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Basic Principles and Practical Applications of the Cahn–Hilliard Equation

Author

Listed:
  • Junseok Kim
  • Seunggyu Lee
  • Yongho Choi
  • Seok-Min Lee
  • Darae Jeong

Abstract

The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase separation in binary alloys by Cahn and Hilliard. Since then the equation has been extended to a variety of chemical, physical, biological, and other engineering fields such as spinodal decomposition, diblock copolymer, image inpainting, multiphase fluid flows, microstructures with elastic inhomogeneity, tumor growth simulation, and topology optimization. Therefore, it is important to understand the basic mechanism of the CH equation in each modeling type. In this paper, we review the applications of the CH equation and describe the basic mechanism of each modeling type with helpful references and computational simulation results.

Suggested Citation

  • Junseok Kim & Seunggyu Lee & Yongho Choi & Seok-Min Lee & Darae Jeong, 2016. "Basic Principles and Practical Applications of the Cahn–Hilliard Equation," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, October.
    • Handle: RePEc:hin:jnlmpe:9532608
    DOI: 10.1155/2016/9532608
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    Cited by:

    1. Chaeyoung Lee & Darae Jeong & Junxiang Yang & Junseok Kim, 2020. "Nonlinear Multigrid Implementation for the Two-Dimensional Cahn–Hilliard Equation," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    2. Sungha Yoon & Darae Jeong & Chaeyoung Lee & Hyundong Kim & Sangkwon Kim & Hyun Geun Lee & Junseok Kim, 2020. "Fourier-Spectral Method for the Phase-Field Equations," Mathematics, MDPI, vol. 8(8), pages 1-36, August.
    3. Tan, Zhijun & Yang, Junxiang & Chen, Jianjun & Kim, Junseok, 2023. "An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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