Related papers: Analytical validation of the Yound-Dupr\'e law for…
Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film…
Coherent epitaxial growth allows to produce crystalline films with strained structures which are unstable in the bulk. Thereby, the relationship between the lattice parameters of the overlayer in the interface plane, $(a,b)$, and its…
Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsen the product quality. In this article, we investigate the stability of a thin liquid…
We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic…
In this paper we present a theoretical model for the dewetting of ultra-thin polymer films. Assumming that the shear-thinning properties of these films can be described by a Cross-type constitutive equation, we analyze the front morphology…
Thin liquid films exhibit rich instability and rupture dynamics that critically impact coating performance across many applications. In this work, we use the lattice Boltzmann method (LBM) simulations within a lubrication-theory framework…
A quantitative mathematical model for the critical thickness of strained epitaxial metal films is presented, at which the magnetic moment experiences a reorientation from in-plane to perpendicular magnetic anisotropy. The model is based on…
Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is desired in applications where the…
We study a higher-dimensional thin film equation that incorporates competitive effects between aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and aggregation by backward second-order degenerate diffusion,…
Thin film condensation is commonly present in numerous natural and artificial processes. Phase-change driven passive heat spreaders such as heat pipes, which are widely used in electronics cooling, employ a continuous condensation process…
We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform…
The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped…
The Young's modulus of a two-dimensional truss-like structure is simulated by using the finite element method. A power-law expression is proposed for the effective Young's modulus of the system. The obtained numerical results are compared…
Experimental results for adhesive contacts on substrates coated with elastomeric thin films have recently been obtained by C. Tardivat and L. L\'{e}ger (J. Adhesion Sci. Technol. 15 1055-1078 (2001)) by the so-called JKR test, which…
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmetric exchange as well as an anisotropy term. We devise an…
The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak…
In this work, we study thin-film limits of the full three-dimensional Ginzburg-Landau model for a superconductor in an applied magnetic field oriented obliquely to the film surface. We obtain Gamma-convergence results in several regimes,…
Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low…
The stability of thin liquid films on a surface depends on the excess free energy of the system involving various short-range and long-range interactions. In an unstable condition, thin liquid films may dewet into multiple small-sized…
The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel…