Surface tension in ternary systems

The application of the Gibbs equation to ternary systems can be made only in cross-sections with a constant ratio of the amounts of substances, e.g. in the system A—B—C the pseudo-binary system A/B—C. The Gibbs equation in the ternary system is 

For the dividing plane between the bulk and surface phases, we can choose the condition 

The next procedure and the calculation of the surface adsorption of the third component is analogical as it was shown for binary systems. 

To get some information on the structure of melts in the ternary systems, it is very important to define the course of surface tension in the ideal solutions. The general approach used for the variation of surface tension with composition was given by Guggenheim (1977), who stated that the surface tension of ideal solutions should follow the simple additivity formula with a good approximation. The excess surface tension in real systems could be described by the Redlich and Kister (1948) excess function. For the surface tension of real ternary systems it can then be written 

As an example of calculation of the surface tension in the ternary system, KF-KCI-KBF4 is presented. The surface tension of this system was measured by Lubyova et al. (1997) using the maximum bubble pressure method. The system is a simple eutectic system experimentally attainable in the whole concentration triangle. 

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