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Additional resources for A. Wilhelm Neumann, Robert David, and Yi Zuo (eds): Applied Surface Thermodynamics, 2nd Edition
97) 28 John Gaydos, et al. 98) which means that the surface mechanical equilibrium radius of a cylindrical bubble has to satisfy the simple well-known equation 1 γ = ∆ P. 100) which means that the surface mechanical equilibrium radius of a spherical bubble has to satisfy © 2011 by Taylor and Francis Group, LLC 2 2 γ + C J 2 = ∆ P. 59. , mechanical potentials) along the entire interface. That is, we restrict our consideration to an interfacial system that is homogeneous over the dividing surface.
After a suitable reduction, the total free energy ΩΣ remains a thermodynamic potential with the same extremum properties (yielding the same solution) as any other suitable thermodynamic potential. Mathematically, the difference between the total energy and the total free energy extremum formulations is that the constraints in the first definition (total entropy and masses remaining constant) are replaced by the subsidiary conditions T = T (a constant) and µj + φ = µ j (a constant) in the second definition, such that both problems yield the same solution.
107) 30 John Gaydos, et al. 3 The variation of the surface area due to the variation δz. 104 as dΩ (V ) = − P1δV1 − P2δV2 = − P1 Aδz + P2 Aδz = − ( P1 − P2 ) Aδz. 108) The corresponding variation of the dividing surface area, δA, caused by the normal displacement δz can be written as δA = ( x + δx )( y + δy) − xy ≈ xδy + yδx. 110) where R1 is the radius of the curvature c1 of the area along side x; that is, side BD. 110 can be simplified to © 2011 by Taylor and Francis Group, LLC δx = x δz = xc1δz.