Modelling of the dyeing process of packed cotton threads using reactive dyes |
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Authors: | Selene M A Guelli Ulson de Souza Dilênio Pacheco de Souza Eduardo Alberto Borges da Silva Antônio Augusto Ulson de Souza |
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Institution: | (1) Chemical Engineering Department, Federal University of Santa Catarina, P.O. Box 476, Florianópolis, SC, CEP 88040-900, Brazil |
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Abstract: | The Method of Volume Averaging is used to model the process of dyeing textile threads on bobbins. This analysis allows one
to upscale the relevant information at the micro-scale, composed of the textile fibres of the thread in contact with the dyeing
bath fluid, to the macro-scale, consisting of the bobbins of threads inside the equipment. The final mathematical model consists
of two equations, one for the fluid phase external to the thread and the other for the fluid phase internal to the thread.
In order to solve the partial differential equations obtained in the mathematical model, the authors developed a computation
code using the Method of Finite Volumes. This code utilized a system of generalized coordinates to facilitate application
of the boundary conditions to different bobbin geometries. The numerical results for the kinetics of dyeing packed cotton
threads with reactive dyes are compared to the experimental results obtained in Brazilian textile industries, leading to good
agreement between theory and experiment. This demonstrates that the model developed in this paper is able to predict the operational
conditions to be used in the textile industries, minimizing the consumption of dyes and other auxiliaries necessary for the
dyeing process. |
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Keywords: | Mathematical modelling Mass transfer Method of volume averaging Textile Multiphase Dyeing Diffusion Kinetics |
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