Exact solution for capillary interactions between two particles with fixed liquid volume

doi:10.1007/s10483-016-2142-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1597-1606.doi: https://doi.org/10.1007/s10483-016-2142-8

Exact solution for capillary interactions between two particles with fixed liquid volume

Fengxi ZHOU, Qiang MA

School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China

收稿日期:2016-01-13 修回日期:2016-05-24 出版日期:2016-12-01 发布日期:2016-12-01
通讯作者: Fengxi ZHOU E-mail:geolut@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 51368038 and 11162008), the Alumni Foundation of Civil Engineering of Lanzhou University of Technology (No.TM-QK-0701), and the Environmental Protection Department of Gansu Province of China (No.GSEP-2014-23)

Exact solution for capillary interactions between two particles with fixed liquid volume

Fengxi ZHOU, Qiang MA

School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received:2016-01-13 Revised:2016-05-24 Online:2016-12-01 Published:2016-12-01
Contact: Fengxi ZHOU E-mail:geolut@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 51368038 and 11162008), the Alumni Foundation of Civil Engineering of Lanzhou University of Technology (No.TM-QK-0701), and the Environmental Protection Department of Gansu Province of China (No.GSEP-2014-23)

摘要/Abstract

摘要：

The capillary interactions, including the capillary force and capillary suction, between two unequal-sized particles with a fixed liquid volume are investigated. The capillary interaction model is used within the Young-Laplace framework. With the profile of the meridian of the liquid bridge, the capillary suction, and the liquid volume as state variables, the governing equations with two-fixed-point boundary are first derived using a variable substitution technique, in which the gravity effects are neglected. The capillary suction and geometry of the liquid bridge with a fixed volume are solved with a shooting method. In modeling the capillary force, the Gorge method is applied. The effects of various parameters including the distance between two particles, the ratio of particle radii, and the liquid-solid contact angles are discussed.

关键词: fixed liquid volume, Young-Laplace equation, liquid bridge, shooting method

Abstract:

Key words: shooting method, liquid bridge, Young-Laplace equation, fixed liquid volume

中图分类号:

76B45
76D45

Fengxi ZHOU, Qiang MA. Exact solution for capillary interactions between two particles with fixed liquid volume[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1597-1606.

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Exact solution for capillary interactions between two particles with fixed liquid volume

Exact solution for capillary interactions between two particles with fixed liquid volume

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