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synopsisA treatment of the color of textile materials is proposed which is an extension of G. G. Stokes' "pile of plates" problem. Unlike the conventional treatment of this subject, e.g., that by Kubelka and Munk, this approach permits independent determination of all variables: coefficient of absorption of the dye, refractive indexes of the fibers, the effect on color of the geometry of the fabric and yarn, and the distribution of the dye within the fiber. Here, cylindrical, optically homogeneous fibers in a parallel array are assumed. Experimental data show that this treatment predicts far more satisfactorily the color of fabrics at high dye concentrations and low reflectance values than does the Kubelka-Munk approach.

RRcently, the authors have proposed a new approach to the prediction of the color of absorbing-scattering substrates such as fabrics.' One can expand this treatment to take into account the effect of an inhomogeneity of dye distribution, most easily the condition known as ringdyeing. Garrett and Peters2 dealt with this problem by expanding Atherton's3 treatment of the color of fabrics.Since our approach to this problem is based on the optical properties of the fibers and the medium of observation and on the geometry of the system, it is believed to be potentially more significant than the older treatments.In our paper, we showed that the pathlength (Zp) of light in the fiber is (under the restrictions outlined there)

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SynopsisIt is known from experience that light scattering-absorbing substrates are darker when the continuous medium is water instead of air. This is due to the decrease in scattering efficiency of the scattering particles caused by the smaller value of the ratio nl/nz of the refractive indices of the scattering particles (n, = 1.5 to 1.7) to that of water (nz = 1.33) as compared to that ratio when the continuous medium is air (nt = 1). Experimental evidence for this phenomenon is presented for polyester fabric viewed in air, water, and a concentrated sucrose solution. The wavelength range from 0.4 to 0.7 microns, and absolute "dry" reflectances from 0.02 t o 0.7 were covered. The phenomenon cannot be adequately described with the Kubelka-Munk theory of the color of scattering-absorbing substrates.' Evidence is presented that a t high reflectance values (O.P0.7), the theory describes the color adequately and the results are consistent with a prediction based on a modified Mie equation for the scattering efficiency of "large" particles.2.3 At low reflectance values (<0.05), the Kubelka-Munk theory breaks down completely. This is consistent with the observation that this theory is not capable of predicting precisely high dye concentrations on textiles but is quite adequate for low concentrations.

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