Dynamic Modelling of the Diffusion in a Dyeing Process

Abstract

A common goal of all dyers is to achieve the correct shade as early as the first dyeing. But the disperse dyeing process is very complex, being characterized by the diffusion-controlled sorption of dyes that depends on several physicochemical parameters such as dye concentration and temperature of application. Wilson and Hill developed equations describing the uptake of disperse dyes by cylindrical fibres as a function of the diffusion coefficient and the nature of the dyebath. This coefficient is a physical term that permits comparison between different dyeing experiments. However, the literature reveals no equation that expresses the influence of experimental parameters on the diffusion coefficient value. Thus, this work proposes a mathematical model describing the evolution of this diffusion coefficient for disperses dyes as a function of time, initial dye concentration, and the nature of the dyebath (finite or infinite).

Key Words:

• Modelling
• polyester
• disperse dye
• diffusion coefficient

Additional information

Notes on contributors

V. Koncar

Vladan Koncar received his BA degree in May 1986 from the University of Belgrade, Department of Electronic Engineering, Yugoslavia. His Master's degree and Ph.D. degree, in 1988 and 1991 respectively, both from the Univesity of Lille 1, Prance, Automation Control Laboratory. He is currently an Associate Professor at Ecole Nationale Superieure des Arts et Industries Textiles, Roubaix, Prance in the Genie et Materiaux Textiles laboratory. His current research interests include predictive control, compound control, robust control of complex systems, modelling of dyeing processes, nonlinear optimization, virutal reality and communicated objects.

M. Casetta

Mathilde Casetta received her BA degree in June 1996 from ENSAIT, Department of Textile Chemistry. She received her Master's degree in June 1997 from the University of Lille 1, Prance, GEMTEX Laboratory and her Ph.D. degree in December 2000, at the same university. Dr. Casetta is currently a Researcher at the Ecole Nationale Superieure des Arts et Industries Textiles (ENSIT), Roubaix, Prance in the G⁄'enie et Matériaux Textiles laboratory (GEMTEX). Her current research interests include physicochemistry of dyeing and of polymers, diffusion phenomena, modelling of dyeing processes and fibres recycling.