Related papers: Phase separation on varying surfaces and convergen…
The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
In this work we define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area. A highly accurate density-profile equation is thus derived, which is physically favorable and…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
We present a generalized theory for studying phase separation in blends of polymers containing dipoles on their backbone. The theory is used to construct co-existence curves and to study the effects of dipolar interactions on interfacial…
We consider a diffuse interface model for phase separation of an isothermal incompressible binary fluid in a Brinkman porous medium. The coupled system consists of a convective Cahn-Hilliard equation for the phase field $\phi$, i.e., the…
We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand…
We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the…
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, R\"atz, R\"oger and the second author. The model is an extended Cahn-Hilliard equation which contains…
Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or…
We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully…
We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of…
Sharp interfaces in miscible fluids have long been observed, yet classical theory associates them only with phase coexistence and non-convex free energies. We present a minimal variational frame work where adding a Fermi-Dirac (FD) free…
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be…
We present a theoretical analysis of phase separations between two repulsively interacting components in an ultracold fermionic gas, occurring at the dimensional crossover in a harmonic trap with varying aspect ratios. A tailored kinetic…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
We construct a mean-field formulation of the thermodynamics of ion solvation in immiscible polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of different constant dielectric medium, we…