2. Area of dyebath closely relating to the material

First, consider a model of a dyeing system where the dyebath is static and both the fiber and the dye are distributed evenly in the dyebath, and the diffusion of the dye in the dyebath is not impeded.

In this dyeing system, the balance between the rate of absorption (the rate of exhaustion) and the equalization of the dye concentration in the dyebath by thermal diffusion is maintained although both the fiber and the dye are in a static state. In other words, the dye is always evenly distributed in the system, then, level dyeing can be achieved.

There exists a critical density of fiber assembly where the level dyeing of this assembly can be achieved in the static state, which is defined as “critical density”. On the other hand, there exists a volume of dyebath corresponding to the critical density, which is called “absolute area” of the dyebath.

Next, consider a state where the distribution of fiber becomes denser and an uneven state (it is supposed that the dyebath conditions do not differ and also the thermal diffusion rate of the dye does not differ from that mentioned before). In this case, when the density of fiber assembly exceeds a critical value, the dye concentration in the dyebath will vary in individual parts of the fiber in contact with the dyebath, then the absorption of the dye by individual fiber may vary.

Further, the area of the dyebath where the fiber is contained is defined as “the area relating to fiber” and the minimum area of the dyebath occupied by the fiber is defined as ”the minimum area”.

In the dynamic dyeing system, where the dyebath is circulated or the material is transferred, the absolute area for level dyeing can be decreased by an increase of the dyebath movement throughout the material.