Modeling and simulation of multi-component immiscible flows based on a modified Cahn–Hilliard equation

Qing Xia, Junseok Kim, Yibao Li

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


In this study, an efficient method will be developed for the phase-field model of multi-component immiscible phases. The formulation of surface tension requires the interfaces to satisfy the hyperbolic tangent property. However, the interfacial transitions between different phases are not hyperbolic tangent profiles. The enclosed area is not preserved although the total mass is conserved by the original Cahn–Hilliard equation. This study is an extended research based on our previous study (Li et al., 2016). This work aims to apply the modified Cahn–Hilliard model into the multi-phase system. The interface is forced to be hyperbolic tangent by the modified Cahn–Hilliard system. The computational accuracy of the surface tension is improved under our multiphase framework. The mass loss of each phase can be reduced and the enclosed area can be preserved by the proposed method. We show various numerical results to demonstrate the robustness of the proposed modified model.

Original languageEnglish
Pages (from-to)194-204
Number of pages11
JournalEuropean Journal of Mechanics, B/Fluids
Publication statusPublished - 2022 Sept 1

Bibliographical note

Funding Information:
J.S. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Republic of Korea ( NRF-2019R1A2C1003053 ). The corresponding author(Y.B. Li) is supported by the Fundamental Research Funds for the Central Universities, China (No. XTR042019005 ). The authors would like to thank the reviewers for their constructive and helpful comments regarding the revision of this article.

Publisher Copyright:
© 2022 Elsevier Masson SAS


  • Cahn–Hilliard model
  • Hyperbolic tangent property
  • Multi-component flow
  • Navier–Stokes equation

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy


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