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The initialization procedure proposed by Michelsen for locating stationary points in the tangent plane distance function was applied to several cases considered as challenging in the literature concerning phase equilibrium calculations. For most of the systems studied in the literature, such a simple procedure is enough to detect the phase instability; thus it is unnecessary to resort to more robust, more elaborated, and more time-consuming initialization schemes. For the conditions and systems where problems were found, a simple procedure was proposed to extend Michelsen's original scheme with the aim of increasing the probability of obtaining a negative value of the tangent plane distance function. Two algorithms for phase-split calculations were used. Both algorithms use a relaxation parameter to increase their convergence regions. No difficulties were found to calculate the equilibrium distributions in contrast with several convergence problems reported, in which other approaches were applied to the same two-phase systems.

A model is proposed to predict magnetic susceptibilities in diamagnetic binary fluid mixtures. The model predictions are compared to experimental information for nine binary systems including polar and non-polar compounds. The predictions are also compared to the results obtained from the traditional Boyer-Donzelot equation. For all systems analyzed, the model predicted magnetic susceptibilities closer to the experimental values than those predicted from the Boyer-Donzelot equation. The deviations from the experimental values decrease when the binary system exhibits a positive excess magnetic susceptibility.