5. The ratio of area exchange in package dyeing

As an example of where the material is fixed and the dyebath is circulated, the ratio of area exchange for cheese dyeing is considered.

In the case of cheese dyeing, the effective area (=the minimum area)can be considered to be equivalent to the volume of dye liquor contained in the cheese cone as shown in Figure 1 (the minimum area depends on the winding density of the cheese cone).

Figure 1 Effective area in cheese dyeing

Example of calculation of the ratio of area exchange;

Effective area (minimum area)=Volume of gross cheese cone－Volume occupied by material (2)
Ratio of effective area=Volume of liquor in the effective area÷Total volume of dye liquor (3)
Number of dyebath circulations=Total volume of dye liquor÷Flux of dye liquor (4)

For example,

winding density=0.3kg/L
weight of cheese=180kg
volume of gross cheese=600L (180÷0.3)
specific gravity of polyester=1.38
volume of material=130.4L(180÷1.38=130.4);

then, effective area =600－130.4=469.6(L)

supposing that the total volume of dye liquor is 2700L, and the flux is 5400L,

ratio of effective area=469.6/2700=0.174
number of dyebath circulations=5400÷2700=2(times/min.)
ratio of area exchange= ratio of effective area×number of circulations=0.174×2=0.348 (times/min.)

Ratios of area exchange in two cases, for conventional cheese dyeing machines and for rapid cheese dyeing machines, are calculated and shown in Table 1.

It is said from Table 1 that the rapid cheese dyeing machine has 8 times the capacity of area exchange compared to the conventional one.

In the dyeing of PES with disperse dye, the rate of dyeing is proportional to the rate of temperature rise, therefore, in the rapid cheese dyeing machine, the time for temperature rise can be reduced to one eighth of that for the conventional one.