Line Tension in a Thick Soap Film

The thickness of freshly made soap films is usually in the micron range, and interference colors make thickness fluctuations easily visible. Circular patterns of constant thickness are commonly observed, either a thin film disc in a thicker film or the reverse. In this Letter, we evidence the line tension at the origin of these circular patterns. Using a well controlled soap film preparation, we produce a piece of thin film surrounded by a thicker film. The thickness profile, measured with a spectral camera, leads to a line tension of the order of ${10}^{-10}\mathrm{N}$ which drives the relaxation of the thin film shape, initially very elongated, toward a circular shape. A balance between line tension and air friction leads to a quantitative prediction of the relaxation process. Such a line tension is expected to play a role in the production of marginal regeneration patches, involved in soap film drainage and stability.

Figure 1

Experimental setup and notations used in the text. (a) Image of the film recorded by the top camera. (b) Schematic view of the setup. The black and green thick lines represent, respectively, the static and mobile edges of the frame. The thin film [colored domain in (a), light blue in (b)] is separated from the light gray thick film by the red contour $\mathcal{C}$. (c) Schematic thickness profile along $\mathcal{L}$, in the vicinity of $\mathcal{C}$, on the right-hand side of (b).

Figure 2

Top view of the film before, during, and after deformation, at times $[-1,-0.6,0,1,3,6]\mathrm{s}$. The colored central part is the thin film, the gray part is the thick film. The black boundary is the meniscus.

Figure 3

Shape of the thin film as a function of time. (a) $L$ is half its diameter measured in the $x$ direction, and (b) $A$ is its area. As for the other figures, the data are averaged over 13 experiments, and the shaded area represents the standard deviation. (c) Example of thickness profiles at times 0 s (blue), 0.5 s (green), 1 s (yellow), and 1.5 s (red). The experimental resolution is indicated by the gray zone, and the width of the thin film is indicated by the continuous line at thickness 0. The dotted lines are parabolic interpolations between the measured domains.

Figure 4

(a) Line tension $T$ as a function of time, determined from the thickness profiles using Eq. (6), with ${\ell }_{-\infty }=0$, ${\ell }_{\infty }=3\mathrm{mm}$ and $\xi =y$. The vertical dotted lines are color-matched in time with the thickness profiles of Fig. 3. Inset: partial values of the tension as a function of the integration upper bound ${\ell }_{\mathrm{int}}$, obtained for the profile at $t=1\mathrm{s}$. The tension reaches 80% of its total value for ${\ell }_{\mathrm{int}}={\ell }_{80}$. (b) Mapping of the observed flow on the problem solved in [15]. The thickness transition is shown in gray, with its center line ${\mathcal{C}}^{*}$ (bold black line), at the distance ${\ell }_{80}/2$ outside $\mathcal{C}$ (red line). The subdomains ${\mathrm{\Omega }}^{\pm }$ are the red discs.

Figure 5

Experimental value of the tip velocity $d{L}^{\exp }/dt$, divided by its theoretical value given by Eq. (8), in which $R^{*}=R+{\ell }_{80}/2$ (bold line), $R^{*}=R$ (bottom thin line), and $R^{*}=R+{\ell }_{80}$ (top thin line). Each curve is plotted with a shaded area showing its standard deviation.