Related papers: Cross-diffusion systems coupled via a moving inter…
The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding…
This paper deals with the analysis of qualitative properties involved in the dynamics of Keller-Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study…
The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
A simple fluid, described by point-like particles interacting via the Lennard-Jones potential, is considered under confinement in a slit geometry between two walls at distance Lz apart for densities inside the vapor-liquid coexistence…
We propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous…
In this work, the van der Waals fluid model, a diffuse-interface model for liquid-vapor two-phase flows, is numerically investigated. The thermodynamic properties of the van der Waals fluid are first studied. Dimensional analysis is…
We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different…
Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
This paper presents a method for modelling interfacial mass transfer in Interface Capturing simulations of two-phase flow with phase change. The model enables mechanistic prediction of the local rate of phase change at the vapour-liquid…
Curved fluid interfaces are investigated on the nanometre length scale by molecular dynamics simulation. Thereby, droplets surrounded by a metastable vapour phase are stabilized in the canonical ensemble. Analogous simulations are conducted…
In this contribution, we derive a gas-liquid two-scale multi-fluid model with capillarity effects to enable a novelinterface regularization approach for multi-fluid models. As this unified modelling is capable of switching from theinterface…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…