Comprehensive analysis and modeling of dye diffusion within fibers in supercritical CO2 for sustainable textile dyeing

The textile industry is widely recognized as a high-pollution sector, with conventional dyeing processes marked by excessive water usage, high pollutant discharge, and low efficiency. Supercritical CO₂ dyeing has garnered attention for its environmental benefits; however, its industrial application remains limited due to inefficiencies, primarily governed by the diffusion coefficient of dyes within the fiber matrix. This study compiles and analyzes existing literature to systematically examine how temperature, pressure, dye type, and fiber type influence the diffusion coefficient. Results indicate that higher temperatures significantly enhance diffusion, consistent with the Arrhenius equation. Pressure can promote diffusion through CO₂ plasticization of fibers, but its effect is complex and condition-dependent. Low-molar-mass dyes exhibit better diffusion, and fibers with lower crystallinity—such as PMIA—are more conducive to dye penetration. A multi-variable diffusion coefficient model was developed based on the Arrhenius equation and free volume theory. All model fitting errors were within 10 %, indicating strong descriptive accuracy within the studied parameter window. However, the model is currently limited to 14 data points covering four dyes, and within a temperature range of 353 K to 413 K and a pressure range of 15 MPa to 25 MPa. This model offers a theoretical foundation for optimizing supercritical CO₂ dyeing parameters and may be extended to a broader range of fiber-dye systems in future applications.