Skip to main content

Surface Tension Revisited

  • 229 Accesses

Part of the Advanced Structured Materials book series (STRUCTMAT,volume 156)

Abstract

Inspired by a paper by Prandtl, a simple explanation for the occurrence and the character of the surface tension in liquids is devised, which connects a molecular view with a continuum model of the liquid. Doing so, the nature of the so-called surface tension can be understood as an imbalance between internal pressure and cohesive forces related to (virtual) cut surfaces orthogonal to the liquid’s surface. By including these cohesive forces as part of the stress tensor, a non-isotropic stress tensor is obtained close to the surface.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-79325-8_9
  • Chapter length: 11 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   149.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-79325-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   199.99
Price excludes VAT (USA)
Fig. 9.1
Fig. 9.2
Fig. 9.3
Fig. 9.4
Fig. 9.5
Fig. 9.6

Notes

  1. 1.

    In reality we, of course, are faced with superposed Brownian motion leading to the continuous movement of all individual molecules. For the sake of simplicity, we do not consider this motion and the related additional forces, which here are simply interpreted as superposed noise.

  2. 2.

    Note that here and, in the following, we restrict ourselves to 2D considerations; the generalization to the 3D case is straightforward.

  3. 3.

    By doing so, we not only guarantee that we cover all interactions up to a distance R but also consider some (not all) interactions beyond that distance—for oppositely positioned molecules at the circumference of the circle even in a distance 2R. But since we consider all interaction forces beyond R to be negligible, this partial contribution does not affect our approach.

References

  1. Prandtl, L.: Zum Wesen der Oberflächenspannung. Annalen der Physik 463(1–3), 59–64 (1947)

    CrossRef  Google Scholar 

  2. Jones, J.E.: On the determination of molecular fields.–II. From the equation of state of a gas. Proc. R. Soc. Lond. A 106(738), 463–477 (1924)

    Google Scholar 

  3. Kirkwood, J.G., Buff, F.P.: The statistical mechanical theory of surface tension. J. Chem. Phys. 17(3), 338–343 (1949)

    CrossRef  Google Scholar 

  4. Marchand, A., Weijs, J.H., Snoeijer, J.H., Andreotti, B.: Why is surface tension a force parallel to the interface? Am. J. Phys. 79(10), 999–1008 (2011)

    CrossRef  Google Scholar 

Download references

Acknowledgements

This work has been partly supported by the COMET-K2 Center of the Linz Center of Mechatronics (LCM) funded by the Austrian federal government and the federal state of Upper Austria.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bernhard Jakoby .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Jakoby, B. (2022). Surface Tension Revisited. In: Irschik, H., Krommer, M., Matveenko, V.P., Belyaev, A.K. (eds) Dynamics and Control of Advanced Structures and Machines. Advanced Structured Materials, vol 156. Springer, Cham. https://doi.org/10.1007/978-3-030-79325-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-79325-8_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79324-1

  • Online ISBN: 978-3-030-79325-8

  • eBook Packages: EngineeringEngineering (R0)