The Kinetics of Wool Dyeing

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Abstract
It is shown that the rate controlling mechanism of dyeing wool with the simple acid dye Acid Orange II can be diffusion through an unstirred film of liquid or diffusion through the fiber. At low concentrations of dye, the diffusion of dye through an unstirred film of liquid is the slower of the two processes, whatever the degree of agitation. At higher concentrations of dye, the rate controlling step changes from diffusion through liquid film to diffusion through solid when the stirring of the solution is increased beyond the point at which the reaction becomes stirring- independent and the activation energy, determined from the temperature coefficient, changes from approximately 5 to 13 kg.-cal./mole. At high concentrations of dye the diffusion of dye through the fiber proceeds from a saturated concentration on the fiber surface, which action can be readily treated quantitatively. At low dye concentrations the diffusion through the unstirred liquid film can also be treated by the simple diffusion law. In the intermediate range of dye concentrations, however, the diffusion into the fiber proceeds from a varying concentration on the fiber surface and is treated on the basis of a semi-empirical relationship. From consideration of the diffusion coefficient and the apparent energy of activation it is con cluded that dye is not transported through pores, but rather that the swollen fiber behaves like a gel and diffusion occurs by displacement of peptide molecules.