Related papers: Soap film spanning an elastic link
We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod…
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…
Kirchhoff's kinetic analogy relates the equilibrium solutions of an elastic rod or strip to the motion of a spinning top. In this analogy, time is replaced by the arc length parameter in the phase portrait to determine the equilibrium…
The surface tension of flowing soap films is measured with respect to the film thickness and the concentration of soap solution. We perform this measurement by measuring the curvature of the nylon wires that bound the soap film channel and…
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…
The perturbative stability of catenoidal soap films formed between parallel, equal radii, coaxial rings is studied using analytical and semi-analytical methods. Using a theorem on the nature of eigenvalues for a class of Sturm--Liouville…
We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their…
We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
We study a free boundary problem describing a tubular soap film bridge driven by an electrostatic force. To realize the electrostatic force, the soap film bridge is placed inside an outer metal cylinder and a voltage difference between this…
We study a toy model for electrolytic soap films, the two-dimensional two-component plasma. This model is exactly solvable for a special value of the coulombic coupling constant $\beta q^2=2$. This allows us to compute the disjoining…
Determining the equilibrium configuration of an elastic M\"{o}bius band is a challenging problem. In recent years numerical results have been obtained by other investigators, employing first the Kirchhoff theory of rods and later the…
We derive the variational limiting theory of thin films, parallel to the F\"oppl-von K\'arm\'an theory in the nonlinear elasticity, for films that have been prestrained and whose thickness is a general non-constant function. Using…
Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable $(n-2)$-dimensional submanifold $M$ of $\R^n$. If $M$ is connected, we say a compact set $X$ "spans" $M$ if $X$…
The motion of an elastic solid inside of an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated,…
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…
We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form…
Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film…