Influence of bubble size and thermal dissipation on compressive wave attenuation in liquid foams

Abstract

Acoustic or blast wave absorption by liquid foams is especially efficient and bubble size or liquid fraction optimization is an important challenge in this context. A resonant behavior of foams has recently been observed, but the main local dissipative process is still unknown. In this paper, we evidence the thermal origin of the dissipation, with an optimal bubble size close to the thermal boundary layer thickness. Using a shock tube, we produce typical pressure variation at time scales of the order of the millisecond, which propagates in the foam in linear and slightly non-linear regimes.

Ultrasound transmission through monodisperse 2D microfoams

“…Regardless of the definition used for the bubble radius R, thermal losses turn out to contribute only marginally to the total attenuation. A similar result had already been observed by Pierre et al for 3D polydisperse foam samples [7], while thermal losses had been found dominant in other experiments [5,6].…”

“…On the one hand, studies on macroscopic polydisperse foam samples have demonstrated the highly dispersive behavior of liquid foams at ultrasonic frequencies, due to the mechanical coupling between the liquid network and the thin films separating the bubbles [3,4]. Some studies have identified thermal losses as the main dissipation source in liquid foams [5,6], while another work evidenced an additional dissipation mechanism at low frequencies [7]. However, the bulk structure of those 3D samples is not known precisely, and assumptions have to be made in order to relate the foam structure to its acoustical properties.…”

Investigating the origin of acoustic attenuation in liquid foams

“…If one notes k the complex wavenumber, it can be shown that the reduced thermal attenuatioñ α = Im(k)/Re(k) is expected to scale like ωR 2 /D th , where ω is the angular frequency, D th the thermal diffusivity of the gas, and R the typical radius of the bubbles in the foam. The problem is that, if the scaling law in ωR 2 was indeed observed in several experimental studies [5,6], other authors pointed out that the order of magnitude of the thermal attenuation was not enough to explain the experimental results [7,8]. Even more intriguing, experiments with different types of gas showed that theα ∼ 1/D th scaling law was not respected [9].…”

“…There is still a debate on whether dissipation is mainly viscous or thermal. Some authors claim that thermal losses dominate, and can explain their observation [5,6]. Their argument is based a email: juliette.pierre@upmc.fr b email: valentin.leroy@univ-paris-diderot.fr on a scaling law.…”

Melde’s Experiment on a Vibrating Liquid Foam Microchannel

“…Their acoustic properties are not intermediate between the ones of their constitutive liquid and gas [2]. Foams can both act as metamaterials for given frequencies [3] and be used as efficient barriers against large amplitude or blast waves [4,5]. They also propagate shear waves in bulk [6,7] or at the interfaces [8], and the existence of supershear Rayleigh waves has been proved following the impact of a projectile at high velocity [8].…”