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Coupled diffusion and phase transition: Phase fields, constraints, and the Cahn–Hilliard equation
- Source :
- Meccanica. 56:1707-1725
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We develop a constrained theory for constituent migration in bodies with microstructure described by a scalar phase field. The distinguishing features of the theory stem from a systematic treatment and characterization of the reactions needed to maintain the internal constraint given by the coincidence of the mass fraction and the phase field. We also develop boundary conditions for situations in which the interface between the body and its environment is structureless and cannot support constituent transport. In addition to yielding a new derivation of the Cahn–Hilliard equation, the theory affords an interpretation of that equation as a limiting variant of an Allen–Cahn type diffusion system arising from the unconstrained theory obtained by considering the mass fraction and the phase field as independent quantities. We corroborate that interpretation with three-dimensional numerical simulations of a recently proposed benchmark problem.
- Subjects :
- Physics
Phase transition
Field (physics)
Mechanical Engineering
Phase separation
Scalar (physics)
02 engineering and technology
021001 nanoscience & nanotechnology
Condensed Matter Physics
Free-energy imbalance
01 natural sciences
010101 applied mathematics
Mechanics of Materials
Phase (matter)
Regularization (physics)
Regularization
Boundary value problem
Statistical physics
Microforce balance
0101 mathematics
Diffusion (business)
Allen–Cahn theory
0210 nano-technology
Cahn–Hilliard equation
Subjects
Details
- ISSN :
- 15729648 and 00256455
- Volume :
- 56
- Database :
- OpenAIRE
- Journal :
- Meccanica
- Accession number :
- edsair.doi.dedup.....6bbdf74758bc3fb2acc8e08966c776e7