## Translation of a paper of J D van der Waals

### October 14, 2007

The translation of a Dutch paper (PhD thesis?) of van der Waals into English by J S Rowlinson is available here (Unfortunately, I have no access to the soft copy version):

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 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 /dh 2); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show how 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 (Section 9). Near the critical point varies as ( k )3/2, where 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 varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than (d 2 /dh 2) on the free energy and surface tension (Section 15).

Generally, the origin of the concept (and name) of spinodal decomposition is credited to van der Waals. I do not know if this document discusses that aspect of van der Waals’ work — I have to go to the library tomorrow.