Density fluctuation of a van der Waals fluid in supercritical state

Density fluctuation is one of the fundamental parameters which determine the various physicochemical properties of supercritical fluids. When the contour map of density fluctuation is drawn on the phase diagram, there exists a ridge which separates the supercritical region in two. In order to obtain a phenomenological picture with physical clearness, we formulate the density fluctuation and its ridge for the van der Waals fluid. They are expressed by fairly simple equations with reduced temperature (T-r=T/T-c) and number density (n(r)=n/n(c)). It is analytically ensured that the law of corresponding states is applicable to the density fluctuation and its ridge and the ridge is different from the critical isochore. The ridge is the locus of the points where the third derivatives of the Gibbs free energy become zero, and that drawn on a density-temperature phase diagram directly connects with the locus of the inflection points of the van der Waals isotherms in the unstable region. From the viewpoint of the valance of volumes occupied by molecules and void, the physical meaning of the ridge is also discussed. The consistent agreements are confirmed in the characteristics of the density fluctuation and the ridge for the van der Waals fluid and several real supercritical fluids. (C) 2003 American Institute of Physics.