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The phase separation processes are typically modeled by Cahn-Hilliard equations. This equation was originally introduced to model phase separation in binary alloys, where phase stands for concentration of different components in alloy. When…
Lithium intercalated anatase used in Li-ion batteries has some special features: coexistence of Li-rich and Li-poor phases as well as two possible positions for Li ions in the oxygen tetrahedron. A theoretical description of the compound…
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…
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…
Suspensions of purely repulsive but self-propelled Brownian particles might undergo phase separation, a phenomenon that strongly resembles the phase separation of passive particles with attractions. Here we employ computer simulations to…
A density functional theory for a macroion suspension is examined, where the excess free energy corresponds to the macroion self energy arising from the polarisation of the supporting electrolyte solution. This is treated within a…
Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (e.g., due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which…
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
The influence of an external field acting differently on the two constituents of a binary colloidal mixture performing Brownian dynamics is investigated by computer simulations and a simple theory. In our model, one half of the particles…
Phase separation in charged systems may involve the replacement of critical points by microphase separated states, or charge-density-wave states. A density functional theory for highly charged colloids at low ionic strength is developed to…
Fluid mixtures, such as the cellular cytoplasm and synthetic DNA nanostars, can spontaneously compartmentalize into many coexisting phases through liquid-liquid phase separation. Despite the diversity of fluid structures that emerge from…
Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that…
The influence of immobile filler particles (spheres, fibers, platelets) on polymer blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective…
Implicit-Explicit methods have been widely used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due to the lack of maximum principle and stiffness caused by the…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
We study an alloy system where short-ranged, thermally-driven diffusion competes with externally imposed, finite-ranged, athermal atomic exchanges, as is the case in alloys under irradiation. Using a Cahn-Hilliard-type approach, we show…
Thermodynamic bulk phase diagrams have become the roadmap used by researchers to identify alloy compositions and process conditions that result in novel materials with tailored microstructures. Recent experimental studies show that changes…
In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a…
Living and engineered systems rely on the stable coexistence of two interspersed liquid phases. Yet surface tension drives their complete separation. Here we show that stable droplets of uniform and tuneable size can be produced through…
Catalyst particles or complexes suspended in liquid films can trigger chemical reactions leading to inhomogeneous concentrations of reactants and products in the film. We demonstrate that the sensitivity of the liquid film's gas-liquid…