Applied Mathematics and Mechanics >
Exact solution for capillary interactions between two particles with fixed liquid volume
Received date: 2016-01-13
Revised date: 2016-05-24
Online published: 2016-12-01
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)
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.
Fengxi ZHOU, Qiang MA . Exact solution for capillary interactions between two particles with fixed liquid volume[J]. Applied Mathematics and Mechanics, 2016 , 37(12) : 1597 -1606 . DOI: 10.1007/s10483-016-2142-8
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