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Journal of Mathematical Sciences

, Volume 160, Issue 4, pp 470–477 | Cite as

Pressure of an elastic half space on a rigid base with rectangular hole in the case of a liquid bridge between them

  • R. M. Martynyak
  • B. S. Slobodyan
  • V. M. Zelenyak
Article

A model of contact between an elastic half space and a rigid base with a shallow surface rectangular hole is proposed. The hole contains an incompressible liquid and gas. The liquid occupies the middle part of the hole and forms a capillary bridge between the opposite surfaces. The remaining volume of the hole is filled with gas under a constant pressure. The liquid completely wets the surfaces of the bodies. The pressure drop at the liquid–gas interface caused by the surface tension is defined by the Laplace formula. The corresponding plane contact problem for the elastic half space is essentially nonlinear because the pressure of the liquid and the length of the capillary in the contact-boundary conditions are not known in advance and depend on the external load. The problem is reduced to a system of three equations (a singular integral equation for the function of height of the hole and two transcendental equations for the length of the capillary and the height of the meniscus). An analytic-numerical procedure for the solution of these equations is proposed. Dependences of the length of the capillary and the pressure drop at the liquid–gas interface on the external load, volume of liquid, and its surface tension are analyzed.

Keywords

Surface Tension Pressure Drop Contact Problem Elastic Body Liquid Bridge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • R. M. Martynyak
    • 1
  • B. S. Slobodyan
    • 1
  • V. M. Zelenyak
    • 1
  1. 1.Pidstryhach Institute of Applied Problems of Mechanics and MathematicsUkrainian Academy of SciencesLvivUkraine

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