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 …

Computational methods have been extended recently to allow for the presence of moving
contact lines in simulated two-phase flows. The predictive capability offered by these …

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

The motion of two contiguous incompressible and viscous fluids is described within the
diffuse interface theory by the so-called Model H. The system consists of the Navier--Stokes …

In this article, several efficient and energy-stable semi–implicit schemes are presented for
the Cahn–Hilliard phase-field model of two-phase incompressible flows. A scalar auxiliary …

In this paper, two-phase fluid systems are simulated using a diffusive interface model with
the Peng--Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon …

Many approaches have been developed to study the role that pore structure parameters
play in flow characteristics. In this paper, regular network models are used to study the …

In this paper, we develop a phase-field model for binary incompressible (quasi-
incompressible) fluid with thermocapillary effects, which allows for the different properties …

The hydromechanical interaction of porous media with pore and free fluid widely exists in
geotechnical engineering. In some situations, the solid phase would exhibit large …

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary
condition for binary fluids with moving contact lines are studied by asymptotic analysis and …