The effect of mean flow speed in soap film channels

Abstract

The soap film channel has been developed as a model system for two-dimensional hydrodynamics, but its general applicability has been questioned because the mean flow speed is known to alter the experimental outcome considerably, for reasons that have not been examined. In this study, we experimentally investigate how the geometry of a vortex street in a flowing soap film varies with the mean flow speed, using both an inclined and a vertical channel. We quantify the geometry by the Kármán ratio $q$, the ratio of the transverse to the longitudinal spacing between vortices, and find that the variation of $q$ is accounted for by none of the object size, flow speed $u$, or film thickness $\delta$ alone. However, the data from both channels collapse onto a single curve when plotted against $u\sqrt{\delta }$, which is proportional to a Mach-like number $M\equiv u/v_m$, where $v_m$ is the Marangoni elastic wave speed. The measured collapse follows $q/q_0=1-M^2$, an $\mathcal{O}(M^2)$ correction characteristic of weakly compressible flow. The breakdown of Reynolds similitude in soap film channels therefore originates from the two-dimensional compressibility of the film.

15 pages, 5 figures. Heavily revised from v1. Base experimental data remain the same, but a different physical interpretation is presented. Vertical-channel data added. The retardation interpretation of v1 is superseded by a compressibility interpretation

References in corpus (5)

• Dynamics of a deformable body in a fast flowing soap film
• Surface tension of flowing soap films
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• Tunneling of Micro-sized Droplets Through a Flowing Soap Film
• Flow fields in soap films: relating surface viscosity and film thickness