Related papers: Diffuse interface models of locally inextensible v…
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a…
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…
Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Particles diffusing near interfaces face anisotropic resistance to motion due to hydrodynamic interactions. While this has been extensively studied near \textit{hard} interfaces since the works of Lorentz and Brenner, our understanding of…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
This work demonstrates a computational framework for simulating vaporizing, liquid-gas flows. It is developed for the general vaporization problem which solves the vaporization rate based as from the local thermodynamic equilibrium of the…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Marangoni effects. The governing system consists of modified…
A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
We derive and analyze a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. Our system consists of a Navier--Stokes--Cahn--Hilliard model in the bulk that is coupled to a surface…
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…
By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier--Stokes system with a convective nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently proved…
We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an…
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…