On Measurements of Effective Residual Ink Concentration (ERIC) of Deinked Papers Using Kubelka-Munk Theory

The measurement of effective residual ink concentration (ERIC) in recycled papers depends on their opacity. For opacity less than 97.0%, the method is based on application of the Kubelka-Munk theory to diffuse reflection from papers measured once with a black backing and again with a thick backing of the same papers. At opacities above 97.0%, the two reflection values tend to become statistically indistinguishable. Measured ERIC values are undetermined owing to a logarithmic singularity in the defining equation. This is handled by using an approximate value for the Kubelka-Munk scattering coefficient to remove the singularity. Even when ERIC values can be measured at opacities close to (but slightly less than) 97%, their uncertainty is amplified by the singularity to the point where predicted coefficients of variation (COV) can exceed 50%. In repeat tests of a sample containing five equivalent handsheets, ERIC values for one specimen ranged from 243 to 871 ppm, even though the average opacity for the sample was an acceptable 94.6%. This renders the test marginally useful as a way to monitor the deinking process. Knowledgeable testers may apply an approximate value for at all opacities that show high measurement variability. However, a new approach to ERIC avoids both the uncertainty and the approximation by using the measurement of diffuse reflection and transmission in single sheets. The Kubelka-Munk theory is again applied to the data, and there is no change in the meaning of ERIC. The measurement is valid at any opacity for which the percentage transmission through the sheet is accurately determined in the near-infrared spectral region. Coefficients of variation are as low as or lower than those from the accepted ERIC measurement throughout the range of interest. Coefficients of variation decrease with increasing opacity to a low of 10% for a sheet having 98.7% opacity and 1106 ppm ERIC. In contrast with the accepted method, the COV is remarkably insensitive to the measured value of the scattering coefficient. The new method promises to be a better way to monitor deinking progress in recycled papers.