Applying the Kubelka-Munk Equation to Explain the Color of Blends Prepared from Precolored Fibers

Abstract

A basic form of the Kubelka-Munk equation is proposed to explain the color behavior of blends of precolored fibers. For blends of fibers the textile industry commonly uses, which are not completely opaque, the color mixing mechanism consists of two independent processes acting simultaneously. According to the Kubelka-Munk theory for blended fibers as a translucent medium, among other parameters, the reflectance of each point on the surface is a function of the reflectances of the lower layers. This part of the color mixing mechanism is described by the law of subtractive color mixing that results from the multitude of colored dots formed by the different configurations of the fibers, from which their reflectances can be determined by the basic form of Kubelka-Munk theory. The number of these different colored dots is a function of the number of layers that are necessary to produce an opaque substrate. An increase in the fibers' translucency leads to an increase of the number of these colored dots. For fibers of the same diameter, the probability of the existence of points with a specific reflectance depends on the percentages of fibers in the blend. When this surface is viewed from a distance, the colored dots, like the dots on the screen of a color television set, mix spatially by averaging. Thus a combination of subtractive and partitive color mixing is taking place for blends. Several methods have been introduced to describe the color blending of precolored fibers. The binary behavior of fiber blends. which is a match neither with subtractive nor with additive color mixing laws, leads to different explanations for them. In addition to additive and subtractive mixing, partitive color mixing has also been proposed to explain these phenomena. Before the 1980s, most researchers were looking more for empirical formulas [ 12,9,5 ] rather than theoretical ones. The only formula that was established on a theoretical basis was introduced by Friele [ 6 ] , but this formula required a constant for each fiber type. In 1983-1984 suggested the application of the two-constant Kubelka-Munk theory for blends of fibers. Later Walowit et al. [ 13,14 ] published their papers dealing with the determination of the KubelkaMunk absorption and scattering coefficients for fibers on the basis of a least-squares algorithm. Obviously, the two-constant theory was derived from the basic form of the Kubelka-Munk equation by considering infinite thickness for the medium [ 1 ] . However, fibers commonly used in the textile industry are neither fully opaque nor transparent. Fibers transmit incident light proportional to their optical properties. Burlone [4] ] discussed the effects of fiber translucency in blends and concluded that the Kubelka-Munk two-constant equation was suitable for most blends.In this paper, by applying the basic form of the Kubelka-Munk equation for transparent fibers and using probability, we propose an explanation of the behavior of blends according to the fibers' translucency. The reflectance of the top surface is then...

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