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. 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
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.
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