Cahn–Hilliard equation

E574814

fourth-order partial differential equation mathematical model of phase separation partial differential equation phase-field model

The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.

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Observed surface forms (1)

Surface form	Occurrences
Cahn–Hilliard free energy functional	1

Statements (48)

Predicate	Object
instanceOf	fourth-order partial differential equation ⓘ mathematical model of phase separation ⓘ partial differential equation ⓘ phase-field model ⓘ
appliesTo	spinodally unstable mixtures ⓘ systems with conserved order parameter ⓘ
basedOn	Ginzburg–Landau free energy functional NERFINISHED ⓘ variational principles ⓘ
describes	coarsening dynamics ⓘ conserved order parameter dynamics ⓘ diffusion-driven phase separation ⓘ phase separation in binary mixtures ⓘ spinodal decomposition ⓘ
field	applied mathematics ⓘ computational physics ⓘ materials science ⓘ statistical physics ⓘ thermodynamics ⓘ
governs	evolution of composition field ⓘ evolution of order parameter field ⓘ
hasCharacteristic	double-well free energy density ⓘ fourth-order spatial derivatives ⓘ gradient-flow structure ⓘ mass-conserving dynamics ⓘ nonlinear chemical potential ⓘ
hasComponent	bulk free energy density ⓘ gradient energy coefficient ⓘ mobility coefficient ⓘ
hasForm	conservation law for order parameter ⓘ time derivative equals Laplacian of chemical potential ⓘ
namedAfter	John E. Hilliard NERFINISHED ⓘ John W. Cahn NERFINISHED ⓘ
publishedIn	Acta Metallurgica NERFINISHED ⓘ
relatedTo	Allen–Cahn equation NERFINISHED ⓘ Model B in Hohenberg–Halperin classification NERFINISHED ⓘ phase-field models of solidification ⓘ
solvedBy	finite difference methods ⓘ finite element methods ⓘ spectral methods ⓘ
usedIn	binary fluid mixtures ⓘ image inpainting ⓘ lithium-ion battery modeling ⓘ microstructure evolution modeling ⓘ multiphase flow modeling ⓘ polymer blend phase separation ⓘ spinodal decomposition in alloys ⓘ topology optimization ⓘ
yearProposed	1958 ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

John W. Cahn → knownFor → Cahn–Hilliard equation ⓘ

John W. Cahn → notableConcept → Cahn–Hilliard equation ⓘ

this entity surface form: Cahn–Hilliard free energy functional