Modeling the Effects of Filament Radius and Photochemical Dye Fading on the Perceived Color Depth of a Filament Array

Abstract

An optical model is used for simulating the effects of varying filament radii on the perceived color strength of an array of parallel filament layers representing a textile fabric. As the filament radius decreases, the color yield also decreases in direct proportion. The model predicts that the concentration of dye in the filaments, required to achieve a given color strength, is inversely proportional to the filament radius in agreement with practical experience in dyeing microfiber fabrics. New equations are also derived to calculate the light absorption by each individual filament layer at a given dye concentration. The degree of photochemical dye fading in each layer is simulated using these respective absorbed light intensities leading to a decrease in the overall color strength. Repeated calculations of the absorbed light intensities and decreasing dye concentration and color strength show that pale colors will fade more rapidly than deep colors and that fading will be faster when the filament radius is decreased. Both these results agree with practical observations of the light fastness of dyeings. For deep colors, the upper filament layers absorb all the incident light, and filaments in the center of the array undergo minimal fading, resulting in significant dye concentration gradients in the filament matrix.