Diffusion/adsorption model of cellulose dyeing. II. Ordinary cellulose–direct dye system

The diffusion and adsorption of C.I. Direct Yellow 12 and Blue 15 in water‐swollen ordinary cellophane sheets were examined at various ionic strengths. The concentration dependence of apparent diffusion coefficients, Dc, for these dyes was obtained from the diffusion profiles in the substrate, which were measured by the use of the cylindrical film roll method. The decrease of apparent porosity with an increase in the amounts of adsorption was observed. To explain the diffusion/adsorption behaviors of these systems, a variable porosity model was proposed and was applied to analyze the concentration dependence of Dc's. The diffusion/adsorption behaviors of these dyes could be quantitatively described by this model at relatively low ionic strengths. At higher ionic strengths and/or lower values of C, i.e., at the large values of Cim/Cm, where the C's are the concentrations of immobilized (suffix im) and mobile (suffix m) species, it needed to introduce the concept of dynamic equilibria which occurred simultaneously with diffusion but deviated from the true equiliblia measured by the adsorption experiments.