In textile dyeing

using disperse dyestuff on synthetic fiber is one of the most important typical dyeing combinations.The mathematical model of this typical dyeing process was built by means of combining the existing dyeing theory and human experience through choosing the disperse dyestuff blue RSE on polyester as the representative.Firstly

three temperature-related dyeing characteristic models were built independently.Then

using the reaction rate equation

the three models were integrated to obtain the integrated model of dye uptake rate.During modeling

the grey Verhulst model

for its characteristics of less data and high accuracy

was used

so the integrated model had the advantages of being easy to determine parameters values and small amount of calculation.For the same type combinations of dye and fiber

the model could be equally applicable by changing the parameters values only.The experimental result showed that the integrated model had high accuracy and good generalization ability

and could meet the need for predicting dyeing result.