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.
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Notes
- 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.
Note that here and, in the following, we restrict ourselves to 2D considerations; the generalization to the 3D case is straightforward.
- 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
Prandtl, L.: Zum Wesen der Oberflächenspannung. Annalen der Physik 463(1–3), 59–64 (1947)
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)
Kirkwood, J.G., Buff, F.P.: The statistical mechanical theory of surface tension. J. Chem. Phys. 17(3), 338–343 (1949)
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)
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.
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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
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DOI: https://doi.org/10.1007/978-3-030-79325-8_9
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