title: Analytical expressions to calculate relative amounts of phases in a three-component phase diagram.
abstract: The relative amounts of different phases in multiphase regions in the common three-component phase diagrams are usually estimated graphically using geometrical features of the diagram. The present contribution introduces algebraic expressions for the lines in the diagram, which allow these numbers to be calculated directly from the experimental results. The method is an extension of the classical methods, which were translated into convenient computer programs [Laughlin, R. G. The Aqueous Phase Behavior of Surfactants; Academic Press: New York, 1994] to calculate the amount of different phases for individual compositions. The introduction of analytical geometry allows simplified expressions to be used for the calculations and the amounts to be presented as continuous functions of the total composition.
authors.affiliation: Chemistry Department, University of Virginia, Charlottesville, Virginia 22904, USA. sfbg@bellsouth.net
authors.forename: Stig E
authors.initials: SE
authors.lastname: Friberg
authors.forename: Abeer
authors.initials: A
authors.lastname: AlBawab