By Jean-Louis Salager
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Additional info for A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition
67) where θ κ j is the angle of contact between the curvature vector κ of the contact line and the jth dividing surface, θ js,k is the angle of contact between the curvature vector and the jsth dividing surfaces (where s = 1 or s = 2) and θj1j2 is the angle between the j1th dividing surface and the j2th dividing surface; that is, the angle between the © 2011 by Taylor and Francis Group, LLC 19 Outline of the Generalized Theory of Capillarity surface unit vectors mˆ j1 and mˆ j2 (cf. the definition of the “cusp angle” in Chapter 2).
The bulk phases, previously labeled by the subscripts j or k, will be denoted by the superscripts (s) for the solid phase, (l) for liquid, and (v) for vapor, gas, or second liquid, while the dividing surfaces, previously labeled by the subscripts j, will now be denoted by the double superscripts (sv) for solid–vapor surface, (lv) for liquid–vapor, and (sl) for solid–liquid. 60, the condition of mechanical equilibrium for a dividing line at a solid surface is given by  ( σ + ( Cθ l − Cθv ) θl ) κ gs + ( γ (lv ) + (Cθl − Cθv )( κ ns cos θl − κ gs cos θl )) cos θl = γ ( sv ) − γ ( sl ) + (Cθl − Cθv ) κ ns .
81) and was derived by Schadow in 1922 . 79 is lengthy and involves the fourth-order derivatives of the position vector for the surface. Recent mathematical investigations © 2011 by Taylor and Francis Group, LLC 22 John Gaydos, et al. 77 and its higher dimensional extensions. The case of surfaces with nonfixed or free boundaries “requires the discussion of appropriate boundary conditions and has not attracted much attention so far” [49,51]. Extensions and elucidations of Gibbs and Buff’s efforts, which consider nonfixed boundary conditions, by Murphy , Melrose [53–55], Cahn and Hoffman [56,57], Helfrich , Boruvka and Neumann , Scriven et al.
A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition by Jean-Louis Salager