Derivations of the Young-Laplace equation
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.
Cited as: Siqveland, L. M., Skjaeveland, S. M. Derivations of the Young-Laplace equation. Capillarity, 2021, 4(2): 23-30, doi: 10.46690/capi.2021.02.01
Keywords:
Young-Laplace, space curves, principle radii, linear algebraReferences
Defay, R., Prigogine, I. Surface Tension and Adsorption. London, UK, Longmans, Green & Co. Ltd., 1966.
Howard, A. Elementary Linear Algebra. John Wiley and Sons, 1984.
Landau, L., Lifshitz, E. Fluid Mechanics. Oxford, UK, Pergamon Press, 1987.
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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