Numerical Simulation of Dyeing Process of Cotton with Natural Dye

Cotton dyeing is a very complex process with many variables in which different phenomena occur simultaneously. This study aimed to describe the cotton dyeing process by natural dye, using a mathematical model that consists of three mass conservation equations that depict dyeing cotton in cones, taking a representative volume element at the micro, meso, and macroscales. The first equation describes the concentration changes of the dye in the solution, taking into account the diffusive, convective, adsorptive, and reactive effects. The second equation describes the changes in dye concentration in cotton fiber, considering the diffusive, adsorptive, and reactive effects within an intermediate scale. The last equation describes changes in the concentration of dye in the solution on the macroscale, based on the characteristics of the equipment and the difference in concentration before and after passing through the fiber. In addition, a fluid continuity equation was incorporated, taking into account Darcy’s law. In the simulation of the dyeing process with synthetic dye with initial concentrations of 0.408 and 2.06 kg/m3, RMSE of 0.00221 and 0.0289 kg/m3 were obtained, respectively. For the simulation of a dyeing process with natural dyeing, a behavior similar to the experimental data was obtained.

Thermodynamic properties of cotton dyeing with indigo dyes in non-aqueous media of liquid paraffin and D5

On the basis of investigation into the dyeing equilibrium of cotton fibers with indigo dyes in decamethylcyclopentasiloxane (D5), liquid paraffin and water, the thermodynamic properties of cotton dyeing with indigo dyes in non-aqueous medium systems were studied in comparison with aqueous dyeing. The main works involved are as follows: firstly, the adsorption isotherms were created; then, the three theoretical adsorption models of Nernst, Langmuir and Freundlich were used to fit the adsorption isotherms created; finally, the thermodynamic parameters were calculated. The results showed that the adsorption isotherms were all in line with the Freundlich model. The order of dyeing affinity was in the sequence: liquid paraffin > D5 > water. The dyeing entropy in the three media showed positive values, which is mainly attributed to the adsorption of both indigo-leuco and water onto cotton fibers, thus reducing the ice-like structure formed among the water molecules in the dyeing system and the hydrophobic bonding structure formed among the non-aqueous medium molecules, then leading to an increase in the system disorder. The dyeing heat in the three media also showed positive values, due mainly to the absorption of thermal energy to “melt” the ice-like structure and to “break” the hydrophobic bonding structure. These dyeing thermodynamic properties are conducive to understanding and interpreting the dyeing performance and behavior of indigo dyes in non-aqueous dyeing systems.