Related papers: Nonlinear dynamics of phase separation in ultra-th…
Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation…
When sheets of layered material like C, WS$_2$ or BN are restricted to finite sizes, they generally form single- and multi-walled hollow nanoparticles in order to avoid dangling bonds. Using continuum approaches to model elastic deformation…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of two-phase flows or binary mixtures. In recent years, the dynamic boundary conditions for the Cahn-Hilliard equation have been proposed and…
We present a computational investigation of thin viscoelastic films and drops on a solid substrate subject to the van der Waals interaction force, in two spatial dimensions. The governing equations are obtained within a long-wave…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving…
We report on the effect of intermolecular forces on the fluctuations of supported liquid films. Using an optically-induced thermal gradient, we form nanometer-thin films of wetting liquids on glass substrates, where van der Waals forces are…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic…
It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
The paper presents a complete research cycle comprising continuum-based modeling, computational framework development, and validation setup to predict phase separation and surface hydrodynamics in lipid bilayer membranes. We starting with…
The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the…