Related papers: New Epitaxial Thin Film Models and numerical appro…
We study spinodal phase separation in unstable thin liquid films on chemically disordered substrates via simulations of the thin-film equation. The disorder is characterized by immobile patches of varying size and Hamaker constant. The…
A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are…
In this paper we derive consistent shallow water equations for thin films of power law fluids down an incline. These models account for the streamwise diffusion of momentum which is important to describe accurately the full dynamic of the…
The metastable orthorhombic phase of hafnia is generally obtained in polycrystalline films, whereas in epitaxial films, its formation has been much less investigated. We have grown Hf0.5Zr0.5O2 films by pulsed laser deposition, and the…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
As an organic semiconductor and a prototypical acceptor molecule in organic photovoltaics, C$_{60}$ has broad relevance to the world of organic thin film electronics. Although highly uniform C$_{60}$ thin films are necessary to conduct…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
We examine the applicability of the continuum model to describe the surface morphology of a hetero-growth system: compositionally-graded, relaxed GeSi films on (001) Si substrates. Surface roughness versus lateral dimension was analyzed for…
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single…
A mathematical model is developed to analyze the growth/decay rate of surface perturbations of an ultrathin metal film on an amorphous substrate (SiO_{2}). The formulation combines the approach of Mullins [J. Appl. Phys. v30, 77, 1959] for…
We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys…
Experiments of particle-laden inclined film flow [Zhou, Dupuy, Bertozzi, and Hosoi, Phys. Rev. Lett. 94 (2005)] have displayed different settling behaviors depending on the particle concentration $\phi$ and angle of inclination $\theta$, in…
High quality epitaxial thin-films of EuTiO3 have been grown on the (001) surface of SrTiO3 using pulsed laser deposition. In situ x-ray reflectivity measurements reveal that the growth is two-dimensional and enable real-time monitoring of…
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model involves a partial differential equation describing the…
Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant…
The experimentally measured resistivity of Co(0001) and Ru(0001) single crystal thin films, grown on c-plane sapphire substrates, as a function of thickness is modeled using the semiclassical model of Fuchs-Sondheimer. The model fits show…
The epitaxial growth of complex oxide thin films provide three avenues to generate unique properties: the ability to influence the 3-dimensional structure of the film, the presence of a surface, and the generation of an interface. In all…
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.…
In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid…
We review recent experiments on dewetting thin films of evaporating colloidal nanoparticle suspensions (nanofluids) and discuss several theoretical approaches to describe the ongoing processes including coupled transport and phase changes.…