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Extra info for A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition

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66. If these two projection relations are squared and added, then one obtains a “cosine-rule” expression among the various forces at the contact line. The expression contains three angles of contact and is given by ( γ ( j ) )2 + ( γ ( j1 ) )2 + ( γ ( j2 ) )2 + 2 γ ( j ) γ ( j1 ) cos θ jj1 + 2 γ ( j ) γ ( j2 ) cos θ j2 j + 2 γ ( j1 ) γ ( j2 )cosθ j1 j2 = (σκ )2 . 68) It is possible to eliminate two of these three angles in favor of the cusp angle θj1j2 by performing a rotation of the horizontal and vertical axes.

57, there are two kinds of mechanical equilibrium conditions that also arise from the mathematical analysis. , dividing surfaces), while the other condition is for three-phase dividing lines. The simplest forms of these mechanical equilibrium conditions are explicitly derived in Chapter 2 for both incompressible and compressible axisymmetric capillary systems. 58) where nˆ is the unit normal by which the dividing surface is oriented, P(β) is the pressure in the bulk phase for which nˆ is directed outward, and ∇ 22 and ∇*2 are surface differential operators [27].

The fundamental equation describes the thermodynamic states in all parts of the fluid system, while the minimum principle determines only the equilibrium states possible from the multitude of thermodynamic states permitted by the fundamental equation. Various forms or representations of the minimum principle and the fundamental equation are possible. , the thermodynamic potentials) is performed by means of a mathematical technique known as a Legendre transformation [6,11,14,17,19]. Using this technique, parameters defining the fundamental equation may be replaced by their corresponding intensive quantities.

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A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition by Jean-Louis Salager

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