| The objective of this research was to develop a mathematical expression for the depth of color obtained on polyester fiber in a 50/50 blend with cotton fiber as a function of both fixed dye content and location of fixed dye in the fabric cross-section. Fixation and reflectance measurements were made on laboratory dyeings in which both dye content and location of dye in the fabric cross-section were carefully controlled. The control was achieved through the use of varying dye and antimigrant concentrations in the pad baths, with all of the other experimental variables held constant.; The experimental methodology which was used resulted in the generation of three primary forms of data: particulate migration, fixation, and reflectance values. Statistical analysis of the data revealed that the contribution to color depth of both uniformly distributed and migrated fixed dye can be quantified--but not derived--independently.; Unification of the two independent effects described above resulted in the construction of a mathematical expression of the form: KN = a(,1)(C(,fx)) + a(,2)(M(,fx)) where KN is the conventional Kubelka-Munk (K/S) value which is associated with both the uniformly distributed fixed dye concentration in the fabric cross-section (C(,fx)) and the concentration of migrated dye fixed in the fabric surface (M(,fx)). The constants a(,1) and a(,2) are the reflectance absorptivity coefficients associated with C(,fx) and M(,fx) respectively.; Tests of the mathematical model with C.I. Disperse Blue 165, Red 60, and Brown 1 on a 50/50 polyester/cotton fabric gave high values of R(,2) in regression analysis of measured values of K/S vs. measured values of C(,fx) and in regression analysis of estimated values of K/S vs. estimated values of M(,fx).; Possible uses of the model in attempts to achieve minimum dyeing costs while maintaining satisfactory uniformity of shade are discussed. Also discussed is the possible use of the model in the development of new textile products. |
