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Analysis of the Cahn–Hilliard Equation with a Relaxation Boundary Condition Modeling the Contact Angle Dynamics

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Abstract

We analyze the Cahn–Hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary. An L ∞ estimate is established which enables us to prove the global existence of the solution. We also study the sharp interface limit of the system. The dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Xinfu Chen

  2. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Xiaoping Wang

  3. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100080, China

    Xianmin Xu

Authors
  1. Xinfu Chen
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  2. Xiaoping Wang
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  3. Xianmin Xu
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Corresponding author

Correspondence to Xinfu Chen.

Additional information

Communicated by D. Kinderlehrer

This work is supported in part by the Hong Kong RGC grants GRF-HKUST 605513, 605311 and NNSF of China grant 91230102. Xinfu Chen would like to thank the Hong Kong University of Science and Technology where most of this work was carry out while he was visiting; he also thanks the financial support from National Science Foundation DMS-1008905. Xianmin Xu would also like to thank the financial support from NSFC 11001260. The authors also thank Professor D. Kinderlehrer and the anonymous referee for their valuable suggestions to make the paper more readable.

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Chen, X., Wang, X. & Xu, X. Analysis of the Cahn–Hilliard Equation with a Relaxation Boundary Condition Modeling the Contact Angle Dynamics. Arch Rational Mech Anal 213, 1–24 (2014). https://doi.org/10.1007/s00205-013-0713-x

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  • DOI: https://doi.org/10.1007/s00205-013-0713-x

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