Prediction of Acid Red 138 solubility in supercritical CO₂ with water co-solvent

Acid Red 138, as a weak acid azo dye with a long alkyl chain, is widely used for protein fiber dyeing while it cannot dissolve in supercritical carbon dioxide. The objective of this study is to investigate the solubility of Acid Red 138 with water at the temperatures of 353.15, 363.15, 373.15, 393.15 and 413.15 K and over a pressure range of 20 to 26 MPa. The test results revealed that the phase equilibrium of water and Acid Red 138 was affected by the competition between pressure and density of supercritical carbon dioxide. Furthermore, the experimental solubilities were correlated by three types of density-based model. Good agreement with less than 3.36% of average absolute relative deviation between the calculated and the experimental data of water was achieved. In addition, the Chrastil model, Mendez-Santiago-Teja model and Sung-Shim model exhibited excellent correlation results for Acid Red 138 solubilities with the AARD values of 8.58%, 6.06% and 5.19%. Better understanding of the solubility behavior of Acid Red 138 in supercritical carbon dioxide displays potential for developing a microemulsion system for the eco-friendly dyeing of natural fibers.