Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

By John W. Cahn, J. Hilliard. 2013

1,905 citations recorded by the source corpus.

Subfields: Atmospheric Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/599c017ee4c41106e3e5112dbfec0d223c1a8707

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Citations in the corpus

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows (2018, methodology): “The SAV approach is proposed for a large class of gradient flows that describe energy dissipative physical systems [1, 4, 8, 14, 6, 3].”
The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property (2017, background): “The Cahn–Hilliard system was proposed in [15] (see also [14]) as a model which provides a macroscopic description of the formation and evolution of microstructures during the phase separation in a binary alloys system.”
On Phase-Separation Models: Asymptotics and Qualitative Properties (2013, neutral): “Ω ε(2)|∇u|(2) + 1 2 (1− u(2))(2) for u ∈ H(1)(Ω) , (see [15]).”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, background): “This is done in order to avoid ambiguities: Cahn and Hilliard, for instance, intended the equations which were subsequently named after them to be valid for the concentration of a solute in motion with respect to a stationary solvent, and deduced them via molecular arguments (modulo some thermodynam”
A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system (2012, methodology): “The scheme allows us to convert the N-component Cahn–Hilliard system into a system of N − 1 binary Cahn–Hilliard equations and significantly reduces the required computer memory and CPU time.”
Evaluation of level set and phase field methods in modeling two phase flow with viscosity contrast through dual-permeability porous medium (2013, background): “Convective Cahn–Hilliard equation (proposed by Cahn and Hilliard (1958)) is the best known example of PFM that can conserve the volume and is relatively easy to implement in two and three dimensions (Jacqmin, 1999).”
On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case (2019, background): “Interfacial dynamics in the mixture of different fluids, solids or gas has been one of the fundamental issues in many fields of science and engineering, particularly in materials science and fluid dynamics, see for instance, [1, 2, 27, 18] and the references therein.”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “22) was introduced in [139] to include certain viscoelastic relaxation effects in the phase separation process, which was neglected in [16].”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, background): “The fourth category, the phase-field LB method, represents the multiphase LB models that are based on the phase-field theory, in which the interface dynamics is described by an order parameter that obeys the Cahn-Hilliard equation or a Cahn-Hilliard-like equation [65].”
A brief review of the phase-field-based lattice Boltzmann method for multiphase flows (2019, methodology): “In the phase-field theory, an order parameter governed by the convection-diffusion type equation [Cahn-Hilliard equation (CHE) (Cahn and Hilliard, 1958; Cahn and Hilliard, 1959) or Allen-Cahn equation (ACE) (Allen and Cahn, 1976)] is used to track the interface.”
A phase field model of deformation twinning: Nonlinear theory and numerical simulations (2011, methodology): “10) Interfacial energy per unit area Γ is defined as [1]”
On a generalized Cahn-Hilliard equation with biological applications (2014, neutral): “, [2], [3], [5], [9], [16], [17], [18], [19], [23] and [24] for more details.”
The scalar auxiliary variable (SAV) approach for gradient flows (2018, background): “Gradient flows are frequently used in mathematical models for problems in many fields of science and engineering, particularly in materials science and fluid dynamics, see, for instance, [4, 1, 15, 6, 13, 2, 8, 25] and the references therein.”
Longtime behavior of nonlocal Cahn-Hilliard equations (2012, methodology): “The Cahn-Hilliard equation was proposed in [7] as a model for (isothermal) phase separation phenomena in binary alloys.”
Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials (2015, background): “1 Introduction The Cahn–Hilliard equation [5,14] yields a famous description of the evolution phenomena on the solid-solid phase separation.”
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions (2014, positive): “1 Introduction The simplest form of the Cahn–Hilliard equation with or without viscosity (see [3, 13, 12]) reads as follows ∂ty −∆w = 0 and w = τ∂ty −∆y +W (y) in Ω× (0, T ) (1.”
Advances in Planar Lipid Bilayers and Liposomes (2011, methodology): “Devil’s Staircase-Type Faceting It was surprising to find that such fuzzy crystals display the so-called devil’s staircase faceting [27,28] expected for solid crystals at low temperatures [24].”
The mechanical response of cellular materials with spinodal topologies (2019, methodology): “One of the most commonly used formulations is the Cahn-Hilliard equation (Cahn and Hilliard, 1958; Sun et al., 2013), which can be written as:”