Related papers: Covers, soap films and BV functions

We consider a porous solid covered with a water film (or with a drop) in situations where the liquid is pumped in, either spontaneously (if the porous medium is hydrophilic) or mechanically (by an external pump). The dynamics of dewetting…

We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining…

Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean…

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we…

We present a quasi-two dimensional model of flowing soap films that bears striking similarity to the compressible Navier-Stokes equations. The variation in soap film thickness that is commonly used for flow visualization in experiments is…

We study generalized minimizers in the soap film capillarity model introduced in [arXiv:1807.05200,arXiv:1907.00551]. Collapsed regions of generalized minimizers are shown to be smooth outside of dimensionally small singular sets, which are…

By integrating the Young-Laplace equation, including the effects of gravity, we have calculated the equilibrium shape of the two-dimensional Plateau borders along which a vertical soap film contacts two flat, horizontal solid substrates of…

Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the…

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…

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…

The interaction that occurs between a light solid object and a horizontal soap film of a bamboo foam contained in a cylindrical tube is simulated in 3D. We vary the shape of the falling object from a sphere to a cube by changing a single…

In this paper, I consider a thin suspended liquid film, surrounded by a different fluid. Examples of such a system are soap films and liquid crystal films, surrounded by air. They are considered good models for two dimensional fluid…

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…

In this paper, we study the formation process of a soap bubble by blowing soap film. Both bubble diameter and formation position were investigated in experiments. We found that the ratio between bubble size and soap film column is constant,…

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…

Can you fill R^n with a froth of "soap bubbles" that meet at most n at a time? Not if they have bounded diameter, as follows from Lebesgue's Covering Theorem. We provide some related results and conjectures.

We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general convex curvature functions inside general Riemannian manifolds.…

By employing the method of moving planes in a novel way we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films.

"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…

All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning and breaking of soap bubble neck when it is stretched. To contrast with the more widely studied film whose boundaries are…