Related papers: Boundary Singularities Produced by the Motion of S…
We study the soap film capillarity problem, in which soap films are modeled as sets of least perimeter among those having prescribed (small) volume and satisfying a topological spanning condition. When the given boundary is the closed…
In hydrodynamic topological transitions, one mass of fluid breaks into two or two merge into one. For example, in the honey-drop formation when honey dripping from a spoon, honey is extended to separate into two as the liquid neck bridging…
The duality between deformations of elastic bodies and non-inertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly-curved liquid film is…
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…
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…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…
We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the M\"obius strip and the catenoid. If the strip is non-orientable this transition is topologically frustrated, and…
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.
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…
Cox & Jones recently devised and studied an interesting variant of the classical Plateau problem, a variant in which a helical soap film is confined to a cylindrical tube with circular cross-section. Through experiments, numerics, and some…
The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air,…
In 1904, while experimenting with high-speed photography, Lucien Bull recorded a pellet passing through a soap bubble. We investigate the dynamics that allow for a rigid body to pass through a hemispherical soap film without rupturing it.…
We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a…
The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface…
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…
We develop a general framework for the description of instabilities on soap films using the Bj\"orling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-\kappa^2$. Using the cone total curvature $TC(\Gamma)$ of a graph $\Gamma$ which was introduced…
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…
We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction…