Abstract
In practical dyeing, the dyebath is not always maintained at a constant temperature for a whole period of dyeing, but the temperature of the dyebath is raised slowly from a low to a certain high temperature and is maintained at that temperature.
In this report, first the rate-of-dyeing equation raising temperature in the finite dyebath, is obtained theoretically on the restricted conditions by using the solution of the diffusion equation for the infinite dyebath obtained by Crank2).
Secondly, the formula of calculation of the rate-of-dyeing raising temperature in the finite dyebath is derived from Vickerstaff's hyperbola equation. Then the calculated curves are compared with experimental values obtained by dyeing 6-nylon yarns with disperse dyes.
Thirdly, using Duhamel's theorem, the rate-of-dyeing equations for the finite dye-bath obtained by Wilson1) and Crank2), are derived from those for the infinite dyebath obtained by Hill5) and Crank2).
