Abstract:K/S and reflectance graphs are essential tools in characterizing the dyeing behavior. In textile coloration, estimating the dye concentration is poor using the Kubelka-Munk model due to its low scalability and deviation of the reflectance function from linearity after low dye concentrations, particularly in the wavelengths where the gradient of K/S against dye concentration is noticeable. This paper focused on extending the validity of the Kubelka-Munk function, which originates from the linearity of reflectan… Show more
“…The reason relates to the deviation of reflectance spectra from linearity due to the limitations in the refractive models, as well as the non-linear dye uptake by the fiber. Such behaviors can be affected by various parameters including the region of concentration, the type of medium (aqueous or fibrous), and the wavelength 33 . Hence, the performance of the model in different ranges of concentrations was aimed and, the applied concentration range was divided into three categories, i.e.…”
Section: Resultsmentioning
confidence: 99%
“…Therefore, as demonstrated in Fig. 6 , the adsorption behavior of a dye on textile material would be described into three zones, linear, non-linear, and saturated stages 33 . Figure 6 Different zones benefit from different adsorption behaviors of Acid Red 128 versus concentration at λ max .…”
Section: Resultsmentioning
confidence: 99%
“…To evaluate the errors, the Error % function was used according to Eq. ( 10 ) 33 . where and represent the calculated variable from the model and the measured variable.…”
Section: Methodsmentioning
confidence: 99%
“…An applicable method was introduced by Safi et al . to determine and extend the range of the scalability of the K-M model as well 33 . Despite the vast applications of the model, studies proved some inconsistencies between the predictions of the model and those obtain practically.…”
If the relationship between the reflectance function (K/S) and dye concentration (C) is known, the color of the dyed textile (R∞) and C could be predicted from each other. In the present work, the concentration value estimated from the reflectance data using two reflective models, i.e. the Kubelka–Munk and the Allen–Goldfinger is compared. First, the Allen–Goldfinger model was run by using the absorption coefficient of dyes in fiber, i.e. the unit k/s values instead of that in the solution. The results showed that the replacement of the unit k/s for the Beer–Lambert absorption coefficient in the Allen–Goldfinger model causes lower error in the prediction of the spectral reflectance factor as well as the dye concentration. However, this model did not lead to better results. Then, an inverse form was used to estimate the concentration of dyes from the corresponding spectral reflectance. Consequently, it was observed that the Kubelka–Munk model is still a more reliable method while benefiting from more simplicity than the Allen–Goldfinger model. The analysis of errors showed that the results deeply depend on different factors such as the applied concentration range as well as the dye spectral adsorption behavior.
“…The reason relates to the deviation of reflectance spectra from linearity due to the limitations in the refractive models, as well as the non-linear dye uptake by the fiber. Such behaviors can be affected by various parameters including the region of concentration, the type of medium (aqueous or fibrous), and the wavelength 33 . Hence, the performance of the model in different ranges of concentrations was aimed and, the applied concentration range was divided into three categories, i.e.…”
Section: Resultsmentioning
confidence: 99%
“…Therefore, as demonstrated in Fig. 6 , the adsorption behavior of a dye on textile material would be described into three zones, linear, non-linear, and saturated stages 33 . Figure 6 Different zones benefit from different adsorption behaviors of Acid Red 128 versus concentration at λ max .…”
Section: Resultsmentioning
confidence: 99%
“…To evaluate the errors, the Error % function was used according to Eq. ( 10 ) 33 . where and represent the calculated variable from the model and the measured variable.…”
Section: Methodsmentioning
confidence: 99%
“…An applicable method was introduced by Safi et al . to determine and extend the range of the scalability of the K-M model as well 33 . Despite the vast applications of the model, studies proved some inconsistencies between the predictions of the model and those obtain practically.…”
If the relationship between the reflectance function (K/S) and dye concentration (C) is known, the color of the dyed textile (R∞) and C could be predicted from each other. In the present work, the concentration value estimated from the reflectance data using two reflective models, i.e. the Kubelka–Munk and the Allen–Goldfinger is compared. First, the Allen–Goldfinger model was run by using the absorption coefficient of dyes in fiber, i.e. the unit k/s values instead of that in the solution. The results showed that the replacement of the unit k/s for the Beer–Lambert absorption coefficient in the Allen–Goldfinger model causes lower error in the prediction of the spectral reflectance factor as well as the dye concentration. However, this model did not lead to better results. Then, an inverse form was used to estimate the concentration of dyes from the corresponding spectral reflectance. Consequently, it was observed that the Kubelka–Munk model is still a more reliable method while benefiting from more simplicity than the Allen–Goldfinger model. The analysis of errors showed that the results deeply depend on different factors such as the applied concentration range as well as the dye spectral adsorption behavior.
“…The reason relates to the deviation of reflectance spectra from linearity due to the limitations in the refractive models, as well as the non-linear dye uptake by the fiber. Such behaviors can be affected by various parameters including the region of concentration, the type of medium (aqueous or fibrous), and the wavelength [20]. Hence, the performance of the model in different ranges of concentrations was aimed and, the applied concentration range was divided into three categories, i.e.…”
Section: Prediction Of Reflectance Factor By the Geometry Modelmentioning
The problem of primary interest in quantitative analysis of a dye bath or a dyed sample of textile is to determine the concentration with a minimum percentage error. The present study describes the applicability of two reflective models i.e. the Kubelka-Munk and the Allen-Goldfinger here called Geometry, to estimate the concentration of dye from the reflectance data. The performance of the Geometry model in predicting the spectral reflectance factor of dyed polyamide fibers is evaluated by the determination of the unit k/s and the Beer-Lambert absorption extinction coefficient. To examine the models, a reflectance dataset is created by dyeing nylon 6 fabrics with four different acid dyes. The results show that the replacement of the unit k/s for the Beer-Lambert absorption coefficient in the Geometry model causes lower error in the prediction of the spectral reflectance factor. However, it is shown that this model, does not lead to better results. Consequently, the Kubelka-Munk model is still found as the most reliable method while benefiting from more simplicity in comparison to the Geometry model. The analysis of errors shows that the results deeply depend on different factors such as the range of applied concentrations as well as the spectral adsorption behaviors of dyes.
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