The Diffusion of Direct Dyes into Cellulose

Earlier work on the measurement of the diffusion coefficient for direct dyes into cellulose sheet is discussed. The variation of this coefficient with dye concentration is considered, and a suggestion is made for improving the aocuracy of the results hy adopting a different method of mathematical analysis. Some recently developed mathematical solutions of the diffusion equation for conditions corresponding to those of the commercial dyebath are shown to lead to calculated rate–of–dyeing curves which are not in agreement with experimental measurements. An interesting result obtained is that, for the cases examined, dyeing from a finite dyebath, e. g. one showing 90% exhaustion, is better represented by* the mathematical solution for an infinite dyebath than by the solution actually corresponding to 90% exhaustion. An explanation is advanced in terms of the electrochemical nature of the system, an aspect of the problem which was previously neglected in deriving the mathematical solutions. Further experimental data are, necessary before the explanation can be adequately tested.