Translation of J. D. van der Waals' ``The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density''
Abstract
Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquidgas system (Sections 14). If density ρ is a function of height h then the local free energy density differs from that of a homogeneous fluid by a term proportional to ( d ^{2} ρ/ dh ^{2}); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show how ρ varies with h (Section 6), how this variation leads to a stable minimum free energy (Section 7), and to calculate the capillary energy or surface tension σ (Section 9). Near the critical point σ varies as ( τ _{ k } τ)^{3/2}, where τ _{ k } is the critical temperature (Section 11). The paper closes with short discussions of the thickness of the surface layer (Section 12), of the difficulty of assuming that ρ varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than ( d ^{2} ρ/ dh ^{2}) on the free energy and surface tension (Section 15).
 Publication:

Journal of Statistical Physics
 Pub Date:
 February 1979
 DOI:
 10.1007/BF01011513
 Bibcode:
 1979JSP....20..197R
 Keywords:

 Capillarity;
 critical point;
 free energy density;
 surface tension