The generation of two-dimensional vortices by transverse oscillation of a soap film

Abstract

An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20–200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, …, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parameter space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes.

Nonlinear generation of vorticity in thin smectic films

“…It is well known that the air around the soap film considerably changes its dynamics. Inspired by papers [5,6], we consider an influence of air to the motion of the thin smectic film and, particular, to the mechanism of the vorticity generation.…”

“…Fortunately, dynamics of the smectic films is simpler than one of the soap films since there is no analog of Marangoni waves [5] in the case. It allows us to construct a quantitative theory of the phenomenon.…”

“…Quantitative experiments were carried out at the end of the 20th century, see, e.g. [4,5], and a qualitative theoretical analysis is presented in the paper [6]. To our knowledge there is no quantitative theory of the phenomenon nowadays.…”

Coupled vibrations of a meniscus and liquid films

“…Moreover, several authors have shown that air inertia plays a major role on soap film vibrations (Couder, Chomaz & Rabaud, 1989, Rutgers et al, 1996, Afenchenko et al, 1998, Kosgodagan Acharige, Elias & Derec, 2014. Indeed, the film displaces a mass of air that scales like ρ a a 3 (the radius of the film a being the only relevant length scale, and ρ a being the density of air), whereas the mass of the film itself scales like ρea 2 .…”

“…In practice, in our experiments the latter is always dominant (the first two effects are approximately ten times weaker than the third one), and simple geometry allows us to correlate the position of the laser spot on the sensor to the local slope of the film in L. Given the range of excitation forcing frequencies tested in this work, the film features an axisymmetric deformation. We have checked that more complex, non-axisymmetric patterns, such as the ones shown in Couder, Chomaz & Rabaud, 1989, Afenchenko et al, 1998, Vega, Higuera & Weidman, 1998, Elias, Hutzler & Ferreira, 2007, appear on the film only above 200 Hz. This allows us to deduce, from this measure of a local slope, its entire profile, see equation (3.13) for the predicted axisymmetric profile.…”