Related papers: Phase separation in the advective Cahn-Hilliard eq…
We present a phase-field model based on the Cahn-Hilliard equation to investigate the properties of phase separation in DNA nanostar systems. Leveraging a realistic free-energy functional derived from Wertheim theory, our model captures the…
In this paper, we present a phase field model for the self-climb motion of prismatic dislocation loops via vacancy pipe diffusion driven by elastic interactions. This conserved dynamics model is developed under the framework of the…
We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase field approach is…
We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…
In this paper we study a non-local Cahn-Hilliard equation with singular single-well potential and degenerate mobility. This results as a particular case of a more general model derived for a binary, saturated, closed and incompressible…
In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is…
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
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…
We quantitatively study the interaction between diffusion and mixing in both the continuous, and discrete time setting. In discrete time, we consider a mixing dynamical system interposed with diffusion. In continuous time, we consider the…
We present a novel spatial discretization for the Cahn-Hilliard equation including transport. The method is given by a mixed discretization for the two elliptic operators, with the phase field and chemical potential discretized in…
We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless…
We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the…
We discuss the interplay between a slow continuous drift of temperature, which induces continuous phase separation, and the non-linear diffusion term in the $\phi^4$-model for phase separation of a binary mixture. This leads to a bound for…
We study the stationary and transient behaviors of the microemulsion phase subjected to a shear flow. The system is described by a diffusion-convective equation which generalizes the usual Cahn-Hilliard equation. Non-linear terms are…
Colloid-polymer mixtures are an archetype for modeling phase transition processes, as they a exhibit low-density gas phase, high-density crystalline phase and an intervening liquid phase. While their equilibrium behavior has been studied…
We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal…
We propose an active Cahn-Hilliard theory for the dynamics of a new type of phase transition where the driving force is not the direct interactions between the two separating components, but their active sorting by a third polar species.…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We study the interactions between the thermodynamic transition and hydrodynamic flows which would characterise a thermo- and hydro-dynamic evolution of a binary mixture in a dissolution/nucleation process. The primary attention is given to…
This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical…