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Original Article | Open Access

Derivations of the Young-Laplace equation

Department of Energy Resources, University of Stavanger, 4036 Stavanger, Norway
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Abstract

The classical Young-Laplace equation relates capillary pressure to surface tension and the principal radii of curvature of the interface between two immiscible fluids. In this paper the required properties of space curves and smooth surfaces are described by differential geometry and linear algebra. The equilibrium condition is formulated by a force balance and minimization of surface energy.

Keywords

Young-Laplacespace curvesprinciple radiilinear algebra

References

 
Defay, R., Prigogine, I. Surface Tension and Adsorption. London, UK, Longmans, Green & Co. Ltd., 1966.
 
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Laplace, P. Supplement to the tenth edition. Méchanique Céleste 10, 1806.
 
Papatzacos, P. Matematisk modellering. Kompendium ved Høgskolen i Stavanger, 1989. (in Norwegian)
 
Shifrin, T. Differential Geometry: A First Course in Curves and Surfaces. University of Georgia, 2013.
 
Tambs Lyche, R. Matematisk Analyse II. Gyldendal Norsk Forlag, Oslo, 1962. (in Norwegian)
 
Weatherburn, C.E. Differential Geometry of Three Dimensions. Cambridge, UK, Cambridge University Press, 2016.
 
Young, T. III. An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 1805, 95: 65-87.
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Capillarity
Volume 4 Issue 2,
June 2021
Pages 23-30
DOI: 10.46690/capi.2021.02.01
Cite this article:
Siqveland LM, Skjæveland SM. Derivations of the Young-Laplace equation. Capillarity, 2021, 4(2): 23-30. https://doi.org/10.46690/capi.2021.02.01

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Received: 10 April 2021
Revised: 25 April 2021
Accepted: 26 April 2021
Published: 28 April 2021
© The Author(s) 2021

This article is distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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