Thomas Young's surface tension diagram: its history, legacy, and irreconcilabilities
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.
scientific article; zbMATH DE number 6122066