Mathematical modeling of absorption behavior of acid dye onto wool fibre using law of conservation of mass

Abstract

The absorption behavior of acid dye on wool fibre has been studied using isotherm, absorption kinetic and law of mass conservation equations. The Langmuir, Freundlich and Freundlich-Langmuir isotherm equations are used to represent the adsorption isotherm of acid dyes on wool. The findings show that the best fit to the adsorption isotherms for acid dyes by wool fibres is obtained by Freundlich-Langmuir model. The pseudo- first and second-order models of absorption kinetics are used to investigate the absorption behavior of acid dye on wool fibre. The obtained result shows good agreement between the practical data and the pseudo- second-order model of absorption kinetic. Also, the law of conservation of mass has been used for modeling the acid dye distribution during dyeing process and the rate of dye uptake by wool fibre. The performance of suggested mathematical model is acceptable.