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Additional info for A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition
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.
At the lowest level of generality, where one ignores the effect of curvature and contact angle potentials on the condition(s) of mechanical © 2011 by Taylor and Francis Group, LLC 18 John Gaydos, et al. 2 Schematic of (a) a side view of an axisymmetric liquid lens at the contact line, and (b) a quadrilateral composition of the three surface tensions, one line tension, and angles present at the contact line. 63, as originally stated in 1805 is recovered; however, the classical Young equation of capillarity and the classical Neumann triangle relation must be corrected via additional terms that represent the influence of the line tension σ into the overall “force” balance at the three-phase contact line.
64 as two scalar relations; one resulting from projecting the vectors into the horizontal plane and another from a corresponding projection into the vertical plane . Both relations represent balances of surface and linear forces in their respective planes. 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.