The mathematical expression of rate constants in empirical rate of dyeing equations in disperse dyeing

Abstract

The relationship between the rate constants in empirical rate of dyeing equations and the diffusion coefficient of dye in the fibre have been clarified by means of a statistical curve fitting method, where the rate of dyeing curves calculated from the theoretical equations (those of Wilson and Newman) have been compared with those from the empirical equations in the range Mt/M∞ from zero to about 0.8. The comparisons revealed that many of the empirical equations are suitable for describing the dyeing rate when there is a delay of dye sorption in the early stages, and one of them is useful for determining the dyeing rate when there is rapid dye sorption at the initial stages. The fact that these empirical equations fit well to practical dyeing can be explained in terms of the sorption delay caused by the stagnant solution layer surrounding the fibres.

A kinetic and thermodynamic study of lac dye adsorption on silk yarn coated with microcrystalline chitosan

“…This result is consistent with the known increase in the rate of dye diffusion with temperature [37]. The a values obtained at different temperatures were <0.70, indicating that the rapid adsorption of lac dye on silk yarn coated with MCCh occurred during the initial stage [41].…”

“…The modified Cegarra-Puente equation is applicable to the dyeing process with rapid dye sorption at the initial stage. The dye adsorption rate constants at different temperatures were calculated using the modified Cegarra-Puente Eqn 5, which is suitable for baths with the full range of exhaustion values [37,40,41]:…”

Combined UV–Vis-absorbance and reflectance spectroscopy study of dye transfer kinetics in aqueous mixtures of surfactants

“…A number of empirical equations have been employed to fit the kinetics of dye absorption onto textile fibres [32]. The physical meaning of the empirical fit parameters have been discussed by Shibusawa [32]. A simple, general form to fit dye kinetics is given by:…”

“…The kinetics of dye adsorption onto a number of fibre types, in particular polyester [19,20], have been the subject of experimental [21][22][23][24][25][26][27] and theoretical [28][29][30][31][32][33][34][35][36][37][38][39] studies. The rate of dyeing of polyester is limited by the diffusion of dye molecules into the textile fibres [28,33,40].…”

“…Given that washing is performed at temperatures much lower than the temperature of the dyeing process, it is unlikely that during the limited time of a washing cycle ( 2hrs) an equilibrium between the dye concentration inside and outside the fibre will be reached [10]. It is then reasonable to assume that dye release during washing tests proceeds dominantly from the outer fibre surface, which contains a higher concentration of dye as compared to the bulk of the fibres (see references [32] and [36] and references therein). Therefore, dye diffusion through the fibre's densely packed crystalline structure can be neglected in considerations of the release kinetics.…”