Alkali Dosing Profiles and Mass Transfer in Jet Dyeing
Controlled progressive alkali dosing matches jet fabric loop velocity to eliminate surface fixation spikes and secure level shade fixation on cellulosic cloth.
Fickian Diffusion Cotton
Transport Model
Mass transport of solute molecules through a porous polymeric substrate proceeds according to a concentration gradient as described by classical diffusion equations. In textile wet processing, fickian diffusion cotton describes the standardized behavior of direct or reactive dyes migrating through the water-swollen pores of cellulose fibres. The rate of dye penetration is proportional to the concentration difference between the fiber surface and the internal regions.
Fibre Interaction
Cellulose fibers in an aqueous dye bath undergo swelling, which increases the accessible pore volume and allows dye molecules to enter the internal structure. This swollen state facilitates the random thermal motion of dye molecules, allowing them to move through the liquid-filled channels of the cotton. Since the diffusion coefficient is heavily dependent on temperature, heating the liquor increases the kinetic energy of the dye molecules and accelerates their movement into the fibre matrix.
This thermal dependency is exploited during industrial dyeing to control the rate of exhaust and secure even dye distribution.
Dyeing Kinetics
Practical measurements of dye uptake over time demonstrate that the rate of penetration conforms to the square root of time relationship during the early stages of the cycle. This kinetic pattern allows the dyers to calculate the diffusion coefficients of specific dye classes on cotton. Knowing these values helps in optimizing the cycle times of dyeing machines.
Model Boundary
Deviations from this transport model occur when strong electrostatic repulsions or attractions exist between the dye molecules and the cellulose surface. When high salt concentrations are added to the dye bath, they screen these electrical charges, restoring the predictable concentration-driven transport. Non-isothermal conditions in the dye bath also alter the diffusion rates, making the classical steady-state assumptions invalid.