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Reduction in vacuum phenomenon for the triple junction in the ternary Cahn–Hilliard model

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Abstract

In this study, we present a modified interfacial parameter to reduce the vacuum phenomenon for the triple junction in the ternary Cahn–Hilliard (CH) equation. The triple junction is the point where three phases meet each other. In the ternary system, we interpret a position as occupied by a phase, if the concentration of the phase is larger than one-half. Therefore, it is well known that there exists a vacuum phenomenon: none of the phases exist, that is, all the concentrations are less than one-half. In the proposed method, we introduce a phase-dependent interfacial coefficient that has a constant value away from the triple junction and smaller values in the neighborhood of the triple junction, which effectively reduces the vacuum region. To validate the superiority of the proposed approach, we present the characteristic numerical experiments for the ternary system. The computational results confirm the superior performance of the proposed method over the conventional method.

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Acknowledgements

The corresponding author (J. S. Kim) was supported by the National Research Foundation (NRF), Korea, under Project BK21 FOUR. The authors thank the reviewers for their constructive comments regarding the revision of this article.

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  1. Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea

    Junxiang Yang, Chaeyoung Lee & Junseok Kim

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  1. Junxiang Yang
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Correspondence to Junseok Kim.

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Yang, J., Lee, C. & Kim, J. Reduction in vacuum phenomenon for the triple junction in the ternary Cahn–Hilliard model. Acta Mech 232, 4485–4495 (2021). https://doi.org/10.1007/s00707-021-03072-8

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  • DOI: https://doi.org/10.1007/s00707-021-03072-8

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