This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

Diffuse-interface models may be used to compute moving contact lines because the Cahn–
Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the …

Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in
phase separation with the thermodynamically relevant logarithmic potentials; in particular …

The Cahn–Hilliard equation and some of its variants Home 8.{{subColumn.name}} AIMS
Mathematics Search Advanced Home {{newsColumn.name}} 1.{{subColumn.name}} {{newsColumn.name}} …

In this paper, we propose several second order in time, fully discrete, linear and nonlinear
numerical schemes for solving the phase field model of two-phase incompressible flows, in …

This is the first paper in a two-part series in which we analyze two model systems to study
pinchoff and reconnection in binary fluid flow in a Hele-Shaw cell with arbitrary density and …

This work presents a three-dimensional finite-element algorithm, based on the phase-field
model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive …

The Cahn–Hilliard model uses diffusion between fluid components to regularize the stress
singularity at a moving contact line. In addition, it represents the dynamics of the near-wall …