Related papers: A phase-field description of surface-tension-drive…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…
We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…
Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
A Darcy-Cahn-Hilliard model coupled with damage is developed to describe multiphase-flow and fluid-driven fracturing in porous media. The model is motivated by recent experimental observations in Hele-Shaw cells of the fluid-driven…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying temperature is not constant. The aim of this…
The Phase-Field Method (PFM) is employed to simulate two-phase flows with the fully-coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations governing the temporal evolution. The methodology minimizes the total energy functional, accounting for…
An electric-field-induced phase transition and pattern formation in a binary dielectric fluid layer are studied using a coarse-grained free energy functional. The electrostatic part of the free energy is a nonlinear functional of the…
In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
A mesoscopic or coarse-grained approach is presented to study thermo-capillary induced flows. An order parameter representation of a two-phase binary fluid is used in which the interfacial region separating the phases naturally occupies a…
This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total)…
A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from…
In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur…
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…