Dyebath Exhaustion Kinetics & Cycle Time Fit

The fit uses one point, so it inherits everything that point carries: a sample drawn while the bath is still climbing to temperature describes a system that was never at the temperature the constant is supposed to belong to, and the resulting K will flatter the cycle. Draw the sample during the isothermal hold and take the equilibrium figure from a deliberately over-run laboratory dyeing rather than from the recipe sheet. Equilibrium exhaustion is a property of the whole system and moves with liquor ratio, electrolyte and temperature, so a constant fitted at one liquor ratio does not transfer to a machine running a different one - which is the usual reason a laboratory cycle fails to reproduce in bulk. The model describes exhaustion, not fixation: for reactive dyes a bath can be handsomely exhausted and still fix badly, and the hydrolysed fraction that follows is a wash-off problem rather than a kinetic one. Time to 99 percent is reported because it is a useful bound, not because it is a target; the last percent of equilibrium is almost never worth the steam, and the honest reading of a large extra-time figure is usually that the recipe should change rather than that the cycle should lengthen.