Novel Linearisation of the Single Constant Kubelka-Munk Equation for Accurate Textile Dye Recipe Prediction and Determination of Fixation of Reactive Dyes to Cotton Fabrics

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Abstract

This thesis introduces novel methods of dye recipe prediction based on the single constant Kubelka-Munk model. A new model for dye recipe prediction has been developed and tested with a novel dataset of coloured textile materials. The substrates used to test the model included cotton, wool, nylon, polyester substrates and were dyed with reactive dyes (Procion and Remazol dyes), acid dyes and disperse dyes respectively In addition the model has been used to successfully predict the fixation required for different depths of shade.“Right first time” dye recipe prediction where the shade of a fabric sample of unknown coloration is to be replicated is the ultimate goal for dyers and colourists in the textile industry. Since the 1960s computer-based colour recipe prediction systems for textiles have been developed based on the single constant Schuster-Kubelka-Munk theory. One limitation of the single constant Kubelka-Munk theory is its poor linearisation performance when relating the dyed fabric absorption properties to the applied dye concentration, particularly at higher levels of dye concentration as the fabric becomes saturated with dye. A new model, the Mrango-Owens (M-O) model, based on a modified version of the single constant Kubelka-Munk theory, improves the linearity between the fabric absorption properties and the applied dye concentration at all wavelengths across the visible spectrum, especially at higher depths of shade. This leads to a significant improvement in the accuracy of dye recipe predictions when compared to the original single constant Kubelka-Munk equation and selected derivatives (Pineo, Derbyshire-Marshall and McDonald equations). The Mrango-Owens equation accurately predicts the applied dye concentration for a novel dataset of cotton, wool, nylon and polyester fabrics dyed with Procion and Remazol dyes. The accuracy of the dye concentration prediction of the respective dyes from low depths of shade (e.g. 0.5%, o.w.f) to heavy depths of shade (e.g. 10%, o.w.f) is significantly improved with the majority of predicted samples having CIE colour differences (〖∆E*〗_00 ) of less than 1. The overall error (∑▒〖∆c〗^2 ) of prediction for the applied dye concentration levels (o.w.f %) was reduced by 65% when compared to the original single constant Kubelka-Munk equation and its selected derivatives. This significant improvement in the accuracy of textile dye recipe prediction for the reproduction of the target shade saves both time and resources thus contributing to the sustainability of the textile industry in minimizing its impact on the environment.The developed M-O equation was tested and used to determine the amount of dye that was fixed in the fabric for dyed cotton fabrics. The known amount of dye that was fixed in the fabric was determined by the successful dissolution of the dyed cotton fabric in a solution of 70% concentrated sulphuric acid. The derived 〖M-O〗_fixed equation was successfully used to predict the amount of fixed dye concentration,. This model was found to have a very close match to the measured results obtained by dissolution of the dyed cotton fabric samples in the concentrated sulphuric acid. The results of the derived 〖M-O〗_fixed equation were accurate for fabric samples dyed from very low (i.e. 0.5%[o.w.f%]) to high (i.e. 8%[o.w.f%]) levels of applied dye concentration. The derived 〖M-O〗_fixed equation accurately calculated the amount of fixed dye in the fabric with an average error of 2% in comparison to the measured sample values obtained by dissolution of the dyed cotton sample in the concentrated sulphuric acid.

Keyword(s)

Colour; Derbyshire Marshall; Dye recipe prediction; Exhaustion; Fixation; Kubelka Munk; Linearisation; Pineo; Reflectance

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