Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

doi:10.1007/s10483-023-3002-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (6): 997-1006.doi: https://doi.org/10.1007/s10483-023-3002-9

Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

C. Q. RU

Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada

收稿日期:2023-01-28 修回日期:2023-04-10 出版日期:2023-06-01 发布日期:2023-05-29
通讯作者: C. Q. RU, E-mail: cru@ualberta.ca
基金资助:
the Natural Science & Engineering Research Council (NSERC) of Canada (No. NSERC-RGPIN204992)

Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

C. Q. RU

Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada

Received:2023-01-28 Revised:2023-04-10 Online:2023-06-01 Published:2023-05-29
Contact: C. Q. RU, E-mail: cru@ualberta.ca
Supported by:
the Natural Science & Engineering Research Council (NSERC) of Canada (No. NSERC-RGPIN204992)

摘要/Abstract

摘要： Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate. Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature, particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.

关键词: Neumann equation, Young's equation, liquid droplet, membrane, pretension

Abstract: Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate. Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature, particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.

Key words: Neumann equation, Young's equation, liquid droplet, membrane, pretension

中图分类号:

74B05
74F10

C. Q. RU. Axisymmetric wetting of a liquid droplet on a stretched elastic membrane[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 997-1006.

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Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

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