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Applied Mathematics and Mechanics

, Volume 37, Issue 12, pp 1597–1606 | Cite as

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

  • Fengxi ZhouEmail author
  • Qiang Ma
Article

Abstract

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.

Key words

liquid bridge Young-Laplace equation fixed liquid volume shooting method 

Chinese Library Classification

O363.2 

2010 Mathematics Subject Classification

76B45 76D45 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Civil EngineeringLanzhou University of TechnologyLanzhouChina

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