Related papers: A Geometric Diffuse-Interface Method for Droplet S…
Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque…
In this work we derive a class of geometric flow equations for metric-scalar systems. Thereafter, we construct them from some general string frame action by performing volume-preserving fields variations and writing down the associated…
The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…
The coalescence of droplets plays a crucial role in nature and modern technology. Various experimental and theoretical studies explored droplet dynamics in 3D and on 2D solid or liquid substrates. In this paper, we demonstrate the…
Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…
Drops on a free-flow/porous-medium-flow interface have a strong influence on the exchange of mass, momentum and energy between the two macroscopic flow regimes. Modeling droplet-related pore-scale processes in a macro-scale context is…
We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global…
In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framework is introduced aiming for describing such processes as…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details and an implementation of higher-order spatial and temporal…
Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the…
Although the drainage and spreading processes of thin liquid films on substrates have received growing attention during the last decades, the study of three-dimensional cases is limited to a few studies on flat and axisymmetric substrates.…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
The role of incoherent tunneling in the diffusion of light atoms on surfaces is investigated. With this purpose, a Chudley-Elliot master equation constrained to nearest neighbors is considered within the Grabert-Weiss approach to quantum…
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
This work outlines a new three-dimensional diffuse interface finite volume method for the simulation of multiple solid and fluid components featuring large deformations, sliding and void opening. This is achieved by extending an existing…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the…
The study of the shape of droplets on surfaces is an important problem in the physics of fluids and has applications in multiple industries, from agrichemical spraying to microfluidic devices. Motivated by these real-world applications,…