Bobbin dyeing is a low-liquor-ratio technique that consumes less water and generates less wastewater. However, the bobbin dyeing is carried out in a closed kettle body, and many interfering factors that affect dyeing rate and dyeing uptake concentration cannot be observed and controlled in real time. Dyeing digitization can be used to achieve real-time monitoring of the amount of dyeing on the yarn bobbin, and is an important means of obtaining information on bobbin dyeing. To achieve digital dyeing, in this paper, a mathematical model for mass transfer based on yarn dyeing principles is established first, describing the process of dyeing from the beginning to equilibrium. Subsequently, by using anti-overlap winding principles and Darcy’s law, the anisotropic permeability in yarn bobbins is calculated. Then, a two-dimensional axisymmetric finite-element model describing the bobbin yarn’s dyeing behavior is constructed. Finally, the flow characteristics and the dye amounts are obtained. The results reveal that unevenness occurs in the initial dyeing stage but is gradually alleviated with dyeing continuation. After 3300 s, dye concentration stabilizes at 2.11 mol/m3 across most areas. Moreover, operating pressures significantly affect the dyeing rate and the time needed to reach dyeing equilibrium. The model proposed in this paper offers real-time prediction of the flow characteristics and the distribution of dye uptake. It is helpful for evaluating different schemes, such as different inlet and outlet pressures, different dyeing times, etc., to improve the uniformity of dyeing.
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