Related papers: A Cahn-Hilliard-Biot system and its generalized gr…
In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering and environmental protection. This study…
We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between…
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 consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized…
Consider the consolidation process typical of soils, this phenomenon is expected not to exhibit a unique state of equilibrium, depending on the \textit{external loading} and the constitutive parameters. Beyond the standard solution, also…
The paper deals with a phase field system of Cahn-Hilliard type. For positive viscosity coefficients, the authors prove an existence and uniqueness result and study the long time behavior of the solution by assuming the nonlinearities to be…
The appearence of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon.…
We use the Navier-Stokes-Cahn-Hilliard model equations to simulate phase separation with flow. We study coarsening - the growth of extended domains wherein the binary mixture phase separates into its component parts. The coarsening is…
In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method…
The paper presents a new type of weakly nonlinear two-scale model of inflatable periodic poroelastic structures saturated by Newtonian fluids. The periodic microstructures incorporate fluid inclusions connected to the fluid channels by…
This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…
A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that gives a quantitative description of the slowly evolving spatial correlations and structures in density and flow fields in the early stages of evolution of freely…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
This document is a presentation of the equations of simultaneous water and oil flow in deformable porous medium and linear poromechanics as well as the staggered solution algorithm to solve the coupled system of equations.
This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three dimensional bounded domain. The model is governed by a coupled system of…
We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…
We derive and study a new hyperbolic two-phase model of a porous deformable medium saturated by a viscous fluid. The governing equations of the model are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC)…