Related papers: A phase-field model for solutions of DNA-made part…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization…
A MATLAB program has been developed for simulation of polymer blend self-assembly with nano-scaled features. The Cahn-Hilliard equation is implemented to calculate the free energy profile of the polymer blends. The Flory-Huggins type of…
The coupled Cahn-Hilliard and Navier-Stokes (CH-NS) equations provide a powerful framework for modeling multiphase flows with diffuse interfaces, enabling simulations of droplet breakup, bubble dynamics, and hydrodynamic instabilities.…
We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane…
The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…
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…
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…
In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
Motivated by recent experimental and theoretical work on the control of phase separation by (electro-)autocatalytic reactions, we analyze pattern formation in externally driven phase separating systems described by a generalization of the…
Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic…
Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front.…
Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the…
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…
We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order…
We present a coarse-grained model of DNA-functionalized colloids that is computationally tractable. Importantly, the model parameters are solely based on experimental data. Using this highly simplified model, we can predict the phase…
The phase-field system is a nonlinear model that has significant applications in material sciences. In this paper, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisting of…