Skip to main content
SpringerLink
Log in

Duality in interaction potentials for curved surface bodies and inside particles

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yin, Y. J., Chen, C., Lü, C. J., and Zheng, Q. S. Shape gradient and classical gradient of curvatures: driving forces on micro/nano curved surfaces. Applied Mathematics and Mechanics (English Edition), 32(5), 533–550 (2011) DOI 10.1007/s10483-011-1436-6

    Article  MathSciNet  MATH  Google Scholar 

  2. Wu, J. Y., Yin, Y. J., Wang, X. G., and Fan, Q. S. Interaction potential between micro/nano curved surface and a particle located inside the surface (I): driving forces induced by curvatures. Science China: Physics Mechanics and Astronomy, 55(6), 1066–1076 (2012)

    Google Scholar 

  3. Wu, J. Y., Yin, Y. J., Huang, K., and Fan, Q. S. Interaction potential between micro/nano curved surface and a particle located inside the surface (II): numerical experiment and equipotential surfaces. Science China: Physics Mechanics and Astronomy, 55(6), 1077–1082 (2012)

    Google Scholar 

  4. Wang, X. G., Yin, Y. J., Wu, J. Y., and Wang, D. Curvature-based interaction potential between an isolated particle and micro/nano space curve. Physica E: Low-Dimensional Systems and Nanostructures, 67, 178–191 (2015)

    Article  Google Scholar 

  5. Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Interaction potential between parabolic rotator and an outside particle. Journal of Nanomaterials, 2014, 1–6 (2014)

    Google Scholar 

  6. Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Curvature-based interaction potential between micro/nano curved surface body and an outside particle. Journal of Computational and Theoretical Nanoscience, 12(12), 1–12 (2015)

    Google Scholar 

  7. Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Curvature-based interaction potential between micro/nano curved surface body and a particle on the surface of the body. Journal of Biological Physics, 42(1), 33–51 (2015)

    Article  Google Scholar 

  8. Peter, J. Y., Tim, S., Matthew, A. L., and Yodh, A. G. Suppression of the coffee-ring effect byshape-dependent capillary interactions. nature, 476(18), 308–311 (2011)

    Google Scholar 

  9. Zhao, Y. P. Physical Mechanics of Surfaces and Interfaces, Science Press, Beijing (2012)

    Google Scholar 

  10. Johnson, H. H. Hydrogen embrittlement. Science, 179, 228–230 (1973)

    Article  Google Scholar 

  11. Rustom, A., Saffrich, R., and Markovic, I. Nanotubular highways for intercellular organelle transport. Science, 303, 1007–1010 (2004)

    Article  Google Scholar 

  12. Blanchfield, R. C. Intersection theory of manifolds with operators with applications to knot theory. Annals of Mathematics, 65(2), 340–356 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination, 2nd ed., Chelsea, New York, 119–128 (1952)

    MATH  Google Scholar 

  14. Negrepontis, J. W. Duality in analysis from the point of view of triples. Journal of Algebra, 19(2), 228–253 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  15. Israelachvili, J. Intermolecular and Surface Forces, 3nd ed., Academic Press, London (2011)

    Google Scholar 

  16. Su, B. Q., Hu, H. S., Shen, C. L., Pan, Y. L., and Zhang, G. L. Differential Geometry, People’s Education Press, Beijing, 16–18 (1979)

    Google Scholar 

  17. Wu, J. Y. Biomembrane Free Energy and the Driving Forces Induced by Curvature Gradients (in Chinese), Ph. D. dissertation, Tsinghua University, 40–45 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Dan Wang & Yajun Yin

  2. Department of Civil Engineering, Nanjing Tech University, Nanjing, 211800, China

    Jiye Wu

  3. Department of Engineering Mechanics, Tongji University, Shanghai, 200092, China

    Zheng Zhong

Authors
  1. Dan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yajun Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiye Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zheng Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yajun Yin.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11672150 and 11272175), the Natural Science Foundation of Jiangsu Province (No.BK20130910), and the specialized Research Found for Doctoral Program of Higher Education (No. 2013000211004)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, D., Yin, Y., Wu, J. et al. Duality in interaction potentials for curved surface bodies and inside particles. Appl. Math. Mech.-Engl. Ed. 38, 1071–1090 (2017). https://doi.org/10.1007/s10483-017-2223-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-017-2223-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation