TRANSLATION OF VANDERWAALS,JD THE THERMODYNAMIC THEORY OF CAPILLARITY UNDER THE HYPOTHESIS OF A CONTINUOUS VARIATION OF DENSITY

Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquid-gas system (Sections 1-4). 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 (d2ρ/dh2); 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 (τk-τ)3/2, where τk 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 (d2ρ/dh2) on the free energy and surface tension (Section 15). © 1979 Plenum Publishing Corporation.