Stability of polydisperse fluid mixtures

The stability of a polydisperse fluid mixture is treated in the framework of continuous thermodynamics based on an equation of state with two parameters. The polydispersity is described by a distribution function depending on one identification variable M, such as molar mass or number of carbon atoms. Assuming the pure component parameters to be simple functions of M, and presuming simple mixing rules, equations to calculate the spinodal and the critical point are derived. As a demonstration, the proposed method is applied to continuous n-alkane mixtures described by gamma distributions using the van der Waals equation of state. The polydispersity results in a considerable increase in the spinodal temperature and the critical temperature. Furthermore, because of the polydispersity the maxima of the spinodal and the critical points no longer coincide.