The tables in this example are DyeLogic's starter reference pack, encoded from a dye supplier's published exhaust application table for cotton. They show the method. Your own approved tables and lab trials decide the values you use.
The recipe we will calculate
- Fabric weight5 g
- Liquor ratio1:8
- CottonBleached, un-mercerized
- Alkali systemSingle alkali (soda ash)
- DyesRed 1.20, Yellow 0.80, Blue 0.15 %owf
- Stock solutionsSalt 200 g/L, soda ash 100 g/L
Step 1. Bath volume
The bath volume is the fabric weight multiplied by the liquor ratio. One gram of fabric at 1:8 takes 8 mL of liquor.
5 g × 8 = 40 mL
Step 2. Dye required for each line
Each dye's mass is the fabric weight times its dosage. Working in milligrams keeps lab-scale numbers readable.
mg of dye = fabric g × %owf × 10 · Red: 5 × 1.20 × 10 = 60 mg
Step 3. Choose a stock solution for each dye, from that dye's own dosage
A small dosage needs a weak stock solution, otherwise the volume to pipette is too small to measure. So the stock strength is chosen per dye line, not once for the whole recipe. The starter pack uses these ranges. A stock of 1 % w/v holds 10 g of dye per litre.
| Dye dosage %owf | Stock % | Concentration g/L |
|---|---|---|
| 0.0001–0.00099 | 0.001 | 0.01 |
| 0.001–0.0099 | 0.010 | 0.1 |
| 0.01–0.099 | 0.100 | 1 |
| 0.10–0.99 | 0.500 | 5 |
| 1.00–1.99 | 1.000 | 10 |
| 2.00–4.00 | 2.000 | 20 |
| Above 4.00 | 4.000 | 40 |
Red at 1.20 % falls in 1.00–1.99, so it uses a 1 % stock. Yellow and Blue both fall in 0.10–0.99 and use 0.5 %.
Step 4. Volume of stock solution to dispense
A stock of 10 g/L contains 10 mg in every millilitre, so the volume is the milligrams needed divided by the concentration in g/L.
| Dye | %owf | Required mg | Dosage range | Stock | Dispense |
|---|---|---|---|---|---|
| Red | 1.20 | 60.000 | 1.00–1.99 | 1.000 % · 10.000 g/L | 6.000 mL |
| Yellow | 0.80 | 40.000 | 0.10–0.99 | 0.500 % · 5.000 g/L | 8.000 mL |
| Blue | 0.15 | 7.500 | 0.10–0.99 | 0.500 % · 5.000 g/L | 1.500 mL |
Red: 60 mg ÷ 10 g/L = 6.0 mL
Step 5. Salt and soda ash from the total shade
Electrolyte and alkali are not chosen per dye. They depend on the total shade, which is the sum of all dosages, together with the cotton condition, the alkali system and the liquor ratio.
Total shade = 1.20 + 0.80 + 0.15 = 2.15 %owf
In the bleached, single-alkali table, 2.15 % falls in the 2.10–3.00 row. At 1:8 that row gives Glauber's salt 60–70 g/L and soda ash 14 g/L. DyeLogic proposes the middle of the printed salt range, 65 g/L, and shows the range beside it.
| Chemical | In the bath | Required | Stock | Dispense |
|---|---|---|---|---|
| Glauber's salt | 65 g/L | 65 × 0.040 L = 2.60 g | 200 g/L | 13.0 mL |
| Soda ash | 14 g/L | 14 × 0.040 L = 0.56 g | 100 g/L | 5.6 mL |
Step 6. Make-up water
Every stock solution added is part of the 40 mL bath, so the water to add is what remains after all liquid additions.
40 − (6.0 + 8.0 + 1.5 + 13.0 + 5.6) = 40 − 34.1 = 5.9 mL of water
When the table has a gap, stop
Printed application tables are not continuous. This one jumps from 2.00 % to 2.10 %. A recipe of Red 1.20, Yellow 0.80 and Blue 0.05 totals 2.05 %, which no row covers. Picking the nearest row, or averaging two rows, is a decision someone should make on purpose, not a silent rounding in a spreadsheet.
DyeLogic stops that calculation, names the gap and the reason the source leaves it, and asks for an override with a written reason that a technical approver then reviews.
Four mistakes this method prevents
- One stock strength for every dye. Small dosages end up as volumes too small to pipette accurately.
- Reading the wrong liquor-ratio column. The same shade needs different salt and alkali at 1:6 and at 1:8.
- Forgetting that additions are part of the bath. Filling to 40 mL of water before adding stocks dilutes the bath.
- Interpolating across a printed gap. The result looks precise but has no source behind it.
How DyeLogic runs this calculation
DyeLogic performs these steps from your site's own approved reference pack and records each result with the rule, range and pack version it came from. The recipe then goes to an independent approver before production receives it. The recipe approval workflow from lab to bulk explains that part, and the security model for recipe data covers who can see and change what.