Solitary-like waves in a liquid foam microchannel

Abstract

International audiencePlateau borders are liquid microchannels located at the contact between three bubbles in liquid foams. They are stable, deformable and can be thought of as quasi-1D model systems to study surface waves in fluid dynamics. We show that the burst of a bubble trapped in a PB produces local constrictions which travel along the liquid channel at constant velocity, without significant change in shape. These patterns are reminiscent of the depression solitary waves encountered in nonlinear systems. By coupling flow inertia to capillary stresses, we derive a simple model that admits solitonic solutions, which we characterized numerically and analytically in the limit of small deformation. These solutions capture most of the features observed experimentally

Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves

“…The KdV equation in the variable can then be derived from (5.8) as The KdV equation in the width variable () then reads We then have a soliton solution (5.14) that reads, for and : Experimentally, Bouret et al. (2016) found , whereas we have , which yields a relative error of %, improving the model used by Argentina et al. (2015), who found , namely a relative error of %.…”

“…The method we have presented to derive the KdV equation is generic and it can be applied to other free-interface systems with a cylinder-type geometry. As an illustration of the generality of the method, we will consider the case of Plateau borders, along which the observation of the propagation of depression solitary waves has been reported in experiments using soap films (Argentina et al 2015;Bouret et al 2016).…”

Melde’s Experiment on a Vibrating Liquid Foam Microchannel

“…Taking λ (1.7-6.7 cm in this study) instead of R for the length scale leads to a higher value and the same conclusion holds. The existence of inertial flows inside PBs has recently been proved and the coupling between the capillary and inertial effects shown to exhibit highly nonlinear features such as the propagation of hydraulic jumps and solitons [15][16][17]. Assuming a capillaryinertial mechanism, we write a Bernoulli-like relation by balancing a typical kinetic energy per volume ρ(A P B f ) 2 and the pressure difference…”