Related papers: A phase-field approach to Eulerian interfacial ene…
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…
We construct the complete $U$-$\mu$ phase diagram for harmonically confined ultracold fermionic atoms with repulsive and attractive interactions. ($\mu$ is the chemical potential and $U$ the interaction strength.) Our approach is based on…
This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…
Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…
The force fields of interior boundaries of matters are calculated as superposition of fields of modified Sierpinski carpet. The long-range effect interaction in irradiated crystals is introduced as various manifestations of second order…
Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…
We study properties of the solutions of a family of second order integro-differential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with particle conserving dynamics. We first…
An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…
In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid,…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
In this paper, we introduce an interfacial profile-preserving approach for phase field modeling for simulating incompressible two-phase flows. While the advective Cahn-Hilliard equation effectively captures the topological evolution of…
We consider a family of vectorial models for cohesive fracture, which may incorporate $\mathrm{SO}(n)$-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic)…
Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to…
We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and…
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…
Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough…
Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the…
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…
In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a…