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Soap bubbles occupy the rare position of delighting and fascinating both young children and scientific minds alike. Sir Isaac Newton, Joseph Plateau, Carlo Marangoni, and Pierre-Gilles de Gennes, not to mention countless others, have…
The paper is of scientific-methodical character. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings. An analytical approach based on relations to the…
Vertical soap films drain under the influence of gravity, as indicated by the downward motion of colorful horizontal interference fringes observed on their surfaces. In this study conducted with rectangular soap films, we experimentally…
Minimal surfaces with uniform curvature (or area) bounds have been well understood and the regularity theory is complete, yet essentially nothing was known without such bounds. We discuss here the theory of embedded (i.e., without…
We simulate the quasi-static motion of a spherical particle through a stable, horizontal soap film. The soap film subtends a fixed contact angle, in the range $10-135^\circ$, where it meets the particle. The tension and pressure forces…
Modern telescopes provide breathtaking images of nebulae, clouds and galaxies shaped by gravity-driven interactions between complex bodies. While such structures are prevalent on an astrophysical scale, they are rarely observed at the human…
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place…
We study the Plateau problem with a lower dimensional obstacle in $\mathbb{R}^n$. Intuitively, in $\mathbb{R}^3$ this corresponds to a soap film (spanning a given contour) that is pushed from below by a "vertical" 2D half-space (or some…
We follow the diffusive motion of colloidal particles of diameter $d$ in soap films of varying thickness $h$ with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of…
We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. We make soap films with a variety of water-glycerol mixtures and of differing thicknesses. The single-particle…
"The Life of a Free Soap Film" is a fluid dynamics video for the Gallery of Fluid Motion intended to showcase the novel experimental techniques that we have developed in our laboratory to study the retraction of planar liquid films of…
The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that…
Minimal surfaces and Einstein manifolds are among the most natural structures in differential geometry. Whilst minimal surfaces are well understood, Einstein manifolds remain far less so. This exposition synthesises together a set of…
We classify cylindrical surfaces in the Euclidean space whose mean curvature is a $n$th-power of the distance to a reference plane. The generating curves of these surfaces, called $n$-elastic curves, have a variational characterization as…
We combine experiments and theoretical derivations to study the evolution of a stretched soap bubble and compare it with an open film to highlight the effect of volume conservation. We identify a critical length for both surfaces, beyond…
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…
We provide, in the setting of Gauss' capillarity theory, a rigorous derivation of the equilibrium law for the three dimensional structures known as Plateau borders which arise in "wet" soap films and foams. A key step in our analysis is a…
A soap film, or a flexible membrane without bending and torsional stiffness, that is confined in a cylinder is shown to be susceptible to a surface-tension-driven instability when it is stretched or twisted. This leads to its breakdown and…
Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. They can…
Liquid foams are widely used in industry for their high effective viscosity, whose local origin is still unclear. This Letter presents new results on the extension of a suspended soap film, in a configuration mimicking the elementary…