Fluid Phase Equilibria 394 (2015) 175–185 Contents lists available at ScienceDirect Fluid Phase Equilibria jou rn al h om epage: www.elsevier.com/locate/fluid Barotropic phenomena in binary mixtures Héctor Quinteros-Lama a,∗ , Gerardo Pisoni b , José Matías Garrido a , Andrés Mejía a , Hugo Segura a a Department of Chemical Engineering, Universidad de Concepción, Concepción 4070386, Chile b Facultad de ciencias exactas físicas y matemáticas, Universidad Nacional de Córdoba, Córdoba X5016GCA, Argentina a r t i c l e i n f o Article history: Received 7 January 2015 Received in revised form 27 February 2015 Accepted 3 March 2015 Available online 12 March 2015 Keywords: Barotropy Isopycnicity Mass density inversion Equations of State (EoS) Global phase diagram (GPD) a b s t r a c t This contribution aims to theoretically describe the most common cases of mass and molar density inver- sions, as they can be observed in multi-component fluid mixtures in sub-critical phase equilibrium. These phenomena – also known as barotropy – affect the relative position of phases in a gravitational field for the case of mass barotropy, while the total population of species along the interfacial length is drasti- cally affected for the case of molar barotropy. Rigorous and analytical relationships are developed here to detect both mass and molar density inversions ending at the critical points of mixtures. These condi- tions, which are useful to describe the existence and persistence of density inversions, are then applied to unequivocally demonstrate that mass and molar barotropy are physically independent phenomena. Qualitative evidence pointing to that conclusion is discussed at the light of the global phase diagram of van der Waals mixtures composed by molecules of different size. Particularly, it has been established that molar density inversions appearing in feasible temperature ranges are sensitive to differences between the molecular hard core volumes of the constituents, a conclusion that is well supported by experimen- tal results. Mass density inversions, in contrast, depend not only on the molecular size but also in the molecular weights of the constituents, in such a way that mixtures may exhibit mass barotropy without exhibiting molar inversions, and vice versa. Analytical relationships for establishing the slope of density inversions on a P–T projection have also been obtained both for mass and molar barotropy. From the comparison with the temperature slope of the three-phase line, we conclude about the possibility of observing density inversions between immiscible liquid phases or between a liquid and a gas phase. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Barotropy – also known as density or volume inversions – corresponds to a singular condition of phase equilibrium where it is observed that the densities of – at least – two phases coexisting in a heterogeneous mixture invert [1–3]. Isopycnicity, in turn, corresponds to the condition where a barotropic point or a density inversion exactly occurs [3]. In general, density inversions may be primarily classified in terms of mass or molar barotropy depending on the units in which volumes become equivalent at the specific isopycnic conditions. Particularly, from a mechanical viewpoint, mass barotropy is a phenomenon that affects the relative position of the involved phases in a gravitational field, while it has been reported that the total population of species (or total density ∗ Corresponding author. Tel.: +56 412981359. E-mail address: hquinteros@me.com (H. Quinteros-Lama). profiles) is affected along the interfacial length for the case of molar barotropy [4]. In a recent publication, Tardón et al. [4] developed a set of rigorous mathematical conditions for detecting ranges of molar isopycnicity. As it was established in that paper, in addition to the necessary conditions of phase equilibrium, a heterogeneous mixture exhibiting molar isopycnicity between its ˛-ˇ phases is characterized by an inversion of molar volumes, ˜ v (or molar densi- ties ), ˜ v ˛ = ˜ v ˇ ⇔  ˛ =  ˇ (1) From their results systematically applied to mixtures in the vicinity of the critical point, Tardón et al. [4] were able to demon- strate that a stable critical molar density inversion point (CMoDIP) of a binary mixture satisfies the following relationships, ˜ A 2x = ˜ A 3x = ˜ A xv = 0 (2) Here, ˜ A corresponds to the Helmholtz energy function of the mixture while ˜ A mxnv is a shorthand notation for the partial http://dx.doi.org/10.1016/j.fluid.2015.03.004 0378-3812/© 2015 Elsevier B.V. All rights reserved.