Vapor-liquid equilibria using the Gibbs energy and the common tangent plane criterion

Phase thermodynamics is often perceived as a difficult subject that many students never become fully comfortable with. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based on the common tangent plane criterion (the Gibbs stability test), is presented in this paper. From a T-composition phase diagram for the mixture, the temperature is set at different values: above, intermediate to, and below the boiling temperatures of the pure components, to intersect different regions of the system. Students prepare an Excel spreadsheet where the Gibbs energy of mixing of the vapor and liquid mixtures are calculated and represented over the whole range of compositions and then, apply the Gibbs stability test to ascertain the aggregation state of the system and to calculate the VL phase equilibrium compositions. Finally, Matlab is used to generate the 3D Gibbs energy of mixing surfaces for both phases over the whole range of temperatures which facilitates the geometrical interpretation of the vapor-liquid equilibrium.

Visibility of sparkle in metallic paints

For suitable illumination and observation conditions, sparkles may be observed in metallic coatings. The visibility of these sparkles depends critically on their intensity, and on the paint medium surrounding the metallic flakes. Based on previous perception studies from other disciplines, we derive equations for the threshold for sparkles to be visible. The resulting equations show how the visibility of sparkles varies with the luminosity and distance of the light source, the diameter of the metallic flakes, and the reflection properties of the paint medium. The predictions are confirmed by common observations on metallic sparkle. For example, under appropriate conditions even metallic flakes as small as 1 μm diameter may be visible as sparkle, whereas under intense spot light the finer grades of metallic coatings do not show sparkle. We show that in direct sunlight, dark coarse metallic coatings show sparkles that are brighter than the brightest stars and planets in the night sky. Finally, we give equations to predict the number of visually distinguishable flake intensities, depending on local conditions. These equations are confirmed by previous results. Several practical examples for applying the equations derived in this article are provided.