中国物理B ›› 2018, Vol. 27 ›› Issue (2): 24501-024501.doi: 10.1088/1674-1056/27/2/024501

所属专题： SPECIAL TOPIC — Soft matter and biological physics

• SPECIAL TOPIC—Soft matter and biological physics • 上一篇    下一篇

Thin film dynamics in coating problems using Onsager principle

Yana Di(邸亚娜), Xianmin Xu(许现民), Jiajia Zhou(周嘉嘉), Masao Doi   

  1. 1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    3. Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing 100191, China;
    4. Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China;
    5. Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
  • 收稿日期:2017-09-28 修回日期:2018-01-05 出版日期:2018-02-05 发布日期:2018-02-05
  • 通讯作者: Xianmin Xu E-mail:xmxu@lsec.cc.ac.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91630208, 91641107, and 11771437).

Thin film dynamics in coating problems using Onsager principle

Yana Di(邸亚娜)1,2, Xianmin Xu(许现民)1,2, Jiajia Zhou(周嘉嘉)3,4, Masao Doi4,5   

  1. 1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    3. Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing 100191, China;
    4. Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China;
    5. Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
  • Received:2017-09-28 Revised:2018-01-05 Online:2018-02-05 Published:2018-02-05
  • Contact: Xianmin Xu E-mail:xmxu@lsec.cc.ac.cn
  • About author:45.10.Db; 68.15.+e; 47.85.mb; 47.55.N-
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91630208, 91641107, and 11771437).

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摘要： A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.

关键词: Onsager principle, thin films, coating flows, interfacial flows

Abstract: A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.

Key words: Onsager principle, thin films, coating flows, interfacial flows

中图分类号:  (Variational and optimization methods)

  • 45.10.Db
68.15.+e (Liquid thin films) 47.85.mb (Coating flows ?) 47.55.N- (Interfacial flows)