Surface tension profiles in vertical soap films

Surface tension profiles in vertical soap films are experimentally investigated. Measurements are performed by introducing deformable elastic objets in the films. The shape adopted by those objects once set in the film is related to the surface tension value at a given vertical position by numerically solving the adapted elasticity equations. We show that the observed dependency of the surface tension versus the vertical position is predicted by simple modeling that takes into account the mechanical equilibrium of the films coupled to previous thickness measurements.

Figure 1

Illustrative picture of an elastic rectangle plugged into a vertical soap film, taken at an angle of ${60}^{\circ }$ with respect to the normal to the film, so that both the inflated rectangle and the interference pattern are visible. Note that the deflection measurements (see text for details) are performed with a normal incidence with respect to the film interfaces, as illustrated in Fig. 2.

Figure 2

Left: Sketch of the experimental setup. The slit pipe, the soap film, the camera, and the deflected object are represented. Right: Schematic of the bottom meniscus linking the film to the bottom of the frame (not to scale). See next sections for details.

Figure 3

Left: Geometrical characteristics of the rectangles used to perform surface tension measurements in soap films ($l=24\mathrm{mm},w=12\mathrm{mm},\zeta =3\mathrm{mm}$, and $\epsilon =0.8\mathrm{mm}$). Right: Typical shape adopted by rectangles when introduced in the soap films.

Figure 4

Left: Superposition of images of a rectangle when set inside and outside the soap film, as used to measure $\delta$ versus $H$. Right: Enlarged view of the bottom part. The dashed lines indicate the position of the bottom part of the rectangle with and without the soap film inside the rectangle, illustrating the existence of $l^{\prime }$.

Figure 5

Nondimensional deflection $\delta /l$ vs the control parameter $E{I}_0/2\gamma l^3$ as obtained by solving Eqs. (4) and (5) as previously described.

Figure 6

Thickness profiles vs the vertical coordinate for the different $Q$ values involved in our experiments. The error bar represents the typical dispersion of the measurements of $e\left(H\right)$ for a fixed value of $Q$. The inset represents the evolution of $a$ (see text) with $Q$.

Figure 7

Surface tension profiles in vertical soap films as a function of the vertical position. The solid line is Eq. (10) expressed for the mean $a$ value. The dashed lines show the dispersion of this expression around the mean curve. Values of $\gamma <{\gamma }_0$ are not physically permitted and correspond to the grayed area. The error bar represents the typical magnitude of the standard deviation linked to the measurements characterized by a given $(H,Q)$ couple.