Surface modeling as a tool for constructing pseudo ternary diagrams

Juliana Verdan Silva Camilo, Anna Áurea Gomes Ferreira, Josane Assis Costa, Claudia Regina Elias Mansur, Fernando Gomes de Souza Junior


Microemulsions have been developed and evaluated for application in various fields. For their development, ternary phase diagrams are initially constructed, obtained by investigating mixtures of the aqueous and oil phases and a surfactant, to determine the regions composed of liquid microemulsions. However, the construction of these diagrams requires many steps, so simplification of this method can be useful for the formulation and application of these microemulsified systems. Therefore, this article proposes a method to obtain these diagrams employing mathematical modeling, by testing systems composed of kerosene (as oil phase), a nonionic surfactant based on ethoxylated nonylphenol (NP80), and salt water. The study aimed to ascertain which models (linear, quadratic or special cubic) were able to describe the empirical observations, i.e., the ternary phase diagram containing 99 points. The results obtained showed that a quadratic model with a smaller sample (31 points) was able to represent these systems with 61% variability of the observed data and a confidence level higher than 99.9%. The smaller sample (31 points) was defined by means extrapolation lines, as described in the standard ISO11358, permitting identifying the liquid microemulsion regions of the system composed of kerosene, NP80 and salt water. This result is very promising since it permits determining the conditions of interest with significantly less experimental work, and commensurate reduction of the final cost of the experiments.


Microemulsions; Phase Diagrams; Mathematical Modeling

Full Text:




  • There are currently no refbacks.

Copyright (c) 2021 Brazilian Journal of Experimental Design, Data Analysis and Inferential Statistics