GENERALIZED KORTEWEG EQUATIONS FOR PHASE-SEPARATION NEAR THE CRITICAL-POINT IN BINARY GAS-LIQUID MIXTURES

This paper deals with the definition of the order parameter in a binar y gas-liquid system in the neighborhood of the critical point. The iso thermal volume-composition (or V,x) diagram of a binary gas-liquid sys tem may show one (or more) critical point(s). If a critical point is p resent, we determine the orientation of the tieline in the neighborhoo d of this point from the equation of state, using algebraic means. Thi s orientation is needed to determine the proposed order parameter: the length of the tieline. The method is similar to the method based on t he work of Korteweg, however, his calculation was restricted to the sp ecial case that the critical point lies close to the critical point of the pure component. Consequently, the character of such a critical po int is mainly vapor-liquid-like in his work. For this reason Korteweg' s approach deals with a special situation and cannot be applied to the general case in which the phase separation is neither pure liquid-vap or, nor exclusively liquid-liquid, i.e., without vapor. The present me thod is based on a coordinate rotation in the V,x plane. It is shown t hat the end points of the tieline for a given pressure can be expresse d in terms of the Taylor series coefficients of the equation of state evaluated around the critical point.