.124.104502
Notice biblio : Benjamin Dollet, Elise Lorenceau, François Gallaire, Transition from exponentially damped to finite-time arrest liquid oscillations induced by contact angle hysteresis, Physical Review Letters 124, 104502 (2020).

Evolution temporelle des oscillations d'une colonne d'eau dans un tube en U
Evolution temporelle des oscillations d’une colonne d’eau dans un tube en U
(i) dans un cas de mouillage partiel, où la ligne triple glisse sur une paroi sèche (courbe pleine en bleu), voir le schéma dans le graphique où l’angle de contact θ à la ligne triple est représenté, et (ii) dans un cas de mouillage total, où l’interface glisse sur un film liquide prédéposé sur la paroi (courbe en pointillés rouge). La grande différence entre les deux cas illustre l’importance des conditions de mouillage sur l’amortissement des mouvements du liquide.