Simulation of aqueous and supercritical fluid dyeing of a spool of yarn

Aim of the present work is to propose a simple model that simulates the dyeing process of a spool of yarn both with the aqueous and supercritical techniques pointing out the main characteristic times and allowing calculation of dye concentration profiles both in the dyeing 'bath' and along the yarn spool. The analysis of the influence of characteristic times ratios gives some indications on the best operative conditions that should be attained to guarantee an uniform dye distribution along the package radius both for aqueous and supercritical dyeing; the two processes, in fact, mainly differ for the order of magnitude of the characteristic times. To support the discussion arisen from the different roles of characteristic times on the model, a practical example of supercritical dyeing simulation is also performed for a specific PET package with a disperse dye already used in the literature at well defined working conditions.