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 be havior 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.