Sudden Thickening in Flowing Soap Films

There is no difficulty in creating soap films that flow vertically downward under gravity at speeds of the order of a m/s. If the height of the film $L_0$ is of the order of 1 m or less, the film thickness $h(x)$ is a few microns (The coordinate $x$ increases downward below the injection point at $x$ = 0.) However if $L_0$ is of the order of 2 m, one finds that $h$ abruptly increases at a sharply defined value of $x =L$. In the experiments to be described, $L \simeq$ =.9 m. As expected, the vertical film velocity $v_x(x)$ correspondingly drops to a small fraction of its upstream value at $x \simeq L$. In the narrow transition region from thin to thick film at $x=L$, both $h(x)$ and the $v_x(x)$ oscillate at a well-defined frequency of the order of 1 Hz. The abrupt thickening is expected on the basis of singular perturbation theory (T. Tran, following paper).