Related papers: Dynamical Behaviour of a Soap Film Bridge Driven b…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in…
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…
An isolated charge-neutral drop suspended in an unbounded medium does not migrate in a uniform DC electric field. A nearby wall breaks the symmetry and causes the drop to drift towards or away from the boundary, depending on the electric…
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…
A model of unsteady filtration (seepage) in a porous medium with capillary retention is considered. It leads to a free boundary problem for a generalized porous medium equation where the location of the boundary of the water mound is…
Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that…
A variational model is used to study the stability of a soap film spanning a flexible loop. The film is modeled as a fluid surface endowed with constant tension and the loop is modeled as an elastic rod resistant to both bending and twist.…
We investigate the sliding dynamics of a millimeter-sized particle trapped in a horizontal soap film. Once released, the particle moves toward the center of the film in damped oscillations. We study experimentally and model the forces…
It is well known that electro-hydrodynamical effects in freely suspended liquid films can flow the liquid. Here we report a purely electrically driven rotation in water and some other liquid suspended films with full control on the velocity…
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 a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a…
We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities, using a multicomponent pseudopotential lattice Boltzmann method. For…
The interaction of electrical fields and liquids can lead to phenomena that defies intuition. Some famous examples can be found in Electrohydrodynamics as Taylor cones, whipping jets or non-coalescing drops. A less famous example is the…
We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i)…
We study a free boundary problem which is motivated by a particular case of the flow of a non-Newtonian fluid, with a pressure depending yield stress given by a Drucker-Prager plasticity criterion. We focus on the steady case and…
We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…
We have observed that a rotating liquid soap film generates electricity when placed between two non-contact electrodes with a sufficiently large potential difference. In our experiments suspended liquid film (water + soap film) is formed on…
This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…