Thomas Young's surface tension diagram: its history, legacy, and irreconcilabilities
type: Item
instance of: scholarly article
title: Thomas Young's surface tension diagram: its history, legacy, and irreconcilabilities
zbMATH Open document ID: 1306.76011
author: Robert Finn
author: John McCuan
author: Henry C. Wente
published in: Journal of Mathematical Fluid Mechanics
publication date: 2013-01-04T00:00:00Z
review text: The authors point out that Young's surface tension diagram is not correct in general. Consider a floating ball which is in an equilibrium in the case of zero gravity. Then, for every given contact angle \(\gamma\in(0,\pi)\), there is a horizontal capillary surface, see [\textit{R. Finn}, Phys. Fluids 18, No. 4, Art. 047102, 7 p. (2006; Zbl 1185.76470); erratum ibid. 20, No. 10, Paper No. 109901, 1 p. (2008; \url{doi:10.1063/1.2981835})]. Let \(\sigma_1, \sigma_2\) be the components of surface tension tangential to the solid ball at the contact line \(\Gamma\) between the liquid and the ball, and let \(\sigma_0\) be the component of surface tension tangential to the liquid interface at \(\Gamma\), where \(\sigma_2\) points into the liquid, \(\sigma_1\) into the opposite direction and \(\sigma_0\) points out of the solid ball. Then Young's formula \(\sigma_1=\sigma_0\cos\gamma+\sigma_2\) fails in the considered example if \(\gamma\not=\pi/2\). Moreover, the authors show that Young's formula is in conflict with the Wilhelmy method for measuring surface tension at liquid/liquid interfaces.
Mathematics Subject Classification ID: 76B45
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 6122066
zbMATH Keywords: Wilhelmy method
zbMATH Keywords: counterexample
zbMATH Keywords: contact angle
reviewed by: Erich Miersemann
MaRDI profile type: Publication
full work available at URL: s00021-011-0079-5
OpenAlex ID: W1964370085
cites work: The contact angle in capillarity
cites work: Q4446075
cites work: Young’s law and the effects of interfacial energy on the pressure at the solid-fluid interface
cites work: On Young's (1805) equation and Finn's (2006) `counterexample'
cites work: Stability of liquid layers on solid materials
cites work: Equilibrium configurations of an infinite cylinder in an unbounded fluid
DOI: 10.1007/S00021-011-0079-5
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description: scientific article; zbMATH DE number 6122066