Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (8): 1165-1172.doi: https://doi.org/10.1007/s10483-018-2357-6

• 论文 • 上一篇    下一篇

Dripping retardation with corrugated ceiling

Dong LUO, Jianjun TAO   

  1. CAPT-HEDPS, SKLTCS, Collaborative Innovation Center of IFSA, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2018-01-12 修回日期:2018-03-06 出版日期:2018-08-01 发布日期:2018-08-01
  • 通讯作者: Jianjun TAO,E-mail:jjtao@pku.edu.cn E-mail:jjtao@pku.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos. 91752203, 11490553, and 11521091)

Dripping retardation with corrugated ceiling

Dong LUO, Jianjun TAO   

  1. CAPT-HEDPS, SKLTCS, Collaborative Innovation Center of IFSA, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
  • Received:2018-01-12 Revised:2018-03-06 Online:2018-08-01 Published:2018-08-01
  • Contact: Jianjun TAO E-mail:jjtao@pku.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 91752203, 11490553, and 11521091)

摘要:

The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.

关键词: periodic solutions, equation of neutral type, existence, uniqueness, necessary and sufficient, pendent film, surface tension, corrugated wall, Rayleigh-Taylor instability (RTI)

Abstract:

The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.

Key words: pendent film, periodic solutions, equation of neutral type, existence, uniqueness, necessary and sufficient, Rayleigh-Taylor instability (RTI), corrugated wall, surface tension

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