Dyebath exhaustion profiles

Variation of the concentration of dye in the dyebath during the dyeing is referred to as the exhaustion profile, and the shape of this profile has been believed by many researchers to be the greatest determining factor in levelness of dyeing. ... 

Medley and Holdstock developed a mathematical model of the dyeing process, defined as simple depletion theory . Using this theory, they were able to show that an exponential exhaustion profile should give the optimum levelness for the same reasons as Brooks empirical argument - that at the end of the exhanstion phase the risk of nnlevelness is greatest. Their work also involved the development of a commercial dyebath monitoring system in order to apply their theoretical work to a real dyehorrse situation. ... 

Experimental work on dyebath exhaustion control was also carried out using a pilot-scale radial flow package dyeing machine, and the results supported the flndings of the theoretical model. In particular, it was found that a quadratic profile was preferable to an exponential profile, which in turn was preferable to a linear profile. All controlled exhaustion dyeings gave better levelness than a standard (constant temperature ramp) dyeing method. This work was continued by Illett, who improved the mathematical solution of the Nobbs-Ren model and applied it to axial flow machines. 

A close look at the reported exhaustion values at the end of each dyeing profile suggests that complete exhaustion of dye from dyebath is impractical in many cases. Given the number of factors that could affect the outcome of the dyeing process, it is difficult to suggest any one profile as the best profile in terms of overall performance. Various researchers, however, have promoted different exhaustion profile shapes as producing the overall best results compared with the average. However, no conclusive evidence in support of any of the models for use on all fibres has so far been reported. 

As can be seen in this profile, the exhaustion rate is dependent on the total time of dyeing and the current concentration of dye in the dyebath. 

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