Damping of liquid sloshing by foams

Abstract

When a container is set in motion, the free surface of the liquid starts to oscillate or slosh. Such effects can be observed when a glass of water is handled carelessly and the fluid sloshes or even spills over the rims of the container. However, beer does not slosh as readily as water, which suggests that foam could be used to damp sloshing. In this work, we study experimentally the effect on sloshing of a liquid foam placed on top of a liquid bath. We generate a monodisperse two-dimensional liquid foam in a rectangular container and track the motion of the foam. The influence of the foam on the sloshing dynamics is experimentally characterized: only a few layers of bubbles are sufficient to significantly damp the oscillations. We rationalize our experimental findings with a model that describes the foam contribution to the damping coefficient through viscous dissipation on the walls of the container. Then we extend our study to confined three-dimensional liquid foam and observe that the behavior of 2D and confined 3D systems are very similar. Thus we conclude that only the bubbles close to the walls have a significant impact on the dissipation of energy. The possibility to damp liquid sloshing using foam is promising in numerous industrial applications such as the transport of liquefied gas in tankers or for propellants in rocket engines.

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

“…This result was expected for h = 0 as the deep water condition H > 2R is satisfied and the container size is well above the capillary length, 1 i.e., γ/ρgR 2 ≪ 1. This frequency is found unchanged when adding foam (0 < h < 6.5 mm), as observed in previous experiments 4 and discussed later on in the model derivation. The attenuation of the gravity waves is investigated by recording the motion X(t) of the water-foam interface at the azimuth corresponding to the largest wave oscillation.…”

“…2(a) for values of h ranging from 2.5 mm to 6.5 mm. We find D to be concave down and negatively correlated to h. In other words, the damping rate is greater with foam as evidenced by previous experiments 4 but also evidently increases as the amplitude of oscillations decreases. In particular, this result translates into the fact that the interface does not relax exponentially at a given rate, but instead its decay is progressively hastened.…”

“…4(a) we report the sublinear model (SLM) envelope a(t) in the particular, yet representative, case h = 4 mm. Its concave down behavior contrasts with the classical exponential relaxation adopted by previous works, 4 indicated by the blue line. This effect is due to an increase of the relative importance of sublinear friction forces compared to the inertial and restoring terms as the amplitude of oscillation decreases.…”

“…1), and explore the dramatic change in its mechanistic properties. It has been recently shown 4 that sloshing in a rectangular basin could be strongly damped by the addition of a shallow foam layer at the top. While foam is a complex medium with visco-elasto-plastic rheological properties, 5 this significant attenuation was attributed to friction between the foam and the wall, which dominates the dissipation in the foam bulk.…”

“…While foam is a complex medium with visco-elasto-plastic rheological properties, 5 this significant attenuation was attributed to friction between the foam and the wall, which dominates the dissipation in the foam bulk. 4 In this work, we focus our attention on the nonlinear nature of the dissipation occurring in the foam layer. This source of dissipation emanates from the relative displacement of the liquid channels separating adjacent foam bubbles, known as Plateau borders.…”