Propagation of a transverse wave on a foam microchannel

¹ Laboratoire Matière et Systèmes Complexes (MSC) - Université Paris-Diderot, CNRS UMR 7057 - Paris, France
² Sorbonne Universités, UPMC Université Paris 6, UFR 925 - Paris, France

Received: 1 August 2015
Accepted: 5 November 2015

Abstract

In a dry foam, soap films meet by three in the liquid microchannels, called Plateau borders, which contain most of the liquid of the foam. We investigated here the transverse vibration of a single Plateau border isolated on a rigid frame. We measured and we computed numerically and analytically the propagation of a transverse pulse along the channel in the 20–2000 Hz frequency range. The dispersion relation shows different scaling regimes, which provide information on the role of inertial and elastic forces acting on the Plateau border. At low frequency, the dispersion relation is dominated by the vibration of the air set into motion by the transverse vibration of the adjacent soap films. The inertia of the liquid in the Plateau border plays a role at high frequency, the critical frequency separating the low-frequency and the high-frequency regimes being a decreasing function of the radius R of the Plateau border.