English
Related papers

Related papers: Dynamical Behaviour of a Soap Film Bridge Driven b…

200 papers

The complex behavior of drop deposition on a hydrophobic surface is considered by looking at a model problem in which the evolution of a constant-volume liquid bridge is studied as the bridge is stretched. The bridge is pinned with a fixed…

Soft Condensed Matter · Physics 2017-04-26 Bian Qian , Kenneth S. Breuer

We consider a two-phase elliptic-parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear…

Analysis of PDEs · Mathematics 2017-02-16 Friedrich Lippoth , Georg Prokert

We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…

Analysis of PDEs · Mathematics 2020-04-22 Olivier Glass , József Kolumbán , Franck Sueur

In this paper a reduced one-dimensional moving boundary model is studied that describes the evolution of a biofilm driven by the presence of a reaction limiting substrate. Global well-posedness is established for the resulting parabolic…

Analysis of PDEs · Mathematics 2025-05-30 Patrick Guidotti , Christoph Walker

A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…

Analysis of PDEs · Mathematics 2022-02-22 Philippe Laurençot , Christoph Walker

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied…

patt-sol · Physics 2009-10-30 Zahir A. Daya , Stephen W. Morris , John R. de Bruyn

This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the…

Mathematical Physics · Physics 2011-02-07 Ivana Bochicchio , Claudio Giorgi , Elena Vuk

We study the equilibrium problem of a system consisting by several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations. We prove the existence of a solution with minimum energy,…

Mathematical Physics · Physics 2017-11-23 Giulia Bevilacqua , Luca Lussardi , Alfredo Marzocchi

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…

Fluid Dynamics · Physics 2019-05-23 Hanna Holmgren , Gunilla Kreiss

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary…

Analysis of PDEs · Mathematics 2007-05-23 Daniel Coutand , Steve Shkoller

By revisiting the century-old problem of water bridge, we demonstrate that it is in fact dynamic and comprises of two coaxial water currents that carry different charges and flow in opposite directions. This spontaneous separation is…

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. The free boundary problem for MHD is an important problem not only for mathematical fluid dynamics…

Analysis of PDEs · Mathematics 2021-01-26 Kenta Oishi , Yoshihiro Shibata

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of…

Analysis of PDEs · Mathematics 2017-01-02 Gui-Qiang Chen , Jun Chen , Mikhail Feldman

A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…

Analysis of PDEs · Mathematics 2021-03-12 Katerina Nik

A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…

Analysis of PDEs · Mathematics 2014-09-10 Philippe Laurencot , Christoph Walker

We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…

Analysis of PDEs · Mathematics 2020-02-17 Sunčica Čanić , Marija Galić , Boris Muha

The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication…

Soft Condensed Matter · Physics 2026-04-29 Anirban Chatterjee , Yacine Amarouchene , Thomas Salez

We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…

Analysis of PDEs · Mathematics 2020-05-20 Julien Berestycki , Éric Brunet , James Nolen , Sarah Penington

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…

Soft Condensed Matter · Physics 2018-11-21 I. T. Davies

Recent work has shown that a M\"obius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a 'neck-pinching' boundary singularity. This behavior is unlike that of the catenoid, which…

Soft Condensed Matter · Physics 2014-07-07 Raymond E. Goldstein , James McTavish , H. Keith Moffatt , Adriana I. Pesci