Related papers: Analytical validation of the Yound-Dupr\'e law for…
We investigate the question of stability of a solid thin film which experiences external interactions such as van der Waals forces from a contacting surface or forces from an external electric field. Both perfectly elastic and viscoelastic…
For uniaxial easy axis films, properties of magnetic domains are usually described within the Kittel model, which assumes that domain walls are much thinner than the domains. In this work we present a simple model that includes a proper…
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…
Motivated by models for thin films coating cylinders in two physical cases proposed by V.I. Kerchman and A.L. Frenkel, we analyze the dynamics of corresponding thin film models. The models are governed by nonlinear, fourth-order,…
This work tackles the problem of achieving consistent drying rates of a solution film deposited on a $20\,\rm{cm}$-wide substrate ($\approx $ silicon-wafer size) that is driven under a narrow air flow ejected by a slot nozzle (or "air…
The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite…
We develop a unified theoretical framework for thin-film hydrodynamics on inclined solid substrates, integrating capillarity, intermolecular forces, gravitational symmetry breaking, confined transport and stochastic wetting into a single…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
We study the dynamics of a small solid particle arising from the dewetting of a thin film on a curved substrate driven by capillarity, where mass transport is controlled by surface diffusion. We consider the case when the size of the…
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, it is hard to treat the Navier--Stokes…
We deal with a nonconvex and nonlocal variational problem coming from thin-film micromagnetics. It consists in a free-energy functional depending on two small parameters $\eps$ and $\eta$ and defined over $S^2-$vector fields $m$ that are…
We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system…
A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical…
We study the static and dynamic wetting of adaptive substrates using a mesoscopic hydrodynamic model for a liquid droplet on a solid substrate covered by a polymer brush. First, we show that on the macroscale Young's law still holds for the…
Thin liquid films on surfaces are part of our everyday life, they serve e.g. as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of…
Compression-induced buckling instability of metal thin films on a compliant base result in surface wrinkles. A stiff thin film, perfectly bonded to an infinitely deep pre-stretched dielectric elastomer (DE) substrate, is considered. Linear…
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 the dynamical properties of spherical galaxies with surface luminosity profile described by the R^{1/m}-law, in which a variable degree of orbital anisotropy is allowed. The parameter m for the present models covers the range…
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale…
We perform a scaling analysis of the mean velocity of extended magnetic domain walls driven in ultrathin Pt/Co/Pt ferromagnetic films with perpendicular anisotropy, as a function of the applied external field for different film-thicknesses.…