Reported here is the development of a comparative reflectance model that predicts the relative change in NIR diffuse reflectance of cotton, a hollow fiber, according to the cross-sectional dimensions of perimeter, wall thickness, and wall area. Two cotton groupings are considered: paired cottons and any number of cottons of the same perimeter. The model is based on a single wavelength of NIR light and the critical assumption that the total fiber length in the optical path is constant for cottons of the same perimeter. Combinations of paired dimensional variables are derived and classified by selection rules as “allowed” or “forbidden.” Seven allowed nontrivial combinations of perimeter, wall thickness, and wall area are identified. On the basis of the derived equation that optical density (O.D., log 1/ R units) is a linear function of wall thickness at constant perimeter, comparative reflectances are predicted for all seven nontrivial combinations. The predicted comparative reflectances at a single wavelength range from nonunique (i.e., overlap or equivalent O.D.) to unique; those across many wavelengths are all unique. Also, a mechanism is proposed to explain the interaction of photons with fiber. Finally, the fundamental fiber property sensed is elucidated in three-dimensional (3-D) and 2-D fiber space.
A fundamental approach is presented to verify the total particulate burden in cotton reference material. The method is founded on a null hypothesis. The hypothesis states that upon rendering a cotton free of foreign material, the recoverable particulate-lint ith property constant & l a m b d a ;i (for example, color) of the calibrated mixture is equal to that for the in situ particulate constant, ψ i . Cotton is mechanically cleaned by cycling through a mechanical cleaner. Particulates recoverable from cleaning are added back to the cleaned lint, and the i th property is measured to facilitate computation of & l a m b d a ;i .Cleaned lint spiked with recoverable particulates constitutes a native standard. Assuming that λ i = ψ i , an apparent particulate concentration in the uncleaned material is computed by measuring the in situ property value. The spiking process is repeated, and different properties are measured. Means of apparent in situ partioulate levels as determined from various properties are measured. Means of apparent in situ particulate levels as determined from various properties are compared to decide which groups, if any, differ because of rejection of the null hypothesis. Particulate burden in the reference material is the average of the accepted group means. The method is demonstrated on ginned cotton... Introduction Accomplishment of the Southern Regional Research Center's (SRRC) agriparticulates objectives in studying cotton requires an awareness of interaction between the commodity and its environment. Particulates (r onlint particles of trash and dust) in cotton correlate with several precursors to byssinosis [2] and to rotor spinning performance [3]. Lint-cleaning efficiency at gins and in textile mills is based on the initial foreign matter content of cotton and the amount remaining after cleaning [5].
In Part I of this series, a model was proposed to predict the comparative NIR reflectance of cottons grouped according to cross-sectional dimensions. The critical assumption in the model is that total fiber length in the diffuse reflectance optical path is constant among cottons of the same perimeter. This paper introduces an alternative assumption: that the volume of solid cellulose (i.e., mass) in the diffuse reflectance optical path is constant for cottons of the same perimeter. Optical path simulations are used to predict the consequences of either assumption. One method of simulation is based on diffuse reflectance calculations and the other on relating diffuse reflectance to diffuse transmittance. In the diffuse reflectance calculations, 13 variables are included in the simulation model. Relating reflectance to transmittance is justified because sample weights for the latter can be selected a priori to produce either a constant total fiber length or a constant volume of solid cellulose in the optical path. The simulations support the premise that the critical assumption in the comparative reflectance model is correct. The study goes further to produce diagnostic criteria from the simulation results for testing the assumptions.
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