相关论文: A phase-field model for the evaporation of thin fi…
It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…
Numerical Simulations are employed to create amorphous nano-films of a chosen thickness on a crystalline substrate which induces strain on the film. The films are grown by a vapor deposition technique which was recently developed to create…
Various experimental settings that involve drying solutions or suspensions of nanoparticles -- often called nanofluids -- have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks…
This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of…
Thin films are usually obtained by depositing atoms with a continuous flux. We show that using a chopped flux changes the growth and the morphology of the film. A simple scaling analysis predicts how the island densities change as a…
Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…
Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the…
Water evaporation is critically important for hydrogels in open-air applications, but theoretically modeling is difficult due to the complicated intermolecular interactions and sustained deformation. In this work, we construct a simplified…
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
In this paper, we address the well-posedness of an evaporation model for a spherical liquid droplet taking into account the convective impact of an air flow in the ambient gas phase. From a mathematical perspective, we are dealing with a…
This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition…
The dynamics of the interaction of a system of two thin volatile liquid droplets resting on a soft viscoelastic solid substrate are investigated theoretically. The developed model fully considers the effect of evaporative cooling and the…
Nanoporous structures including single nanopores and nanoporous membranes have been utilized as a platform to study fundamental liquid-vapor phase change heat transfer (PCHT) processes as well as a promising candidate for high flux heat…
When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size,…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
We consider a free surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a setup where the heat absorption depends on the local film thickness. Our focus is on modeling film evolution while…
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…
Gravitational settling of a droplet in air onto a soft substrate is a ubiquitous event relevant to many natural processes and engineering applications. We study this phenomenon by developing a three-phase lubrication model of droplet…
The bi-layered structure has drawn a wide interest due to its good performance in solar steam generation. In this work, we firstly develop a calculation model which could give a good prediction of experimental results. Then, this model is…
We propose the generalization of the thin film equation (TFE) to arbitrarily many immiscible liquid layers. Then, we provide different pathways for deriving the hydrodynamic pressure within the individual layers, showing how to understand…