Using Algebraic Geometry to Describe Boundaries of Microemulsion Regions in Nonionic Systems

This study aimed to propose an empirical polynomial function based on algebraic geometry which could represent microemulsion regions in nonionic systems. The systems composed of olive oil (OO), water (W) and various ratios of sorbitan monooleate (SMO) and polyoxyethylene 20 sorbitan monooleate (PSMO) mixtures were investigated for their microemulsion regions obtained on the phase diagrams. Concept of algebraic geometry in this study was that description of close-boundary shape was cross-sectioning of a 3D-geometrical object with a plane which could be explained by an empirical polynomial function of the {oil, water, surfactant mixture}. In-house ad hoc software was created according to the proposed concept. It was found that this method could describe boundaries of microemulsion regions in the studied systems. Although this method could not reduce time consumption since it required intensive computational powers, the software could automatically run. Moreover, the developed program could provide acceptable level of accuracy.