Liquid surfaces: theory of surface tension

Abstract

The theory of equilibrium liquid surfaces is reviewed from the macroscopic (thermodynamic) and microscopic (statistical) points of view. Although emphasis is placed on the surface tension, other surface thermodynamic quantities are treated, especially the contact angle and work of adhesion. The Gibbs scheme is used to describe the surface thermodynamics. The equivalent hydrostatic approach, the curvature dependence of the surface tension and its relation to other surface quantities are presented. T h e effect of solid surface topology on the contact angle is discussed, together with the controversial Young's equation. Good's and Fowkes' theories are described and criticised from the statistical point of view, The surface tension theories for simple liquids (Kirkwood and Buff), simple metals (Evans) and solid-fluid interphases (NavascuCs and Berry) are deduced from a single statistical mechanical formalism. The van der Waals theory of the liquid vapour interphase is presented. Thermodynamic perturbation theory for the interphase (Toxvaerd, Abraham) and the analysis of the free energy density as a functional of the interphase density (Yang, Flemming and Gibbs) are discussed. Theoretical predictions for the surface tension of argon are compared with both laboratory experimental and computer 'experimental' data. A statistical mechanical theory of wetting is presented. Other topics such as the temperature dependence of the surface tension are also discussed in this review. Experimental methods of determining the surface tension and contact angle are briefly described.

On the nuclear curvature energy

“…6b) as needed for 8geo (12): this makes the Thomas-Fermi result have even globally the wrong sign as compared to the final result. Still, ze~(z) is well converged to order h 4 and again the semiclassical result up to order h 4 represents the average of the quantal one (Fig.…”

“…The constant Zo in (9c) stands for the effective location of the sharp surface previously defined in connection with R by u =0 (this is equivalent to the definition of the Gibbs' dividing surface [12]): …”

“…Nevertheless, for the calculation of expectation values they are very efficient. For more detailed discussions, the graphs for the semiclassieal surface energy density e~(z) and for ZSs(Z) (entering (12)) are shown in Fig. 6 at different orders of h 2.…”

“…4). This investigation was one reason why we introduced the quantity c7~ g~~ (12) in the first place. Now, the influence of the quantal Friedel oscillations on the surface and geometrical curvature energies can be discussed.…”

Calculation of the interfacial free energy of a fluid at a static wall by Gibbs–Cahn integration

“…Mechanical approaches rely on the equality of surface free energy and surface tension, which is true for a fluid-solid interface as long as the solid is treated as a static external field and not a fully interacting elastic system. 22 In this method, [23][24][25][26] ␥ wf is determined from simulation using the Kirkwood-Buff equation 27 for the surface tension,…”