Mathematical Models to Follow the Dyeing of Cotton Knitted Garment Using the Capillary Rise Technique

This paper presents the study of the application of direct dyes on pre-treated cotton jersey knitted fabric using an experimental system based on the capillary rise technique. The developed device ensures the vertical suspension of a cloth surface in contact with a dyeing bath and allows the capillary rise of the dye bath in the textile structure. A series of experiments were carried out using cotton jersey knitted fabric as textile fabric model and the direct dyes bath (wetting agent, salt, sodium carbonate and direct dye) as wicking liquids by using an electronic microbalance. A mathematical model was developed to interpret the experimental data in terms of kinetic parameters of the absorbed dye bath amount and the diffusion of the molecule into the cotton jersey knitted fabric. The results show that the double-exponential kinetics model and the simplified Crank solution to Fick’s second law equation are in reasonable agreement with experimental data of the absorbed dye bath amount and the diffusion of the molecule of dye into the cotton jersey knitted fabric, respectively.