Kinetics Study of Forced Textile Dyeing Process

The use of computational methods to simulate the textile dyeing process provides a powerful tool to allow an understanding of the mass transfer kinetics in aqueous solutions during the dyeing process. Moreover, analysis of the time scales associated with the main phenomena can lead to a precise knowledge of the dyeing kinetics during the process, which in turn can be used to improve the process control, reliability and, perhaps most importantly, the environmental impact of the dyeing process. Traditionally, dyeing techniques are carried out in a batch process. The bobbins of thread are fixed to perforated supports and receive dye from the liquid passing across the bobbins and re-circulating to a mixing tank. Inside the bobbins dye has to be transported by convection and dispersion to the inner core of the threads. Under normal operating conditions the dye is added at the beginning of a dyeing cycle in the mixing bath and the process runs under batch conditions, that is, without changing the amount of dye in the system. In general, dye distribution factor (DDF) and dye uptake (CDEP) benefit from high recirculation flux values and low dispersion resistances. In order to investigate possible improvements to the traditional dyeing process the effect of periodic variations in the boundary conditions (reverse flow operation) on the bobbin thread dyeing process was studied. The system is operated by periodically reversing the conditions of the dyeing bath fluid external to the thread bobbins and inside the bobbins. The periodic forcing is modeled by an ad hoc discontinuous periodic function and a partial differential equations mathematical model that takes this function into account is developed. A comparison between the forced and unforced processes was conducted by analyzing the dye distribution factor and the total amount of dye adsorbed during the transient regime for the two processes. Due to the batch nature of the dyeing process under study there are no differences between the regime values for the forced and unforced processes. In other words, asymptotically (after more than three hours) the two processes reach the same dye distribution. On the other hand, the transient forced and unforced processes exhibit qualitative and quantitative differences.Finally, we demonstrate that to benefit from the reverse flow operation the switch time magnitude has to be comparable with the time scales of the main transport phenomena, the convection time being the most important transfer phenomenon.