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Journal of Mathematical Sciences

, Volume 240, Issue 2, pp 162–172 | Cite as

Contact Between an Elastic Body and a Rigid Base with Periodic Array of Quasielliptic Grooves Partially Filled with Liquid Wetting the Surfaces of the Bodies

  • O. P. Kozachok
  • B. S. Slobodian
  • R. M. Martynyak
Article
  • 14 Downloads

We model the frictionless contact between an elastic body and a rigid base with periodically placed quasielliptic grooves in the case where an incompressible liquid wetting the surfaces of the bodies is present near the edges of interface gaps. The middle parts of the gaps are filled with a gas under a constant pressure. Due to the surface tension of the liquid, a pressure drop described by the Laplace equation is formed in the liquid and in the gas. The posed contact problem for the elastic half space is reduced to a singular integral equation with Hilbert kernel for the derivative of the height of gaps and to a transcendental equation for the width of the area filled with gas. We analyze the dependences of the width of an area filled with gas, pressure drop, shape of the gaps, and the contact approach of the bodies on the applied load, volume of the liquid, and its surface tension.

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References

  1. 1.
    S. A. Artsybyshev, A Course of Physics. Pt. 1. Mechanics and Heat [in Russian], Uchpedgiz, Moscow (1951).Google Scholar
  2. 2.
    I. G. Goryacheva and Yu. Yu. Makhovskaya, “Adhesive interaction of elastic bodies,” Prikl. Mat. Mekh., 65, No. 2, 279–289 (2001); English translation: J. Appl. Math. Mech., 65, No. 2, 273–282 (2001).Google Scholar
  3. 3.
    G. S. Kit, R. M. Martynyak, and I. M. Machishin, “The effect of a fluid in the contact gap on the stress state of conjugate bodies,” Prikl. Mekh., 39, No. 3, 52–60 (2003); English translation: Int. Appl. Mech., 39, No. 3, 292–299 (2003).Google Scholar
  4. 4.
    O. P. Kozachok, B. S. Slobodian, and R. M. Martynyak, “Interaction of two elastic bodies in the presence of periodically located gaps filled with a real gas,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 1, 103–111 (2015); English translation: J. Math. Sci., 222, No. 2, 131–142 (2017).Google Scholar
  5. 5.
    O. P. Kozachok, B. S. Slobodyan, and R. M. Martynyak, “Contact of elastic bodies in the presence of gas and incompressible liquid in periodic interface gaps,” Fiz.-Khim. Mekh. Mater., 51, No. 6, 50–57 (2015); English translation: Mater. Sci., 51, No. 6, 804–813 (2016)Google Scholar
  6. 6.
    O. P. Kozachok, B. S. Slobodyan, and R. M. Martynyak, “Interaction of elastic bodies with periodic surface topography in the presence of liquid bridges in interface gaps,” Teor. Prikl. Mekh., Issue 7(53), 45–52 (2013).Google Scholar
  7. 7.
    O. Kozachok, B. Slobodyan, and R. Martynyak, “Influence of interface liquid bridges on the contact of an elastic body and a rigid base with periodic system of rectangular grooves,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 22, 67–76 (2015).Google Scholar
  8. 8.
    O. Kozachok, B. Slobodyan, and R. Martynyak, “Influence of interface liquid bridges on the contact interaction of bodies with wavy surface topography,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 24, 34–46 (2016).Google Scholar
  9. 9.
    R. M. Martynyak, “The contact of a half-space and an uneven base in the presence of an intercontact gap filled by an ideal gas,” Mat. Met. Fiz.-Mekh. Polya, 41, No. 4, 144–149 (1998); English translation: J. Math. Sci., 107, No. 1, 3680–3685 (2001).Google Scholar
  10. 10.
    R. M. Martynyak and B. S. Slobodyan, “The interaction of two bodies in the presence of capillaries in the intercontact gap,” Mat. Met. Fiz.-Mekh. Polya, 49, No. 1, 164–173 (2006).zbMATHGoogle Scholar
  11. 11.
    R. M. Martynyak and B. S. Slobodyan, “Influence of liquid bridges in the interface gap on the contact of bodies made of compliant materials,” Fiz.-Khim. Mekh. Mater., 44, No. 2, 7–13 (2008); English translation: Mater. Sci., 44, No. 2, 147–155 (2008).Google Scholar
  12. 12.
    R. M. Martynyak and B. S. Slobodyan, “Contact of elastic half spaces in the presence of an elliptic gap filled with liquid,” Fiz.-Khim. Mekh. Mater., 45, No. 1, 62–65 (2009); English translation: Mater. Sci., 45, No. 1, 66–71 (2009).Google Scholar
  13. 13.
    R. M. Martynyak, B. S. Slobodyan, and V. M. Zelenyak, “Pressure of an elastic half space on a rigid base with rectangular hole in the case of a liquid bridge between them,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 1, 150–156 (2008); English translation: J. Math. Sci., 160, No. 4, 470–477 (2009).Google Scholar
  14. 14.
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Leyden (1977).CrossRefGoogle Scholar
  15. 15.
    B. S. Slobodyan, “Pressure of an elastic body on a rigid base with a recess partially filled with a liquid that does not wet their surfaces,” Fiz.-Khim. Mekh. Mater., 47, No. 4, 122–128 (2011); English translation: Mater. Sci., 47, No. 4, 561–568 (2012).Google Scholar
  16. 16.
    B. Slobodian, S. Chyzhyk, and R. Martynyak, “Contact interaction of bodies in the presence of an ideal gas and liquid bridges in the interface gap,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 18, 189–197 (2013).Google Scholar
  17. 17.
    T. Kato, S. Watanabe, and H. Matsuoka, “Dynamic characteristics of an in-contact headslider considering meniscus force: Part 1: Formulation and application to the disk with sinusoidal undulation,” Trans. ASME. J. Tribol., 122, No. 3, 633–638 (1999).CrossRefGoogle Scholar
  18. 18.
    T. Kato, S. Watanabe, and H. Matsuoka, “Dynamic characteristics of an in-contact headslider considering meniscus force: Part 2: Application to the disk with random undulation and design conditions,” Trans. ASME. J. Tribol., 123, No. 1, 168–174 (2000).CrossRefGoogle Scholar
  19. 19.
    S. Kobatake, Y. Kawakubo, and S. Suzuki, “Laplace pressure measurement on laser textured thin-film disk,” Tribol. Int., 36, No. 4–6, 329–333 (2003).CrossRefGoogle Scholar
  20. 20.
    Y. I. Rabinovich, M. S. Esayanur, and B. M. Moudgil, “Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment,” Langmuir, 21, No. 24, 10992–10997 (2005).CrossRefGoogle Scholar
  21. 21.
    L. Shi and A. Majumdar, “Thermal transport mechanisms at nanoscale point contacts,” Trans. ASME. J. Heat Transfer, 124, No. 2, 329–337 (2001).CrossRefGoogle Scholar
  22. 22.
    J. Zheng and J. L. Streator, “A liquid bridge between two elastic half spaces: A theoretical study of interface instability,” Tribol. Lett., 16, Nos. 1-2, 1–9 (2004).CrossRefGoogle Scholar
  23. 23.
    L. Zitzler, S. Herminghaus, and F. G. Mugele, “Capillary forces in tapping mode atomic force microscopy,” Phys. Rev. B, 66, No. 15, 155436 (8 pages) (2002).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • O. P. Kozachok
    • 1
  • B. S. Slobodian
    • 1
  • R. M. Martynyak
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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