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We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible…

Analysis of PDEs · Mathematics 2025-12-12 Mario Bukal , Igor Kukavica , Linfeng Li , Boris Muha

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described…

Computational Engineering, Finance, and Science · Computer Science 2022-01-05 Mostafa Faraji , Alexander Seitz , Christoph Meier , Wolfgang A. Wall

In this report we formulate and analyse a mathematical model describing the evolution of a thin liquid film coating a wire via an extrusion process. We consider the Navier-Stokes equations for a 2D incompressible Newtonian fluid coupled to…

Fluid Dynamics · Physics 2021-01-08 Maria Aguareles , Francesc Font , Tim Myers , Jordi Ripoll

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and…

Soft Condensed Matter · Physics 2012-04-11 Desislava Todorova , Uwe Thiele , Len M. Pismen

We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…

Optimization and Control · Mathematics 2024-07-10 Oscar A. Holroyd , Radu Cimpeanu , Susana N. Gomes

In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary…

Analysis of PDEs · Mathematics 2019-07-15 Ian Tice , Lei Wu

The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to…

Classical Physics · Physics 2009-11-13 Henri Gouin

In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…

Fluid Dynamics · Physics 2015-06-16 Kyle Mahady , Shahriar Afkhami , Lou Kondic

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation.…

Analysis of PDEs · Mathematics 2008-05-08 Lennon O Naraigh , Jean-Luc Thiffeault

In recent years, there has been a considerable interest in the mechanics of soft objects meeting fluid interfaces (elasto-capillary interactions). In this work we experimentally examine the case of a fluid resting on a thin film of rigid…

Soft Condensed Matter · Physics 2018-04-24 Timothy Twohig , Sylvio May , Andrew B. Croll

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…

Analysis of PDEs · Mathematics 2012-10-23 Sebastian Jachalski , Robert Huth , Georgy Kitavtsev , Dirk Peschka , Barbara Wagner

We consider a power-law thin-film equation for strongly shear-thinning fluids. Weak solutions to this equation have been constructed more than twenty years ago by Ansini and Giacomelli. Here, we pass over to analyzing strong solutions with…

Analysis of PDEs · Mathematics 2026-04-27 Manuel V. Gnann , Christina Lienstromberg , Katerina Nik

In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…

Analysis of PDEs · Mathematics 2020-10-30 Tania Pernas-Castaño , Juan J. L. Velázquez

We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact…

Numerical Analysis · Mathematics 2024-07-09 T. H. B. Demont , S. K. F. Stoter , C. Diddens , E. H. van Brummelen

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a Lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects…

Fluid Dynamics · Physics 2009-11-13 R. Ledesma-Aguilar , A. Hernandez-Machado , I. Pagonabarraga

Consider the thin-film equation $h_t + \left(h h_{yyy}\right)_y = 0$ with a zero contact angle at the free boundary, that is, at the triple junction where liquid, gas, and solid meet. Previous results on stability and well-posedness of this…

Analysis of PDEs · Mathematics 2020-08-25 Manuel V. Gnann , Slim Ibrahim , Nader Masmoudi

We investigate experimentally the receding of a contact line when a Peltier module is pulled out of a water bath at constant speed, while a ice layer is also growing at constant speed on the Peltier module. A steady regime is therefore…

Fluid Dynamics · Physics 2024-09-04 Rodolphe Grivet , Axel Huerre , Thomas Séon , Laurent Duchemin , Christophe Josserand

We study a nonlinear, moving boundary fluid-structure interaction problem between an incompressible, viscous Newtonian fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The…

Analysis of PDEs · Mathematics 2016-03-07 Boris Muha , Suncica Canic

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier-Stokes equations for the fluid…

Fluid Dynamics · Physics 2021-08-11 Quan Zhao , Weiqing Ren , Zhen Zhang