A Study of the Interplay between Global and Phase Compositions at Four-Phase Equilibrium in Ternary Systems

Ternary systems at set global composition (z) under four-phase equilibrium conditions present a rich variety of possible behaviors, such as:

1. Presence of a single trace phase, i.e., a microphase coexisting with three macrophases. Two out of the four phases can assume the trace-phase role, depending on the value of a global variable. This is the regular behavior for ternary four-phase points (T-4PPs). A trace phase is a phase of infinitesimal size. For instance, in a bubble point, the vapor is the trace phase and the liquid is the macrophase. A trace phase may be incipient or evanescent, depending on how the equilibrium point featuring the trace phase is approached.
2. Simultaneous presence of two trace phases (ternary double-tracency four-phase point, T-DT-4PP). Here, two microphases are at equilibrium with two macrophases.
3. Simultaneous presence of two trace phases, but occurring in two different possible ways (ternary dual double-tracency four-phase point, T-D-DT-4PP).
4. Simultaneous presence of three trace phases (triple saturation point).

Situations 1 through 3 occur within the heterogeneous region of the isopleth at global composition z, whereas situation 4 occurs on its phase envelope. Indeed, none of these situations will be observed if the ternary system does not exhibit four-phase behavior. In this work it is shown that, through a relatively simple criterion, it is possible to distinguish among the possible behaviors that a T-4PP may exhibit as a result of the phase compositions and the global composition. This work not only considers the case in which, on the Gibbs triangle, the compositions of the four phases define a convex quadrilateral, but also the case of concave (or arrow-shaped) quadrilaterals. Finally, a number of computed ternary isopleths exhibiting four-phase equilibria, with T-4PPs of some of the previously mentioned types, are presented. These isopleths, which cover wide ranges of conditions, show a rich variety of topologies.