Related papers: Motion of three-dimensional elastic films by aniso…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…
A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel…
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…
A simplified, pseudoplastic rheology characterized by constant viscosity plateaus above and below a transition strain rate is applied to axisymmetric, gravitationally driven spreading of a thin fluid film with constant volume flux source in…
Substrate defects crucially influence the onset of sliding drop motion under lateral driving. A finite force is necessary to overcome the pinning influence even of microscale heterogeneities. The depinning dynamics of three-dimensional…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existence of smooth flow, starting from a regular droplet and…
We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We…
The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution…
For the development of porous materials with improved transport properties, a key missing ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying…
We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films identified by the authors in the companion paper [Davoli E., Piovano P., Derivation of a heteroepitaxial thin-film model.…
We study existence and long-time behavior of weak solutions to a thin-film equation with a confinement potential and a second-order degenerate diffusion term. It is known that in absence of second order effects, solutions for general…
The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with…
The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We…
The roughness of vapor-deposited thin films can display a nonmonotonic dependence on film thickness, if the smoothening of the small-scale features of the substrate dominates over growth-induced roughening in the early stage of evolution.…
We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that…
Given a planar crystalline anisotropy, we study the crystalline elastic flow of immersed polygonal curves, possibly also unbounded. Assuming that the segments evolve by parallel translation (as it happens in the standard crystalline…
This paper is devoted to the asymptotic analysis of a thin film equation which describes the evolution of a thin liquid droplet on a solid support driven by capillary forces. We propose an analytic framework to rigorously investigate the…