Desorption Kinetics of Hydrolyzed Reactive Dyes in Continuous Wash Ranges
Continuous wash ranges clear hydrolyzed reactive dye by maximizing thermal diffusion and maintaining steep counter-current concentration gradients across wash stages.
Fickian Desorption Model
Mathematical Description
Mathematical principles describe the rate at which solutes migrate from a saturated solid substrate back into a surrounding liquid medium. The fickian desorption model provides the equations used to predict how unfixed reactive dyes leave cellulose fibers during the wash-off stage.
Diffusion Rate
Movement follows the law where the flux is proportional to the concentration gradient across the fiber diameter. In the fickian desorption model, the diffusion coefficient remains constant regardless of the local concentration of the solute. This assumption simplifies the calculation of washing times in continuous processing because it eliminates the need for complex adjustments as the dye level drops.
Designers use these equations to determine the length of the ranges required to remove every trace of hydrolyzed pigment.
Boundary State
Surface concentration drops to zero the moment the fiber enters a clean water bath. When applying the fickian desorption model, the calculation assumes the bath remains perfectly mixed and large enough to prevent solute buildup. Rapid water exchange maintains the gradient necessary for efficient extraction.
Laboratory Calibration
Technical teams use the model to optimize water consumption in industrial laundries. Precise use of the fickian desorption model allows a plant to reach target cleanliness levels with minimal rinsing cycles.