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

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.

Sloshing in a Hele-Shaw cell: experiments and theory

“…In wetting conditions, as in our experiments, this dissipation is associated with a friction force scaling as the capillary number at the power 2/3. This result is identical to what is found when pulling a plate out of a bath and in Tanner's problem (Cantat 2013), or when a foam layer is present over the sloshing liquid (Sauret et al 2015;Viola et al 2016). We believe that these dissipative phenomenon at the free liquid surface and at the dynamic meniscus, related to wetting effects (Keulegan 1959;Cocciaro et al 1991), are present in our experiments, but are overshadowed by the viscous dissipation in the oscillating boundary layers that becomes dominant when the confinement or the viscosity are large enough, as confirmed by the very good matching between theory and experiments for ν 3.7 mm 2 /s.…”

Dynamics of non-wetting drops confined in a Hele-Shaw cell

“…Following recent work on the motion of wetting droplets in Hele-Shaw cells (Reyssat 2014) or on the dissipation involved in the displacement or deformation of foams (Cantat 2013;Sauret et al 2015;Viola et al 2016), we expect the friction force resulting from the flow in the advancing and receding menisci of water around the drop to follow F menis w 20γRCa 2/3 w . Comparing Equation 3.6 with this force yields: Figure 7b, this ratio is of the order of 0.2 for the largest gaps, but lower than 0.1 for more confined drops, which justifies that the contribution of the menisci may be neglected in the overall estimation of the friction.…”

The fluid mechanics of bubbly drinks

“…Depends on who you ask and where do they come from! A recent study suggests that having a layer of foam reduces the sloshing in a vibrated container 16 ; so, if you prefer not to spill your beer while walking, it is better to have it with foam. It has also been shown that foam slows down degassing of beer and also serves as a thermal insulator.…”